The frequency distribution table below shows the masses (in \text{kg}) of 40 cassava tubers harvested from an agricultural test plot: | Mass (\text{kg}) | Frequency (f) | | :---: | :---: | | 10 - 14 | 4 | | 15 - 19 | 8 | | 20 - 24 | 12 | | 25 - 29 | 10 | | 30 - 34 | 6 | What is the estimated mean ma

The frequency distribution table below shows the masses (in \text{kg}) of 40 cassava tuber… — JAMB UTME

The frequency distribution table below shows the masses (in $\text{kg}$ ) of $40$ cassava tubers harvested from an agricultural test plot:

What is the estimated mean mass of the harvested cassava tubers?

22.75\text{ kg}

The value

22.75\text{ kg}

is correct because the mean for grouped data is obtained by multiplying each class midpoint by its frequency, summing these products to get

910

, and dividing by the total frequency of

40

Find the class midpoint (

x

) for each class interval using

x = \frac{\text{Lower limit} + \text{Upper limit}}{2}

Midpoints are:

12

for

10-14

17

for

15-19

22

for

20-24

27

for

25-29

, and

32

for

30-34

Grouped data calculations require representative central values for each class interval.

Multiply each class midpoint (

x

) by its corresponding frequency (

f

) to get

fx

, then sum all

fx

values.

\sum fx = (4 \times 12) + (8 \times 17) + (12 \times 22) + (10 \times 27) + (6 \times 32) = 48 + 136 + 264 + 270 + 192 = 910

This calculates the total estimated mass of all harvested cassava tubers.

Sum the frequencies to get the total number of items

\sum f

\sum f = 4 + 8 + 12 + 10 + 6 = 40.

The mean formula divides the total sum by the total frequency.

Compute the grouped mean using

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

\bar{x} = \frac{910}{40} = 22.75\text{ kg}.

Dividing the sum of products by the total frequency yields the estimated mean.

Grouped Mean Calculation