Three balls marked with l, 2 and 3 are placed in an um. One ball is drawn, its number is noted, then the ball is returned to the um. This process is repeated and then repeated once more. Each ball is equally likely to be drawn on each occasion. If the sum of the numbers noted is 6, then the probability that the ball numbered with 2 is drawn at all the three occasions, is
Twelve balls are placed in three boxes. The probability that the first box contains three balls is
The mode of the following data 120 , 110 , 130 , 110 , 120 , 140 , 130 , 120 , 140 , 120 , is
If the mean of 26 , 19 , 15 , 24 , x is x .Then median of the data is
The mean of the numbers a, b, 8, 5, 10, is 6 and the variance is 6.80 . Then a 2 + b 2 =
If the mean of x + 2 , 2 x + 3 , 3 x + 4 , 4 x + 5 is x + 2 , then x =
The variable X takes two values x 1 and x 2 with frequencies f 1 and f 2 respectively. If σ denotes the standard deviation of X , then σ 2 =
The arithmetic mean of first n odd natural numbers, is
If S.D. of X is σ , then S.D. of the variable U = a X + b c , where a , b , c are constants, is
If three squares are selected at random from chessboard, then the probability that they form the letter “L” is
The standard deviation of some temperature data in o C is 5. If the data were converted into o F, the new variance would be
In a moderately skewed distribution, the values of mean and median are 5 and 6, respectively. The value of mode in such a situation is approximately equal to
Three randomly chosen non-negative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probability that z is even, is
The mean of the series a , a + d , a + 2 d , … , a + 2 n d , is
If the mean and standard deviation of 5 observations x 1 , x 2 , x 3 , x 4 , x 5 are 10 and 3 respectively, then the variance of 6 observations x 1 , x 2 , … , x 5 and – 50 is equal to
The median of a set of a observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set is
The average of n numbers x 1 , x 2 , … , x n is M . If x n is replaced by x ‘ , then the new average is
The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by q , where p ≠ 0 and q ≠ 0 . If the new mean and new s.d. become half of their original values, then q is equal t o :
Let the observations x i ( 1 ≤ i ≤ 10 ) satisfy the equations, ∑ i = 1 10 x i – 5 = 10 and ∑ i = 1 10 x i – 5 2 = 40 . If μ and λ are the mean and variance of the observations, x 1 – 3 , x 2 – 3 , … x 10 – 3 , then the ordered pair ( μ , λ ) is equal to:
A random variable X takes the values – 2, -1, 1 and 2 with probabilities 1 − a 4 , 1 + 2 a 4 , 1 − 2 a 4 and 1 + a 4 respectively then
Runs scored by a batsman in 10 innings are:38,70,48,34,42,55,63,46,54,44. The mean deviation about median, is
Find mean deviation about the mean for the following data:
Calculate the mean deviation about median for the following data:
The AM of the series 1 , 2 , 4 , 8 , 16 , … , 2 n is
Runs scored by a batsman in 10 innings are: 38,70, 48, 34, 42, 55,63,46, 54,44 The mean deviation is
Find the standard deviation for the following data:
Find the standard deviation for the following data:
If a variable takes the discrete values α+4, α− 7 2 , α − 5 2 , α − 3 , α − 2 , α + 1 2 , α − 1 2 , α + 5 ( α > 0 ) t h e n t h e m e d i a n i s
If μ is the mean of distribution y i , f i , then Σ f i y i − μ =
The mean of n items is X ¯ . If the first item is increased by 1 , second by 2 and so on, then the new mean is
The following data gives the distribution of height of students: The median of the distribution is
The harmonic mean of 4,8, 16 is
Number of steps (in thousands) taken by 1 persons in a day are: 12, 7 , 15, 10, 17, 19, 25 The Quartile deviation is
If the arithmetic mean of the numbers x 1 , x 2 , x 3 , … , x n is x ¯ , then the arithmetic mean of the numbers a x 1 + b , a x 2 + b , a x 3 + b , … , a x n + b , where a , b are two constants, would be
Consider the first 10 positive integers. If we multiply each number by -1 and then add 1 to each number, the variance of the numbers so obtained is
The median of a set of nine distinct observations is 20.5. If each of the last four observations of the set is increased by 2, then the median of the new set
The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all the observations is
A student obtain75 %,80% and 85% in three subjects. If the marks of another subject is added, then his average cannot be less than
Coefficients of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25, respectively. Difference of their standard deviations is
The standard deviation of the data 6, 5 , 9 , 13, 12, 8, 10 is
The mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20,50, respectively. The correct mean is
The variance of the first n natural numbers is
A bag contains 5 balls of unknown colors such that a ball is drawn at random from it and is found to be white. The probability that bag contains only white balls is
A sample space consists of 3 sample points with associated probabilities given as 2p, p 2 , 4p – 1. Then the value of p is
South African cricket captain lost the toss of a coin 13 times out of 14. The chance of this happening was
In a game called “odd man out” m(m > 2) persons toss a coin to determine who will buy refreshments for the entire group. A person who gets an outcome different from that of the rest of the members of the group is called the odd man out. The probability that there is a loser in any game is
