Study MaterialsCBSE NotesImportant Questions for Class 10 Maths Chapter 14 Statistics

Important Questions for Class 10 Maths Chapter 14 Statistics

Key questions for Class 10 Mathematics Chapter 14 on Statistics can be found on IL. These questions are crafted according to the latest exam format by consulting CBSE board sample papers. Students getting ready for the CBSE class 10 board exams in 2022-23 can utilize these Statistics questions to aim for top marks in this chapter.

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    Also Check: CBSE Class 10 Maths Important Question Chapter 8 Tribometry

    Statistics Class 10 Important Questions Short Answer

    Q.1. Find the mean of the 32 numbers, such that if the mean of 10 of them is 15 and the mean of 20 of them is 11. The last two numbers are 10.

    Solution: The given mean of 10 numbers = 15

    So, Mean of 10 numbers = sum of observations/ no. of observations

    15 = sum of observations / 10

    Sum of observations of 10 numbers = 150

    Similarly, Mean of 20 numbers = sum of observations/ no. of observations

    11 = sum of observations / 20

    Sum of observations of 20 numbers = 220

    Hence, Mean of 32 numbers = (sum 10 numbers + sum of 20 numbers + sum of last two numbers)/ no. of observations

    Mean of 32 numbers = (150 + 220 + 20 ) / 32 = 390 /32 = 12.188

    Also Check: Important Questions for Class 10 Maths Chapter 14 Statistics

    Q.2. Find the mean of the first 10 natural numbers.

    Solution: The first 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

    Mean = (1 + 2 +3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) / 10 = 55/10 = 5.5

    Q.3. Find the value of y from the following observations if these are already arranged in ascending order. The Median is 63.

    20, 24, 42, y , y + 2, 73, 75, 80, 99

    Solution:

    As the number of observations made is odd, so the median will be the middle term, i.e. y + 2.

    Therefore,

    y + 2 = 63

    y = 63 – 2 = 61

    Q.4. While checking the value of 20 observations, it was noted that 125 was wrongly noted as 25 while calculating the mean and then the mean was 60. Find the correct mean.

    Solution:

    Let y be the sum of observation of 19 (20 – 1) numbers leaving 125.

    So, y + 25 = 20 × 60 = 1200 {Mean = (sum of observations/ no. of observations)}

    As we know,

    x + 25 = 20 × 60 = 1200

    Also

    x + 125 = 20 × y = 20y

    Next, Subtract 125 − 25 = 20y − 1200

    20y = 1300

    y = 65

    Also Check: Surface Areas and Volumes Class 10 Extra Questions Maths Chapter 13

    Q.5. Find the mode of the following items.

    0, 5, 5, 1, 6, 4, 3, 0, 2, 5, 5, 6

    Solution: On arranging the items in ascending order, we get:

    0, 0, 1, 2, 3, 4, 5, 5, 5, 5, 6, 6

    As we can see 5 occurs the maximum number of times.

    Therefore, the mode of the given items = 5

    Q.6. A student scored the following marks in 6 subjects:

    30, 19, 25, 30, 27, 30

    Find his modal score.

    Solution: If we arrange his marks in ascending order

    19, 25, 27, 30, 30, 30

    As we can see, 30 occurs a maximum number of times.

    Therefore, the modal score of the student = 30

    Q.7.The daily minimum steps climbed by a man during a week were as under:

    Monday Tuesday Wednesday Thursday Friday Saturday
    35 30 27 32 23 28

    Find the mean of the steps.

    Solution: Number of steps climbed in a week: 35, 30, 27, 32, 23, 28.

    So, we get,

    Mean = sum of observation (steps) / total no of observations

    = (35 + 30 + 27 + 32 + 23 + 28) / 6

    = 175/6

    = 29.17

    Also Check: Polynomials Class 10 Extra Questions Maths Chapter 2

    Q. 8. If the mean of 4 numbers, 2,6,7 and a is 15 and also the mean of other 5 numbers, 6, 18, 1, a, b is 50. What is the value of b?

    Solution:

    Mean = sum of observations / no. of observations

    15 = (2 + 6 + 7 +a)/4

    15 = (15 + a) / 4

    15 x 4 = 15 + a

    60 – 15 = a

    a = 45

    Similarly,

    Mean = sum of observations / no. of observations

    50 = (18 + 6 + 1 +a + b)/5

    50 = (18 + 6 + 1 +45 + b)/5

    50 = (70 + b)/5

    250 = 70 + b

    b = 250 – 70 = 180

    So, The value of b = 180.

    Q.9: If the mean of first n natural numbers is 15, then find n.

