The distribution of the masses of a group of…

Question 1 Report

The distribution of the masses of a group of persons is shown in the following table

Mass/kg	10.5 - 14.4	14.5 - 24.4	24.5 - 44.4	44.5 - 47.4	47.5 - 49.4
Number of Persons	2	6	18	2	1

Draw a histogram for the distribution

Answer

Answer Details

Histogram of Mass Distribution

Since the class intervals are unequal, the vertical axis is frequency density:

\[\text{Frequency density}=\frac{\text{frequency}}{\text{class width}}\]

Mass (kg)	Class boundaries	Class width	Frequency	Frequency density
10.5–14.4	10.45–14.45	4	2	0.50
14.5–24.4	14.45–24.45	10	6	0.60
24.5–44.4	24.45–44.45	20	18	0.90
44.5–47.4	44.45–47.45	3	2	0.67
47.5–49.4	47.45–49.45	2	1	0.50

The required histogram is:

For example, the area of the bar from \(24.45\) kg to \(44.45\) kg is \(20\times0.90=18\), equal to its frequency.

The distribution of the masses of a group of persons is shown in the following table Mass/kg 10.5 - 14.4 14.5 - 24.4 24.5 - 44.4 44.5 - 47.4 47.5 - 49.4 Num...