The table below shows the distribution of weights (in kg) of 10 packages in a warehouse: | Weight Interval (kg) | Frequency (f) | |---|---| | 10 - 14 | 2 | | 15 - 19 | 3 | | 20 - 24 | 5 | What is the mean weight of the packages?

The table below shows the distribution of weights (in kg) of 10 packages in a warehouse: |… — JAMB UTME

The table below shows the distribution of weights (in kg) of 10 packages in a warehouse:

What is the mean weight of the packages?

The mean weight of the packages is

18.5\text{ kg}

The correct mean is calculated by finding the midpoint of each class interval (

12, 17, 22

), multiplying each by its frequency to obtain

fx

(

24, 51, 110

), and dividing the sum of

fx

(

185

) by the total frequency (

10

), giving

18.5\text{ kg}

Calculate the class midpoint (

x

) for each interval

Midpoints are:

\frac{10+14}{2} = 12

\frac{15+19}{2} = 17

, and

\frac{20+24}{2} = 22

For grouped data, each class interval is represented by its midpoint.

Multiply each midpoint (

x

) by its corresponding frequency (

f

) to find

fx

2 \times 12 = 24

3 \times 17 = 51

, and

5 \times 22 = 110

This yields the total contribution of values from each class interval.

Sum the frequencies (

\sum f

) and the products (

\sum fx

)

\sum f = 2 + 3 + 5 = 10

and

\sum fx = 24 + 51 + 110 = 185

These sums are needed to compute the weighted mean.

Divide

\sum fx

\sum f

Mean

\bar{x} = \frac{185}{10} = 18.5\text{ kg}

The mean formula for grouped data is

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

Mean of Grouped Data using Class Marks