Q.1 (i) Find the mean of children per family from the data given below.

(ii) Which mathematical concept is used in this problem?

Number of children	0	1	2	3	4	5
Number of families	5	11	25	12	5	2

 

(OR)

 

Q.2 A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball from the bag is thrice that of the red ball, find the number of blue balls in the bag.

 

The mean can be found by taking the ratio of the sum of the product of the number of children and the number of families in each case, and the total number of families.

Here, the total of product of the number of children and the number of families, Σ𝑓_i 𝑥_i = 127
And the total number of families, Σ𝑓_i = 60
So, mean = Σ𝑓_i 𝑥_i/Σ𝑓_i

⇒ 𝑚𝑒𝑎𝑛 = 127/60 
⇒ 𝑚𝑒𝑎𝑛 = 2. 11
Hence, the mean of the given data is 2. 11.
(ii) Here, the concept of grouped data is used, in which the data is given in groups
 

(OR)

We are given the number of red balls, and we have to find the number of blue balls. The number of red balls = 5
Let the number of blue balls in the bag be 𝑥.
So, the total number of balls in the bag = 5 + 𝑥
 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑑 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑎𝑔 
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑏𝑎𝑔
⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑖𝑛𝑑𝑖𝑛𝑔 𝑟𝑒𝑑 𝑏𝑎𝑙𝑙 = $\frac{number of red balls in the bag}{total number of balls in the bag}$
⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑖𝑛𝑑𝑖𝑛𝑔 𝑟𝑒𝑑 𝑏𝑎𝑙𝑙 =  $\frac{5}{5+x}$

⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑖𝑛𝑑𝑖𝑛𝑔 𝑏𝑙𝑢𝑒 𝑏𝑎𝑙𝑙 =   $\frac{number of blue balls in the bag}{total number of balls in the bag}$

⇒ 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓 𝑓𝑖𝑛𝑑𝑖𝑛𝑔 𝑏𝑙𝑢𝑒 𝑏𝑎𝑙𝑙 = $\frac{x}{5+x}$
According to the question,
Probability of drawing a blue ball from the bag = 3 × Probability of drawing a red ball Putting the values of probability, we get
   $\frac{x}{5+x}$    = 3 ×  $\frac{5}{5+x}$

$\frac{x}{5+x}$  = $\frac{15}{5+x}$
As the denominator in both sides of the equation has the same denominator, i.e., 5 + 𝑥, the denominators will be cancelled. Then the equation becomes
𝑥 = 15
Hence, the number of blue balls is 15.