    Solution:

    We know that the sum of first n natural numbers = n(n + 1)/2

    Mean of the first n natural numbers = Sum of first n natural numbers/n

    = [n(n + 1)/2]/ n

    = (n + 1)/2

    According to the given,

    (n + 1)/2 = 15

    n + 1 = 30

    n = 29

    Also Check: Some Applications of Trigonometry Class 10 Extra Questions Maths Chapter 9

    Q.10: Construct the cumulative frequency distribution of the following distribution :

    Class 12.5 – 17.5 17.5 – 22.5 22.5 – 27.5 27.5 – 32.5 32.5 – 37.5
    Frequency 2 22 19 14 13

    Solution:

    The cumulative frequency distribution of the given distribution is given below :

    Class Frequency Cumulative frequency
    12.5 – 17.5 2 2
    17.5 – 22.5 22 24
    22.5 – 27.5 19 43
    27.5 – 32.5 14 57
    32.5 – 37.5 13 70

    Statistics Class 10 Important Questions Short Answer-I (2 Marks)

    Question 6.
    The mean of the following data is 18.75. Find the value of P: (2012, 2017D)
    Important Questions for Class 10 Maths Chapter 14 Statistics 7
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 8

    Question 7.
    Data regarding heights of students of Class X of Model School, Dehradun is given below. Calculate the average height of students of the class. (2015)
    Important Questions for Class 10 Maths Chapter 14 Statistics 9
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 10

    Also Check: Important Questions Class 10 Maths Chapter 4 Quadratic Equations

    Question 8. From the following cumulative frequency table, construct a frequency distribution table: (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 11
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 12

    Question 9.
    Convert the following frequency distribution to a ‘more than’ type cumulative frequency distribution. (2012)
    Important Questions for Class 10 Maths Chapter 14 Statistics 13
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 14

    Question 10.
    The distribution given below gives the daily income of 50 workers in a factory: (2017D)
    Important Questions for Class 10 Maths Chapter 14 Statistics 15
    Convert the above distribution to a less than type cumulative frequency distribution.
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 16

    Question 11.
    Find the mode of the following frequency distribution: (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 17
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 18
    Important Questions for Class 10 Maths Chapter 14 Statistics 19

    Question 12.
    Given below is the distribution of weekly pocket money received by students of a class. Calculate the pocket money that is received by most of the students. (2014)
    Important Questions for Class 10 Maths Chapter 14 Statistics 20
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 21
    ∴ Required pocket money = ₹86.32 (approx.)

    Question 13.
    Find the median of the data using an empirical formula, when it is given that mode = 35.3 and mean = 30.5. (2014)
    Solution:
    Mode = 3(Median) – 2(Mean)
    35.3 = 3(Median) – 2(30.5)
    35.3 = 3(Median) – 61
    96.3 = 3 Median
    Median = \(\frac{96.3}{3}\) = 32.1

    Question 14.
    Show that the mode of the series obtained by combining the two series S1 and S2 given below is different from that of S1 and S2 taken separately: (2015)
    S1 : 3, 5, 8, 8, 9, 12, 13, 9, 9
    S2 : 7, 4, 7, 8, 7, 8, 13
    Solution:
    In S1 : Number 9 occurs 3 times (maximum)
    ∴ Mode of S1 Series = 9
    In S2 : Number 7 occurs 3 times (maximum)
    ∴ Mode of S, Series = 7
    After combination:
    In S1 & S2 : No. 8 occurs 4 times (maximum)
    ∴ Mode of S1 & S2 taken combined = 8
    So, mode of S1 & S2 combined is different from that of S1 & S2 taken separately.

    Statistics Class 10 Important Questions Short Answer-II (3 Marks)

    Question 15.
    Find the mean of the following data. (2012)
    Important Questions for Class 10 Maths Chapter 14 Statistics 22
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 23

    Question 16.
    The following table gives the literacy rate (in %) in 40 cities. Find the mean literacy rate: (2012)
    Important Questions for Class 10 Maths Chapter 14 Statistics 24
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 25

    Question 17.
    If the mean of the following distribution is 50, find the value of p: (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 26
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 27

    Question 18.
    The mean of the following frequency distribution is 62.8. Find the missing frequency x. (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 28
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 29

    Question 19.
    The frequency distribution table of agricultural holdings in a village is given below: (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 30
    Find the Mean area held by a family.
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 31

    Question 20.
    Monthly pocket money of students of a class is given in the following frequency distribution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 32
    Find mean pocket money using step deviation method. (2014)
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 33