One mapping is selected at random from all mappings of the set S = {1, 2, 3, . . ., n} into itself. If the probability that the mapping is one-one is 3/32, then the value of n is
Consider f ( x ) = x 3 + ax 2 + bx + c . Parameters a, b, c are chosen, respectively, by throwing a die three times. Then the probability that f(x) is an increasing function is
The mean of n items is X ¯ . If the first item is increased by 1, second by 2 and so on, then the new mean is
For a normal distribution if the mean is M, mode is M 0 and median is M d , then
The standard deviation of 25 numbers is 40. If each of the numbers in increased by 5, then the new standard deviation will be
The following data give the distribution of heights of students: Height (in cm) 160 150 152 161 156 154 155 Number of students 12 8 4 4 3 3 7 The median of the distribution is
tf X ¯ 1 and X ¯ 2 , are the means of two distributions such that X ¯ 1 < X ¯ 2 and X ¯ is the mean of the combined distribution, then
If the mean of nobsenrations1 2 ,2 2 ,3 2 ………n 2 is 46 n 11 , then n is equal to
If the average of the numbers 148, 146, 144, 142, … in AP, be 125, then the total numbers in the series will be
A batsman scores sums in 10 innings 38, 70, 48,34,42,55, 46, 63, 54 and 44, then the Mean deviation from median is
If ∑ i = 1 18 x i − 8 = 9 and ∑ i = 1 18 x i − 8 2 = 45 , then the standard deviation of x 1 , x 2 , … , x 18 is
The mean deviation from mean of the observations a , a + d , a + 2 d , … , a + 2 nd is
In a class of 100 students, the average amount of pocket money is Rs.35 per student. If the average is Rs.25 for girls and Rs.50 for boys, then the number of girls in the class is
If a variate x is expressed as a linear function of two variates u and v in the form x = au + bv then mean x ¯ of x is
The average salary of male employees in a firm was Rs.520 and that of females was Rs.420. The mean salary of all the employees was Rs.500. The percentage of male employees is
If the observations 2,4,8 and 16 occur 8, 6,4 and 2 times respectively, then the geometric mean of the observations is
If for a distribution Σ ( x − 5 ) = 3 , Σ ( x − 5 ) 2 = 43 and the total number of items is 18, find the mean and standard deviation.
If X is a variate taking values x 1 , x 2 , … , x n .Y is another variate taking values y 1 , y 2 , … , y n such that y i = 2 x i + 3 and σ Y = 8 , then the variance of variable Z taking values 3 2 x i ; i = 1 , 2 , … , n , is
Variance is independent of change of
If a variable takes discrete values x + 4 , x − 7 2 , x − 5 2 x − 3 , x − 2 , x + 1 2 , x − 1 2 , x + 5 , ( x > 0 ) then the median is
If the S.D. of x 1 , x 2 , … , x n is 5, then the SD, of x 1 + 5 , x 2 + 5 , x 3 + 5 , … , x n + 5 , is
The variance of first n natural numbers is
Coefficient of deviation is calculated by the formula
10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. The mean of the combined set is given by
If G is the GM of the product of r sets of observations with geometric means G 1 , G 2 , … , G r respectively, then G is equal to
If variance of first n natural numbers is 10 and variance of first m even natural numbers is 16, then the value of m+n, is
If ∑ i = 1 18 x i – 8 = 9 and ∑ i = 1 18 x i – 8 2 = 45 then the standard deviation of x 1 , x 2 … x 18 is
The variance of first 50 even natural number is
For 200 observations of a specific set of data, the mean was found to be 48 and the standard deviations is 3. Sum of squares of these 200 observations will be
If the median and range of four numbers { x , y , 2 x + y , x − y } , where 0 < y < x < 2 y are 10 , 28 respectively, then the mean of the numbers is
The mean and variance of ‘ n ‘observations x 1 , x 2 , x 3 , … , x n are 6 and 0 , respectively. If ∑ i = 1 n x i 2 = 900 , then the value of n is equal to
For a slightly asymmetric distribution, mean and median are 5 and 6, respectively. What is its mode?
The mean of a set of numbers is X ¯ . If each number is divided by 3 , then the new mean is
A student obtains 75%, 80% and 85% in three subjects.If the marks of another subject is added, then his average cannot be less than
If the arithmetic mean of the numbers x 1 , x 2 , x 3 , … , x k i s x ¯ , t h e n t h e a r i t h m e t i c m e a n o f t h e n u m b e r s a x 1 + b , a x 2 + b , a x 3 + b . . . . . . . . . . a x n + b , w h e r e a , b a r e t w o c o n s t a n t s , w o u l d b e
Find the Variance of the data: 6, 8, 10, 12, 14, 16, 18,20, 22,24
Let a , b , c , d and e be the observations with mean m and standard deviation s . The standard deviation of the observations a + k , b + k , c + k , d + k and e + k is
If a variable takes the discrete values α + 4 , α − 7 2 , α − 5 2 , α − 3 , α − 2 , α + 1 2 , α − 1 2 , α + 5 ( α > 0 ) , then the median is
Let r be the range and S 2 = 1 n − 1 ∑ i = 1 n x i − x ¯ 2 be the SD of a set of observations x 1 , x 2 , … , x n , then
For ( 2 n + 1 ) observations x 1 , − x 1 , x 2 , − x 2 , … , x n , − x n and 0 , where all x ‘s are distinct, let SD and MD denote the standard deviation and median respectively. Then which of the following is always true?
Calculate variance for the following distribution.
What is the standard deviation of the following data?
