The frequency table below shows the distribution of masses (in kg) of 20 packages delivered to a warehouse: | Mass (kg) | Frequency (f) | | :---: | :---: | | 10 – 14 | 3 | | 15 – 19 | 5 | | 20 – 24 | 8 | | 25 – 29 | 4 | What is the mean mass of the packages?

The frequency table below shows the distribution of masses (in kg) of 20 packages delivere… — JAMB UTME

The frequency table below shows the distribution of masses (in kg) of $20$ packages delivered to a warehouse:

What is the mean mass of the packages?

The mean mass of the packages is

20.25\text{ kg}

The mean of grouped frequency distribution is found using the formula

\bar{x} = \frac{\sum fx}{\sum f}

, where

x

represents the midpoint of each class interval. Calculating the midpoints yields

12

17

22

, and

27

. Multiplying each midpoint by its frequency gives products of

36

85

176

, and

108

, totaling

405

. Dividing

405

by the total frequency of

20

produces

20.25\text{ kg}

Find the class midpoint (

x

) for each class interval.

Midpoints are: 10–14

\rightarrow x = 12

; 15–19

\rightarrow x = 17

; 20–24

\rightarrow x = 22

; 25–29

\rightarrow x = 27

The mean of grouped data requires using the midpoint of each interval to represent its data values.

Multiply each class midpoint (

x

) by its frequency (

f

) to find

fx

3 \times 12 = 36

;

5 \times 17 = 85

;

8 \times 22 = 176

;

4 \times 27 = 108

This calculates the total estimated mass for each class interval.

Sum the frequencies (

\sum f

) and the products (

\sum fx

\sum f = 3 + 5 + 8 + 4 = 20

and

\sum fx = 36 + 85 + 176 + 108 = 405

These sums give the total number of packages and the total estimated mass.

Calculate the mean using the formula

\bar{x} = \frac{\sum fx}{\sum f}

\bar{x} = \frac{405}{20} = 20.25\text{ kg}

Dividing the total mass by the total number of items yields the grouped mean.

Mean of Grouped Data

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