    Question 21.
    Find the mean of the following distribution by Assumed Mean Method: (2015)
    Important Questions for Class 10 Maths Chapter 14 Statistics 34
    Important Questions for Class 10 Maths Chapter 14 Statistics 35
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 36

    Question 22.
    Find the mean and median for the following data: (2015)
    Important Questions for Class 10 Maths Chapter 14 Statistics 37
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 38

    Question 23.
    For helping poor girls of their class, students saved pocket money as shown in the following table: (2014)
    Important Questions for Class 10 Maths Chapter 14 Statistics 39
    Find mean and median for this data.
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 40

    Question 24.
    Weekly income of 600 families is given below:
    Important Questions for Class 10 Maths Chapter 14 Statistics 41
    Find the median. (2012)
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 42
    Important Questions for Class 10 Maths Chapter 14 Statistics 43

    Question 25.
    Find the median for the following distribution: (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 44
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 45

    Question 26.
    Heights of students of class X are given in the following frequency distribution: (2014)
    Important Questions for Class 10 Maths Chapter 14 Statistics 46
    Find the modal height.
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 47
    Maximum frequency is 20
    ∴ Modal class is 160 – 165
    Important Questions for Class 10 Maths Chapter 14 Statistics 48
    ∴ The modal height = 163 cm

    Question 27.
    A medical camp was held in a school to impart health education and the importance of excercise to children. During this camp, a medical check of 35 students was done and their weights were recorded as follows: (2016)
    Important Questions for Class 10 Maths Chapter 14 Statistics 49
    Compute the modal weight.
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 50
    ∴ Modal weight = 46.9 kg

    Question 28.
    The average score of boys in the examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of number of boys to the number of girls who appeared in the examination. (2015)
    Solution:
    Let the number of boys = n1
    and number of girls = n2
    Important Questions for Class 10 Maths Chapter 14 Statistics 51
    Important Questions for Class 10 Maths Chapter 14 Statistics 52
    ∴ No. of boys : No. of girls = 3 : 2

    Question 29.
    Following is the age distribution of dengue patients admitted in a hospital during a week of October, 2013: (2014)
    Important Questions for Class 10 Maths Chapter 14 Statistics 53
    Draw a ‘less than type’ ogive for the above distribution. Also, obtain median from the curve.
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 54

    Question 30.
    The lengths of leaves of a plant are measured correct to the nearest mm and the data obtained is represented as the following frequency distribution: (2015)
    Important Questions for Class 10 Maths Chapter 14 Statistics 55
    Important Questions for Class 10 Maths Chapter 14 Statistics 56
    Draw a ‘more than type’ ogive for the above data.
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 57

    Statistics Class 10 Important Questions Long Answer (4 Marks)

    Question 31.
    The mean of the following frequency distribu tion is 53. But the frequencies f1 and f2 in the classes 20-40 and 60-80 are missing. Find the missing frequencies: (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 58
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 59
    ⇒ 2730 + 30f1 + 70f2 = 5300
    ⇒ 30f1 + 70f2 = 5300 – 2730 = 2570
    ⇒ 3f1 + 7f2 = 257 …[Dividing by 10
    ⇒ 3f1 +7(47 – f1) = 257 . [From (i)
    ⇒ 3f1 + 329 – 7f1 = 257
    ⇒ -4f1 = 257 – 329 = -72
    ⇒ f1 = \(\frac{-72}{-4}\) = 18
    Putting the value of f1 in (i), we get
    f2 = 47 – f1
    ⇒ f2 = 47 – 18 = 29
    ∴ f1 = 18, f2 = 29

    Question 32.
    The mean of the following frequency distribution is 62.8 and the sum of frequencies is 50. Find the missing frequencies f1 and f2: (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 60
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 61
    ⇒ 2060 + 30f1 + 70f2 = 3140
    ⇒ 30f1 + 70f2 = 3140 – 2060 = 1080
    ⇒ 3f1 + 7f2 = 108 …[Dividing by 10
    ⇒ 3f1 + 7(20 – f1) = 108 … [From (i)
    ⇒ 3f1 + 140 – 7f1 = 108
    ⇒ -4f1 = 108 – 140 = -32 .
    ∴ f1 = 8
    Putting the value of f1 into (i), we get
    f2 = 20 – 8 = 12
    ∴ f2 = 12

    Question 33.
    In the table below, heart-beats of 30 women are recorded. If mean of the data is 76, find the missing frequencies x and y. (2014)
    Important Questions for Class 10 Maths Chapter 14 Statistics 62
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 63
    ⇒ 1978 + 66.5x + 84.5y = 2280
    ⇒ 1978 + 66.5x + 84.5(4 – x) = 2280 … [From (i)
    ⇒ 1978 + 66.5x + 338 – 84.5x = 2280
    ⇒ 1978 + 338 – 2280 = 84.5x – 66.5x
    ⇒ 36 = 18x ⇒ x = 2
    From (i), y = 4 – x = 4 – 2 = 2 ∴ x = 2, y = 2