If mean and mode in a frequency distribution are 6 and 3 respectively, then their median is
The mean of n items is X ¯ .If the first term, second term, third term … . is increased by 1,2,3… and so on. Then new mean is
A multiple choice examination has 5 questions, each question has three alternative answers of which exactly one is correct. If p is the probability that a student will get 4 or more correct answers just by guessing, then 3 4 p =
If ∑ i = 1 60 x i 2 = 18000 , ∑ i = 1 60 x i = 960 then the standard deviation of x 1 , x 2 , x 3 , − − − x 60 is
Words from the letters of the word PROBABILITY are formed by taking all letters at a time. The probability that both .B’s are not together and both I’s are not together is
Seven girls G 1 , G 2 , G 3 , …, G 7 are such that their ages are in order G 1 < G 2 < G 3 < ….. < G 7 . Five girls are selected at random and arranged in increasing order of their ages. The probability that G 5 and G 7 are not consecutive is
A local post office is to send M telegrams which are distributed at random over N communication channels, (N > M). Each telegram is sent over any channel with equal probability. Chance that not more than one telegram will be sent over each channel is
A and B toss a fair coin each simultaneously 50 times. The probability that both of them will not get tail at the same toss is
A three-digit number is selected at random from the set of all three-digit numbers. The probability that the number selected has all the three digits same is
If a is an integer lying in [- 5, 30], then the probability that the graph of y = x 2 + 2 (a + 4)x – 5a + 64 is strictly above the x-axis is
The probability that a random chosen three-digit number has exactly 3 factors is
Two numbers a, b are chosen from the set of integers 1, 2, 3, . . ., 39 .Then probability that the equation 7a – 9b = 0 is satisfied is
Coefficients of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25, respectively. Difference of their standard deviations is
The mean of a set of numbers is X ¯ . If each number is divided by 3, then the new mean is
If a variable x takes values 0, 1, 2, . . ., n with frequencies proportional to the binomial coefficients n C 0 , n C 1 , n C 2 , … n C n then var(X) is
The variance of the data 2,4,6,8,10 is
If the standard deviation of 0, 1,2,3, …,9 is K, then the standard deviation of 10, 11, 12, 13, …, 19 is
Consider the numbers 1,2,3,4,5,6,7,8,9 and 10. If 1 is added to each number, the variance of the numbers so obtained is
Standard deviations for first 10 natural numbers is
For (2n + 1) observations x 1 , − x 1 , x 2 , − x 2 , … , x n , − x n , and 0, where all x’s are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true?
Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is
There are two red, two blue, two white, and certain number (greater than 0) of green socks in a drawer. If two socks are taken at random from the drawer without replacement, the probability that they are of the same color is 1/5, then the number of green socks are .
A bag contains 10 different balls. Five balls are drawn simultaneously and then replaced and then seven balls are drawn. If the probability that exactly three balls are common to the two draws is p, then the value of 8p is .
The weighted mean of first n natural numbers whose weights are equal to the number of selections out of n natural numbers of corresponding numbers, is
Find the harmonic mean of 1 2 , 2 3 , 3 4 , … , n n + 1 occurring with frequencies 1, 2, 3, …, n, respectively.
The marks of some students were listed out of 75.The SD of marks was found to be 9. Subsequently the marks were raised to a maximum of 100 and variance of new marks was calculated. The new variance is
If the mean deviations about the median of the numbers a, 2a, . . . ,50a is 50, then | a | is equal to
For two data sets, each of size 5, the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is
If the mean deviation of numbers 1, 1+d,1+2d, ………1+100d from their mean is 255,then the d is equal to
The mean of the numbers a, b,8,5 and 10 is 6 and the variance is 6.80. Then, which one of the following gives possible values of a and b?
The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys, in the class is
The AM of n observations is M. If the sum of (n – 4) observations is a ,then the mean of remaining four observations is
The mean and variance of n values of a variable x are 0 and 0 2 , respectively. If the VariabLe y = x 2 then mean of y is
The variance of the numbers 2, 3,11 and x is 49 4 .find the value x .
If any four numbers are selected and they are multiplied, then the probability that the last digit will 1,3,5 or 7 is
For a slightly asymmetric distribution, mean and median are 5 and 6, respectively. What is its mode?
