A) Compute the mean number of children ever born based on the provided frequency distribution.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the computations for the given data:

The table shows the number of children ( $x_i$ ) and the number of women ( $f_i$ ):

Number of children ( $x_i$ )	Number of women ( $f_i$ )	$x_i \cdot f_i$	Cumulative Frequency
0	1	0	1
1	5	5	6
2	8	16	14
3	4	12	18
4	2	8	20
Total	$\sum f_i = 20$	$\sum (x_i f_i) = 41$

The total number of women ( $N$ ) is $\sum f_i = 20$ .

A) Compute the mean number of children ever born?

Calculate the sum of ( $x_i \cdot f_i$ ).
$\sum (x_i f_i) = (0 \times 1) + (1 \times 5) + (2 \times 8) + (3 \times 4) + (4 \times 2) = 0 + 5 + 16 + 12 + 8 = 41$
Calculate the total number of women ( $\sum f_i$ ).
$\sum f_i = 1 + 5 + 8 + 4 + 2 = 20$
Compute the mean.
$\text{Mean} = \frac{\sum (x_i f_i)}{\sum f_i} = \frac{41}{20} = 2.05$
The mean number of children ever born is $\boxed{\text{2.05 children}}$ .

B) What is the modal number of children ever born?
Identify the frequency for each number of children.
The number of women (frequency) for 0 children is 1.
The number of women (frequency) for 1 child is 5.
The number of women (frequency) for 2 children is 8.
The number of women (frequency) for 3 children is 4.
The number of women (frequency) for 4 children is 2.
Determine the value with the highest frequency.
The highest frequency is 8, which corresponds to 2 children.
The modal number of children ever born is $\boxed{\text{2 children}}$ .

C) What is the median number of children ever born?
Determine the position of the median.
Since the total number of data points ( $N=20$ ) is even, the median is the average of the $\frac{N}{2}$ -th and $(\frac{N

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