The table below presents the distribution of weekly expenditure (in thousands of Naira) of 20 small-scale farmers in a rural community: | Weekly Expenditure (\text{N}'000) | Frequency (f) | |---|---| | 10 – 19 | 3 | | 20 – 29 | 7 | | 30 – 39 | 6 | | 40 – 49 | 4 | What is the mean weekly expenditure

The table below presents the distribution of weekly expenditure (in thousands of Naira) of… — JAMB UTME

The table below presents the distribution of weekly expenditure (in thousands of Naira) of $20$ small-scale farmers in a rural community:

What is the mean weekly expenditure of the farmers?

The mean weekly expenditure is

\text{N}30.0\text{ thousand}

(or

\text{N}30,000

The mean of grouped data is computed using the formula

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

. Finding the midpoints (

14.5, 24.5, 34.5, 44.5

), multiplying by their respective frequencies (

3, 7, 6, 4

), and dividing the sum (

600

) by the total frequency (

20

) yields

\text{N}30.0\text{ thousand}

Calculate the midpoint (

x

) for each class interval.

Midpoints are:

14.5

for 10–19;

24.5

for 20–29;

34.5

for 30–39; and

44.5

for 40–49.

Grouped data mean calculations require representing each interval by its class mark (midpoint).

Multiply each class midpoint (

x

) by its corresponding frequency (

f

) to get

f \cdot x

, and sum these values.

\sum (f \cdot x) = (3 \times 14.5) + (7 \times 24.5) + (6 \times 34.5) + (4 \times 44.5) = 43.5 + 171.5 + 207.0 + 178.0 = 600

This yields the total estimated sum of all expenditures across all observations.

Divide the total sum

\sum (f \cdot x)

by the total frequency

\sum f

Mean

\bar{x} = \frac{600}{20} = 30.0

The mean formula for grouped data is

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

Calculation of Mean for Grouped Frequency Data

Estimated Time:1m 0s