The variance of first 20-natural numbers is
The monthly sales for the first 11 months of the year of a certain salesman were Rs. 12,000 but due to his illness during the last month the average sales for the whole year came down to Rs. 11,375. The value of the sale during the last month was
The median of the series 8 , 12 , 15 , 7 , x , 19 , 22 lies in the interval
The daily wages (in ₹) of ten workers are: 20 , 25 , 17 , 18 , 8 , 15 , 22 , 11 , 9 , 14 . The median of wages is
If the range of the scores 18 , 13 , 14 , 42 , 22 , 26 , x is 44 ( x > 0 ) then the sum of the digits of x is
If the arithmetic mean of the following data is 7, then a + b = x i 4 6 7 9 f i a 4 b 5
The arithmetic mean of first n natural numbers, is
The weighted AM of first n natural numbers whose weights are equal to the corresponding numbers is equal to
The GM of the series 1 , 2 , 4 , 8 , 16 , … , 2 n is
If the arithmetic mean of the observations x 1 , x 2 , x 3 , … , x n is 1 , then the arithmetic mean of x 1 k , x 2 k , x 3 k , … , x n k ( k > 0 ) , is
If the mean deviation of the numbers 1 , 1 + d , 1 + 2 d , . . . , 1 + 100 d from their mean is 255 , then d is equal to
If the range of 15 , 14 , x , 25 , 30 , 35 is 23, then the least possible value of x is
Let X be a variate taking values x 1 , x 2 , … , x n and Y be a variate taking values y 1 , y 2 , … , y n such that y i = 6 x i + 3 ; i = 1 , 2 , … , n. If Var ( Y ) = 30 , σ X =
The mean deviation of the numbers 3 , 4 , 5 , 6 , 7 from the mean, is
The arithmetic mean of the numbers 1 , 3 , 3 2 , … , 3 n − 1 , is
Let the data 4 , 10 , x , y , 27 be in increasing order. If the median of the data is 18 and its mean deviation about mean is 7 . 6 , then the mean of this data, is
If in a moderately skewed distribution the values of mode and mean are 6 λ and 9 λ respectively, then the value of the median is
If the variance of the data 2 , 4 , 5 , 6 , 8 , 17 is 23.33 , then the variance of 4 , 8 , 10 , 12 , 16 , 34 , is
If the average of a , b , c and d is the average of b and c , then which one of the following is necessarily true
The arithmetic of 12 observations is 15. If two observations 20 and 25 are removed then the arithmetic mean of remaining observations is
If the standard deviation of the data 1, 3, 5,7, … , 2017 is σ then σ is (where . denotes the greatest interger function)
If mean and variance of 2, 3, 16, 20, 13, 7, x, y are 10 and 25 respectively, then xy =
If the S.D. of a variate X is σ , then the S.D. of a a X + b is
The variance of first n natural numbers, is
The AM of the series 1, 2, 4, 8, 16, … , 2 n , is
The mode of the following discrete series is: x i 1 3 5 6 12 15 f i 5 7 3 8 6 5
If the mean of the squares of first n natural numbers is 105, then the median of first n natural number is
If the variance of the first ‘n’ natural numbers is 10 and the variance of the first ‘m’ even natural numbers is 16, then m + n is equal to .
If the mean and variance of eight numbers 3,7,9,12,13,20, x and y be 10 and 25 respectively, then x.y is equal to
The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1,2 and 6, then the other two are
If ∑ i = 1 18 x i – 8 = 9 and ∑ i = 1 18 x i – 8 2 = 45 , then the standard deviation of x 1 , x 2 , … … … , x 18 is
A box contains 6 tickets. Two of the tickets carry a price of Rs. 5/- each, the other 4 carry a price of Rs.1/-. If one ticket is drawn, the mean value of the price is
Two teams A and B have the same mean and their coefficients of variations are 4,2 respectively. If σ A , σ B are the standard deviations of teams A, B respectively then the relation between them is
If ∑ i = 1 5 x i − 10 = 5 and ∑ i = 1 5 x i − 10 2 = 25 , then standard deviation of observations 2 x 1 + 7 , 2 x 2 + 7 , 2 x 3 + 7 , 2 x 4 + 7 and 2 x 5 + 7 is equal to.
Let x 1 , x 2 , … … x n be n observations such that ∑ i = 1 n x i 2 = 300 and ∑ i = 1 n x i = 60 . Then a possible value of n among the following is.
G i v e n f o u r p a i r o f g l o v e s , t h e y a r e d i s t r i b u t e d t o f o u r p e r s o n s . E a c h p e r s o n i s g i v e n a r i g h t h a n d e d a n d l e f t h a n d e d g l o v e . T h e p r o b a b i l i t y t h a t n o p e r s o n g e t s a p a i r i s e q u a l t o
The first group of two samples has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation 13.44 then the standard deviation of second group is
Find the mean deviation about the mean for the following data: 6,7, 10, 12, 13,4,8, 12
Find the mean deviation about the mean for the following data: 6,7, 10, 12, 13,4,8, 12
Find the mean deviation about the median for the following data; 3, 9, 5, 3, 12, 10, 18, 4, 7 , 19, 21
The variance of 20 observations is 5. If each observation is multiplied by 2, the new variance of the resulting observations is
Coefficient of variation of two distributions are 60 and70, and their standard deviations arc 21 and 16, respectively. The sum of their arithmetic means is
If the mean of the numbers 27+x,31+x,89+x,107+x,156+x is 82, then the mean of 130+x, 126+x,68+x,50+x,1+x is
If a variate X is expressed as a linear function of two variates U and V in the form X = a U + b V , then the mean X of X is
If x 1 , x 2 a r e t h e m e a n s o f t w o d i s t r i b u t i o n s s u c h t h a t x 1 < x 2 a n d x i s t h e m e a n o f t h e c o m b i n e d d i s t r i b u t i o n , t h e n
Let x 1 , x 2 , … , x n be ∑ i = 1 n x i 2 = 400 and ∑ i = 1 n x i = 80 . Then a possible value of n among the following is
The mean deviation of the data 3, 10, 10, 4,7 , 10, 5 from the mean is
When tested, the lives (in hours) of 5 bulbs were noted as follows: 1357, 1090, 1666, 1494, 1623 The mean deviation (in hours) from their mean is
Following are the marks obtained by 9 students in a mathematics test: 50,69,20,33, 53,39, 40, 65, 59 The mean deviation from the median is