    Question 34.
    The following table gives the daily income of 50 workers of a factory. Draw both types (“less than type” and “greater than type”) ogives. (2015)
    Important Questions for Class 10 Maths Chapter 14 Statistics 64
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 65
    Important Questions for Class 10 Maths Chapter 14 Statistics 66

    Question 35.
    Find the values of x and y if the median for the following data is 31. (2012)
    Important Questions for Class 10 Maths Chapter 14 Statistics 67
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 68
    ⇒ 18 – x = (9 – x)10
    ⇒ 18 – x = 90 – 10x
    ⇒ -x + 10x = 90 – 18
    ⇒ 9x = 72
    ⇒ x = 8
    Putting the value of x in (i), we have
    y = 18 – 8 = 10
    ∴ x = 8, y = 10

    Question 36.
    The median of the following data is 525. Find x and y if the sum of all frequencies is 100: (2012, 2017 D)
    Important Questions for Class 10 Maths Chapter 14 Statistics 69
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 70

    Question 37.
    Find the missing frequencies f1 and f2 in the following frequency distribution table, if N = 100 and median is 32. (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 71
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 72
    Important Questions for Class 10 Maths Chapter 14 Statistics 73

    Question 38.
    Find the median of the following data: (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 74
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 75

    Question 39.
    The frequency distribution of weekly pocket money received by a group of students is given below: (2014)
    Important Questions for Class 10 Maths Chapter 14 Statistics 76
    Draw a ‘more than type’ ogive and from it, find median. Verify median by actual calculations.
    Solution:
    n = 90 …[Given
    Important Questions for Class 10 Maths Chapter 14 Statistics 77
    Important Questions for Class 10 Maths Chapter 14 Statistics 78

    Question 40.
    Draw “less than ogive” and “more than ogive” for the following distribution and hence find its median. (2012)
    Important Questions for Class 10 Maths Chapter 14 Statistics 79
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 80
    Important Questions for Class 10 Maths Chapter 14 Statistics 81

    Question 41.
    Draw: (a) more than ogive and (2017OD)
    (b) less than ogive for the following data
    Also find its median.
    Important Questions for Class 10 Maths Chapter 14 Statistics 82
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 83
    Important Questions for Class 10 Maths Chapter 14 Statistics 84

    Question 42.
    Draw a more than ogive for the data given below which gives the marks of 100 students: (2012, 2017D)
    Important Questions for Class 10 Maths Chapter 14 Statistics 85
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 86

    Question 43.
    For the following distribution, draw a ‘more than Ogive’ and hence find the median: (2013)
    Important Questions for Class 10 Maths Chapter 14 Statistics 87
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 88

    Question 44.
    School held sports day in which 150 students participated. Ages of students are given in the following frequency distribution: (2014)
    Important Questions for Class 10 Maths Chapter 14 Statistics 89
    For the above data, draw a ‘more than type’ ogive and from the curve, find median. Verify it by actual calculations.
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 90
    Important Questions for Class 10 Maths Chapter 14 Statistics 91

    Question 45.
    In a class test, marks obtained by 120 students are given in the following frequency distribution. If it is given that mean is 59, find the missing frequencies x and y. (2015)
    Important Questions for Class 10 Maths Chapter 14 Statistics 92
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 93
    Important Questions for Class 10 Maths Chapter 14 Statistics 94

    Question 46.
    Mode of the following frequency distribution is 65 and sum of all the frequencies is 70. Find the missing frequencies x and y. (2015)
    Important Questions for Class 10 Maths Chapter 14 Statistics 95
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 96
    54 + x + y = 70 … [Given
    x + y = 70 – 54 = 16 …(i)
    ∴ Mode = 65
    Modal Class is 60 – 80
    Important Questions for Class 10 Maths Chapter 14 Statistics 97

    Question 47.
    Find the mode of the following frequency distribution: (2015)
    Important Questions for Class 10 Maths Chapter 14 Statistics 98
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 99

    Question 48.
    Cost of Living Index for some period is given in the following frequency distribution: (2014)
    Important Questions for Class 10 Maths Chapter 14 Statistics 100
    Find the mode and median for above data.
    Solution:
    Important Questions for Class 10 Maths Chapter 14 Statistics 101
    Important Questions for Class 10 Maths Chapter 14 Statistics 102

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