Question

1. from the frequency distribution that you worked out of the age of the 50 most powerful women to approximate the mean (frequency distribution). use the formula to calculate the mean of a frequency distribution

use seven classes
26, 31, 35, 37, 43, 43, 43, 44, 45, 47,
48, 48, 49, 50, 51, 51, 51, 51, 52, 54,
54, 54, 54, 55, 55, 55, 56, 57, 57, 57,
58, 58, 58, 58, 59, 59, 59, 62, 62, 63,
64, 65, 65, 65, 66, 66, 67, 67, 72, 86

\

$$\begin{array}{|l|l|l|l|} \\hline \\text{class} & \\text{freq } f & \\text{midpoint } x & xf \\\\ \\hline 26 - 34 & 2 & & \\\\ \\hline 35 - 43 & 5 & & \\\\ \\hline 44 - 52 & 12 & & \\\\ \\hline 53 - 61 & 18 & & \\\\ \\hline 62 - 70 & 11 & & \\\\ \\hline 71 - 79 & 1 & & \\\\ \\hline 80 - 88 & 1 & & \\\\ \\hline & \\sum f = 50 & & \\\\ \\hline \\end{array}$$

Explanation:

Calculate class midpoints

Using the Frequency Distribution knowledge point

$$
LATEXBLOCK0
$$

Calculate products of frequency and midpoint

Using the Frequency Distribution knowledge point

$$
LATEXBLOCK1
$$

Sum the frequencies and products

Using the Frequency Distribution knowledge point

$$
LATEXBLOCK2
$$

Calculate the grouped mean

Using the Frequency Distribution knowledge point

$$
LATEXBLOCK3
$$

Answer:

Class	Freq \(f\)	Midpoint \(x\)	\(xf\)
35 – 43	5	39	195
44 – 52	12	48	576
53 – 61	18	57	1026
62 – 70	11	66	726
71 – 79	1	75	75
80 – 88	1	84	84
Total	\(\sum f = 50\)		\(\sum xf = 2742\)

$$\text{Mean } (\mu) = \frac{\sum xf}{\sum f} = \frac{2742}{50} = 54.84$$