If the mean of the distribution is 2.6, then the value of y is
If the mean of the set of numbers x 1 , x 2 , x 3 , … , x n is x ¯ , then the mean of the numbers x i + 2 i , 1 ≤ i ≤ n is
The average of n numbers x 1 , x 2 , x 3 , … , x n is M . If x n is replaced by x ′ , then new average is
The range of the following set of observations 2,3, 5,9, 8,7,6,5,7,4,3 is
Let x 1 , x 2 , x 3 , x 4 and x 5 be the observations with mean m and standard deviation s . The standard deviation of the observations k x 1 , k x 2 , k x 3 , k x 4 and k x 5 is
Standard deviations for first 10 natural numbers is
Consider the numbers 1 ,2,3, 4, 5, 6,7 ,8, 9 and 10. If 1 is added to each number, the variance of the numbers so obtained is
The following information relates to a sample of size 60: Σ x 2 = 18000 , Σ x = 960 . The variance is
The standard deviation of some temperature data in o C is 5. If the data were converted into o F, the new variance would be
If a variate X is expressed as a linear function of two variates U and V in the form X = a U + b V , then the mean X of X is
If the mean of the numbers 27 + x , 31 + x , 89 + x , 107 + x , 156 + x i s 82 , t h e n t h e m e a n o f 130 + x , 126 + x , 68 + x , 50 + x , 1 + x i s
The mean weight per student in a group of seven students is 55 kg. If the individual weights of six students are 52, 58, 55, 53, 56 and 54, then the weight of the seventh student is
Let x 1 , x 2 , … , x n be n observations such that Σ x i 2 = 400 and Σ x i = 80 . Then a possible value of n among the following is
If in a moderately asymmetrical distribution the mode and the mean of the data are 6 λ and 9 λ , respectively, then the median is
If the MD is 12, the value of SD will be
The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1 ,2 and 6, then the other two are
The weighted mean of the first n natural numbers whose weights are equal to the squares of the corresponding numbers is
The mean weight per student in a group of seven students is 55 kg. If the individual weights of six students are 52, 58, 55, 53, 56 and 54, then the weight of the seventh student is
If a variable x takes values 0 , 1 , 2 , … , n with frequencies proportional to the binomial coefficients n C 0 , n C 1 , n C 2 , … n C n , then var ( x ) is
If each observation of a raw data whose variance is σ 2 is multiplied by h, then the variance of the new set is
The SD of a variate x is σ . The SD of the variate (ax + b)/c, where a, b, c ate constants, is
If the mean deviation about the median of numbers a , 2 a , 3 a , … .50 a is 50 , then | a | equals
If a, b and c are three numbers (not necessarily different) chosen randomly and with replacement from the set { 1 , 2 , 3 , 4 , 5 } , then the probability that ( a b + c ) is even, is
If ∑ i = 1 5 x i − 100 = 5 and ∑ i = 1 5 x i − 100 2 = 25 , then the standard deviation of observations 2 x 1 + 73 , 2 x 2 + 73 , 2 x 3 + 73 , 2 x 4 + 73 , 2 x 5 + 73 is
If A , B are two events such that P ( A ∪ B ) = 0.6 , P ( A ) = P ( B ) , P B A = 0.8 , then the value of P ( ( A ∩ B ¯ ) ∪ ( A ¯ ∩ B ) ) is
Ten pairs of shoes are in a closet. Four shoes are selected at random. The probability that there will be at least one pair among the four shoes selected is
The mean and standard deviation of n observations are 8, 4. If all observations are multiplied by 3 and new mean and new standard deviation are p, q then the value of p + q is
Three identical dice are rolled. The probability that the same number will appear on each of them is
Let E be an event which is neither a certainty nor an impossibility. If probability is such that P ( E ) = 1 + λ + λ 2 and P E ‘ = ( 1 + λ ) 2 in terms of an unknown λ . Then P(E) is equal to
A draws a card from a pack of n cards marked 1,2, …, n. The card is replaced in the pack and B draws a card. Then the probability that A draws a higher card than B is
The probability that in a family of five members, exactly two members have birthday on Sunday is
Three houses are available in a locality. Three persons apply for the houses. Each applies for one houses without consulting others. The probability that all three apply for the same houses is
The numbers 1,2,3, …, n are arrange in a random order. The probability that the digits 1, 2, 3, . . ., k (k < n) appear as neighbors in that order is
A four figure number is formed of the figures 1 ,2,3, 5 with no repetitions. The probability that the number is divisible by 5 is
A cricket club has 15 members, of whom only 5 can bowl. If the names of 15 members are put into a box and 11 are drawn at random, then the probability of getting an eleven containing at least 3 bowlers is
If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers is
If the events A and B arc mutually exclusive events such that P ( A ) = 3 x + 1 3 and P ( B ) = 1 − x 4 , then the set of possible real values of x lies in the interval
A natural number is chosen at random from the first 100 natural numbers. The probability that x + 100 x > 50 is
A dice is thrown six times, it being known that each time a different digit is shown. The probability that a sum of 12 will be obtained in the first three throws is
In a n-sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is
Four die are thrown simultaneously. The probability that 4 and 3 appear on two of the die given that 5 and 6 have appeared on other two die is
A 2n digit number starts with 2 and all its digits are prime, then the probability that the sum of any two consecutive digits of the number is prime is
A composite number is selected at random from the first 30 natural numbers and it is divided by 5. The probability that there will be a remainder is
Forty teams play a tournament. Each team plays every other team just once. Each game results in a win for one team. If each team has a 50% chance of winning each game, the probability that at the end of the tournament, every team has won a different number of games is
