The table below shows the distribution of weekly cassava output (in bags) produced by a sample of farmers in a agricultural cooperative: | Output (Bags) | Number of Farmers (f) | |---|---| | 10 - 14 | 2 | | 15 - 19 | 5 | | 20 - 24 | 8 | | 25 - 29 | 5 | What is the mean weekly output of cassava per f

The table below shows the distribution of weekly cassava output (in bags) produced by a sa… — JAMB UTME

The table below shows the distribution of weekly cassava output (in bags) produced by a sample of farmers in a agricultural cooperative:

What is the mean weekly output of cassava per farmer?

The mean weekly output of cassava per farmer is

21.0\text{ bags}

The correct output of

21.0\text{ bags}

is derived by determining the midpoint of each class interval (

12, 17, 22, 27

), multiplying each by its respective number of farmers, summing these products to get

420\text{ bags}

, and dividing by the total number of farmers (

20

Calculate the class midpoint (

x

) for each class interval.

Midpoints are:

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

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

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

, and

\frac{25+29}{2} = 27

For grouped data, the midpoint represents the central value of each class interval.

Multiply each midpoint (

x

) by its corresponding frequency (

f

) to obtain

f \times x

2 \times 12 = 24

5 \times 17 = 85

8 \times 22 = 176

5 \times 27 = 135

This determines the estimated total output within each interval.

Calculate the sum of frequencies (

\sum f

) and the sum of products (

\sum fx

\sum f = 2 + 5 + 8 + 5 = 20

;

\sum fx = 24 + 85 + 176 + 135 = 420

These totals are needed to apply the grouped mean formula.

Divide

\sum fx

\sum f

to compute the arithmetic mean (

\bar{x}

\bar{x} = \frac{420}{20} = 21.0\text{ bags}

The formula for the mean of grouped frequency distribution is

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

Arithmetic Mean of Grouped Data

Estimated Time:1m 30s