(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

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Detailed Solution

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.

Number of children (x_i)	Number of families (f_i)	f_ix_i
0	5
1	11
2	25
3	12
4	5
5	2
	$\underset{}{\sum f_{i} = 60}$	$\underset{}{\sum f_{i} x_{i} = 127}$

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

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