A bag has 10 balls. Six balls are drawn in an attempt and replaced. Then another draw of 5 balls is made from the bag. The probability that exactly two balls are common to both the draw is
Three integers are chosen at random from the set of first 20 natural numbers. The chance that their product is a multiple of 3 is
Five different marbles are placed in 5 different boxes randomly. Then the probability that exactly two boxes remain empty is (each box can hold any number of marbles)
There are 10 prizes, five A’s, three B’s, and two C’s, placed in identical sealed envelopes for the top 10 contestants in a mathematics contest. The prizes are awarded by allowing winners to select an envelope at random from those remaining. When the 8th contestant goes to select the prize, the probability that the remaining three prizes are one A, one B and one C is
If a and b are chosen randomly from the set consisting of numbers 1, 2, 3, 4, 5, 6 with replacement. Then the probability that lim x 0 a x + b x / 2 2 / x = 6 is
A car is parked among N cars standing in a row, but not at either end. On his return, the owner finds that exactly ”r” of the N places are still occupied. The probability that the places neighboring his car are empty is
Mr. A lives at origin on the Cartesian plane and has his office at (4, 5). His friend lives at (2, 3) on the same plane. Mr. A can go to his office traveling one block at a time either in the +y or +x direction. If all possible paths are equally likely then the probability that Mr. A passed his friends house is (shortest path for any event must be considered)
The AM of the series 1,2,4,8, 16, …,2 n is
An automobile driver travels from a plain to a hill station 120 km away at an average speed of 30 km per hour. He then makes the return trip at an average speed of 25 km per hour. He covers another 120 km on the plain at an average speed of 50 km per hour. His average speed (in km/hr) over the entire distance of 360 km will be
When tested, the lives (in hours) of 5 bulbs were noted as follows: 1357,1090, 1666, 1494, 1623 The mean deviation (in hours) from their mean is
The mean deviation of the data 3,10, 10,4,7,10, 5 from the mean is
. If the mean of the distribution is 2.6, then the value of y is Variate x 1 2 3 4 5 Frequency f of x 4 5 y 1 2
Following are the marks obtained by 9 students in a mathematics test: 50, 69,20,33, 53,39, 40, 65, 59 The mean deviation from the median is
If the mean of the set of numbers x 1 , x 2 , x 3 , … , x n is x ¯ , then the mean of the numbers x i + 2 i , 1 ≤ i ≤ n is
The harmonic mean of 4,8,16 is
The following data gives the distribution of height of students: Height (in cm) 160 150 152 161 156 154 155 Number of students 12 8 4 4 3 3 7 The median of the distribution is
For a slightly asymmetric distribution, mean and median are 5 and 6, respectively. What is its mode?
The average of n numbers x 1 , x 2 , x 3 , … , x n is M. If x n is replaced by x’, then new average is
Runs scored by a batsman in 10 innings are: 38, 70,48,34, 42, 55, 63, 46, 54, 44 The mean deviation is
If μ is the mean of distribution y i , f i , then Σf i y i − μ =
If each observation of a raw data whose variance is σ is multiplied by h, then the variance of the new set is
The range of the following set of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is
For a given distribution of marks, the mean is 35.16 and its standard deviation is 19.76. The coefficient of variation is
The mean and the SD of 1,2,3,4,5,6 are
Consider any set of observations x 1 , x 2 , x 3 , … , x 101 . It is given that x 1 < x 2 < x 3 < … < x 100 < x 101 ; then the mean deviation of this set of observations about a point k is minimum when k equals
The SD of a variate x is σ . The SD of the variate (ax + b)/c, where a, b, c are constants, is
The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all the observations is
The standard deviation of the data 6, 5,9, 13, 12,8,10 is
Let r be the range and S 2 = 1 n − 1 ∑ i = 1 n x i − x ¯ 2 be the SD of a set of observations x 1 , x 2 , … , x n , then
Consider the first 10 positive integers. If we multiply each number by -1 and then add 1 to each number, the variance of the numbers so obtained is
The following information relates to a sample of size Σx 2 = 18000 , Σx = 960 . The variance is
What is the standard deviation of the following data? Measurement 0 – 10 10 – 20 20 – 30 30 – 40 Frequency 1 3 4 2
Let ω be a complex cube root of unity with ω ≠ 1 . A fair die is thrown three times. If r 1 , r 2 and r 3 are the numbers obtained on the die, then the probability that ω r 1 + ω r 2 + ω r 3 = 0 is
If the probability of a six-digit number N whose six digits are 1, 2, 3, 4, 5, 6 written as random order is divisible by 6 it p, then the value of 1/p is .
If the probability that the product of the outcomes of three rolls of a fair dice is a prime number is p, then the value of 1/(4p) is .
A dice is weighted such that the probability of rolling the face numbered n is proportional to n 2 (n = 1, 2, 3, 4, 5, 6). The dice is rolled twice, yielding the numbers a and b. The probability that a < b is p then the value of [2/p] (where [ . ] represents greatest integer function) is .
In a knockout tournament, 2 n equally skilled players; S 1 , S 2 , .…, S 2 n are participating. In each round, players are divided in pairs at random and winner from each pair moves to the next round. If S 2 reaches the semi-final, then the probability that S 1 wins the tournament is 1 84 . The value of n is .
Five different games are to be distributed among four children randomly. The probability that each child get at least one game is p, then the value of [1/p] is, where [.] represents the greatest integer function, .
