The frequency distribution table below shows the daily profits (in thousands of Naira, \te… — JAMB UTME

The frequency distribution table below shows the daily profits (in thousands of Naira, $\text{₦}$ ) recorded by a sample of $40$ small-scale market traders:

Daily Profit ( $\text{₦'000}$ )	Frequency ( $f$ )
$10 - 14$	$6$
$15 - 19$	$10$
$20 - 24$	$12$
$25 - 29$	$8$
$30 - 34$	$4$

What is the mean daily profit of the traders, in thousands of Naira?

Answer: 21.25 thousand Naira

Answer

The mean daily profit of the traders is

21.25

thousand Naira.

The mean daily profit is found by dividing the sum of the product of each class midpoint and its frequency (

\sum fx = 850

) by the total frequency (

\sum f = 40

), yielding

21.25

Step-by-Step Solution

Find the class midpoints (

x

) for each interval

Midpoints are

12

17

22

27

, and

32

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

Calculate the product of frequency and midpoint (

f \cdot x

) for each interval

Products are

72

170

264

216

, and

128

Multiplying class midpoint by class frequency estimates the sum of values within that class.

Calculate total frequency (

\sum f

) and total sum of products (

\sum fx

)

\sum f = 40

and

\sum fx = 850

The sum of frequencies gives the total number of observations, and the sum of products gives the estimated grand total.

Apply the grouped mean formula

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

\bar{x} = \frac{850}{40} = 21.25.

Dividing total sum by total frequency gives the mean value.

Key Concept

Measures of Central Tendency for Grouped Data - Mean

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