The probability that a person will get an electric contract is 2 5 and the probability that he will not get plumbing contract is 4 7 .If the probability of getting at least one contract is 2 3 , the probability that he will get both the contracts is k , then 105k is
Given two events A and B, if the odds against A are 2 to 1 those in favour of AUB are 3 to 1, then
The probability that when 12 distinct balls are distributed among three boxes, the first will contain exactly three balls is
The geometric mean G of the product of n sets of data with geometric means G 1 , G 2 , … … … , G n respectively, then
The mean deviation from the mean of the AP a, a + d , a+2d , ……..a+ nd is
Find the mean deviation about median for the following data. Marks 0-10 10-20 20-30 30-40 40-50 50-60 Number of Girls 6 8 14 16 4 2
The AM of n numbers of a series is x . If the sum of first (n – 1) terms is k, then the nth number is
The mean of the series x 1 , x 2 , … , x n is x ¯ . If x 2 is replaced by λ , then the new mean is
The mean of n items is x ¯ . If the first term is increased by 1, second by 2 and so on, then the new mean is
The weighted A.M of first n natural numbers whose weights are equal to the corresponding numbers is equal to
If the mean of the set of numbers x 1 , x 2 , … , x n is x ¯ , then the mean of the numbers x i + 2 i , 1 ≤ i ≤ n is
The mean of a set of observations is x – . If each observation is divided by, α ≠ 0 and then is increased by 10, then the mean of the new set is
If the standard deviation of x 1 , x 2 , … , x n is 3 .5 , then the standard deviation of − 2 x 1 − 3 , − 2 x 2 − 3 , … − 2 x n − 3 is
The first of two samples has 100 items with mean 15 and SD = 3. If the whole group has 250 items with mean 15.6 and SD = 13.44 , the SD of the second group is
. If the sum of deviations of a number of observations about 4 is 30 and that about 3 is 40. Then, mean of the observations is
There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a test Marks 0 1 2 3 4 5 Frequency x-2 x x 2 (x+1) 2 2x x+1 where, x is a positive integer. Find the mean and standard deviation of the marks.
The AM of 2 n + 1 C 0 , 2 n + 1 C 1 , 2 n + 1 C 2 , … , 2 n + 1 C n is
If a variable takes values 0 , 1 , 2 , … , n with frequencies q n , n 1 q n − 1 p , n ( n − 1 ) 1 ⋅ 2 q n − 2 p 2 , … p n , where p + q = 1 then the mean is
If harmonic mean of first 5 observations is 5 2 and harmonic mean of another 5 observations is 9 2 then harmonic mean of all 10 observations is
Geometric mean of first group of 5 observations is 8 and that of second group of 4 observations is 128 2 . Then, grouped geometric mean is.
Consider the numbers 1 ,2,3, 4, 5, 6,7,8, 9, 10. If 1 is added to each number, then variance of the numbers so obtained is
Mean and standard deviation of 100 observations were found to be 40 and 10, respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 , respectively, find the correct standard deviation.
The AM of the series 1, 2, 4, 8, 16, . . ., 2 n is
The relation between mean, mode, median is
The mean deviation of the data 3,10, 10,4,7,10, 5 from the mean is
If the mean of the distribution is 2.6, then the value of γ is
If each observation of a raw data whose variance is σ is multiplied by h, then the variance of the new set is
If the standard deviation of 0, 1,2,3, .. .,9 is K, then the standard deviation of 10, 11, 12, 13, . . ., 19 is
Runs scored by a batsman in l0 innings are: 38,70,48, 34, 42, 55, 63, 46, 54, 44 The mean deviation is
The average of n numbers x 1 , x 2 , x 3 , … , x n is M. If x n is replaced by x’, then new average is
If μ is the mean of distribution y i , f i , then Σf i y i − μ =
In a set of 20 observations, each of the observation below the median of all observations is increased by 6 and each of the remaining observation is decreased by 2.Then the mean of the new set of observations
The A . M . of the observations 1 . 3 . 5 , 3 . 5 . 7 , 5 . 7 . 9 , … , ( 2 n – 1 ) ( 2 n + 1 ) ( 2 n + 3 ) is
The mean of variable 1 , 2 , … n whose corresponding frequencies are 1 , 2 , … n is given by
If ∑ i = 1 18 x i − 8 = 9 and ∑ i = 1 18 x i − 8 2 = 45 then the standard deviation of x 1 , x 2 … x 18 is
The mean of two samples of sizes 200 and 300 were found to be 25, 10 respectively. Their standard deviations were 3 and 4 respectively. The variance of combined sample of size 500 is
If the median of 21 observations is 40 and if the observations greater than the median are increased by 6 then the median of the new data will be
The mean of 5 observations is 4.4 and the variance is 8.24. If three of the five observations are 1, 2 and 6, the two values are
The mean deviation of an ungrouped data is 50. If each observation is increased by 2%, then the new mean deviation is
If the standard deviation of x 1 , x 2 , … , x n is 3.5, then the standard deviation of − 2 x 1 − 3 , − 2 x 2 − 3 , ….. … , − 2 x n − 3 is
The geometric mean of 3 , 3 2 … , 3 n is
If the mean of a set of observations x 1 , x 2 , … , x 10 is 20 then the mean of x 1 + 4 , x 2 + 8 , x 3 + 12 , … , x 10 + 40 is
If the ratio of mode and median of a distribution is 6 : 5, then the ratio of its mean and median is
The G.M. of the numbers 3 , 3 2 , 3 3 . . . , 3 n is
If the mean of a set of observations x 1 , x 2 , … , x n is X ¯ then the mean of the observations x i + 2 i ; i = 1 , 2 , … , n is
The arithmetic mean of the following frequency distribution: Variable (X) : 0 1 2 3 … . n Frequency (f) : n C 0 n C 1 n C 2 n C 3 … . n C n is
If X is the mean of x 1 , x 2 , x 3 … x n Then, the algebraic sum of the deviations about mean X ¯ is
The mean of 130, 126, 68, 50, 1 is
The arithmetic mean of a set of observations is X. If each observation is divided by R and then is increased by 10, then the mean of the new series is
A boy goes to a school from his home at a speed of x km/hr and comes back at a speed of y km/hr, then the average speed is given by
If the range of 14 , 12 , 17 , 18 , 16 , x is 20 and x > 0 , then the value of x is
A car completes the first half of its journey with a velocity v 1 and the rest half with a velocity v 2 . Then the average velocity of the car for the whole journey is
The mean of the distribution, in which the values of X are 1 , 2 , … , n the frequency of each being unity is:
The semi-interquartile range of the data 3, 6, 5, 4, 2, 1, 7 is
The most stable measure of central tendency is
If the arithmetic mean of the following distribution is 8.2, then a = x i : 1 3 5 9 11 13 f i : 3 2 7 a 4 8
The one which is the measure of the central tendency is
If the quartile deviation of a set of observations is 10 and the third quartile is 35, then the first quartile is
If the mean of first n natural numbers is 5 n 9 ,
The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is
If the mean of first n odd natural numbers is n 2 81 ,
The median of the data 5 , 6 , 7 , 8 , 9 , 10 , is
In a series of observations, coefficient of variation is 16 and mean is 25, find the variance
The arithmetic mean of n C 0 , n C 1 , … , n C n , is
If ∑ i = 1 9 x i − 5 = 9 and ∑ i = 1 9 x i − 5 2 = 45 , then the standard deviation of the 9 items x i , x 2 , … , x 9 is
If the ratio of mean and median of a certain data is 2 : 3 , then the ratio of its mode and mean is
The mean deviation from the mean of the series a , a + d , a + 2 d , … , a + 2 n d is
The quartile deviation of daily wages of 7 persons which are ₹ 12, 7, 15, 10, 17, 17, 25 is
The coefficient of quartile deviation is calculated by the formula
The mean of 5 observations is 5 and their variance is 9 . 2 . If three of the observations are 1 , 2 , and 6 , then the mean deviation from the mean of the data, is
Mean and variance of 20 observations are 10 and 4 respectively. It was found that in place of 11 , 9 was taken by mistake. The correct variance, is
If the arithmetic mean of 7, 8, x, 11, 14 is x , then x =
If each of n numbers x i = i is replaced by ( i + 1 ) x i then the new mean is
The weighted means of first n natural numbers whose weights are equal to the squares of corresponding numbers is
The weighted mean of first n natural numbers whose weights are equal is given by
If the arithmetic mean of first n natural numbers is 15, then n =
Mean deviation about mean from the following data: x i : 3 9 17 23 27 f i : 8 10 12 9 5 , is
If a variable X takes values 0 , 1 , 2 , . . . , n with frequencies n C 0 , n C 1 , n C 2 , … . n C n respectively, then S.D =
The mean of the series x 1 , x 2 , … , x n is X ¯ . If x 2 is replaced by λ , then the new mean is
If the mean of the following data is 5.5 , then x = x i 2 4 6 8 f i 3 5 6 x
If a variable takes values 0 , 1 , 2 , … , n with frequencies 1 , n C 1 , n C 2 , … , n C n then the AM is
For a symmetrical distribution Q 1 = 20 and Q 3 = 40 .The value of 50 t h percentile, is
The mean deviation of the series a , a + d , a + 2 d , . . . . , a + ( 2 n – 1 ) d , a + 2 n d about the mean is
Suppose a population A has 100 observations 101,102, , 200 and another population B has 100 observations 151, 152, 153, , 250. If V A and V B represent the variances of the two populations respectively, then V A V B is
Ina series of observations, S.D. a 7 and mean is 28, the coefficient of variation is
If the S.D. of a set of observations is 8 and if each observation is divided by – 2, the S.D. of the new set of observations will be
Let x i ( 1 ≤ i ≤ 10 ) be ten observations of a random variable X. If ∑ i = 1 10 x i − p = 3 and ∑ i = 1 10 x i − p 2 = 9 , where 0 ≠ p ∈ R , then the standard deviation of these observations is
If the mean and standard deviation of 10 observations x 1 , x 2 , … , x 10 are 2 and 3 respectively, then mean of x 1 + 1 2 , x 2 + 1 2 , … , x 10 + 1 2 is equal to
The standard deviation of a data is 6, when each observation is increased by 1, then the S.D. of the new data is
The variance of the scores 2, 4, 6, 8 and 10 is
If the first item is increased by 1, second by 2 and so on, then the new mean is
The median of the following marks of the students in a class, is 34 , 32 , 48 , 38 , 24 , 30 , 27 , 21 , 35
The variance of first 50 even natural numbers is
The S . D . of scores l, 2, 3, 4, 5, is
If the mean deviation about the median of the numbers a , 2 a , 3 a , … , 50 a ,is 50, then a equals
The sum of the squares deviations for 10 observations taken from their mean 50 is 250 . The coefficient of variation is
The mean and variance of 8 observations are 10 and 13.5 respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is
10 is the mean of a set of 7 observations and 5 is the mean of a set of 2 observations, the mean of the combined set is
The mean deviation about median from the data 340, 150, 210, 240, 300, 310, 320, is
The mean deviation (approximately) from the mode for the data, is 20, 25, 30, 18, 15, 40
If the S.D. of y 1 , y 2 , y 3 , … , y n is 6, then the variance of y 1 − 3 , y 2 − 3 , y 3 − 3 … , y n − 3 , is
The mean of 100 observations is 50 and their standard deviation is 5.The mean of the squares of all observations, is
