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Difficulty: MediumMeasures of Central Tendency

A sample survey of 20 small-scale enterprises in an industrial cluster recorded their daily profit (in thousands of Naira, ₦’000\text{₦'000}) with the following frequency distribution:

Daily Profit (xx in ₦’000\text{₦'000})Number of Enterprises (ff)
103
155
207
253
302

What is the mean daily profit of these enterprises in thousands of Naira?

Answer: 19 ₦'000

Answer

The mean daily profit of the enterprises is 19 thousand Naira.
The arithmetic mean for a frequency distribution is calculated using xˉ=∑fx∑f\bar{x} = \frac{\sum fx}{\sum f}. Multiplying each daily profit by its frequency yields a total sum of 380380. Dividing by the total frequency of 2020 enterprises gives a mean daily profit of 1919 thousand Naira.

Step-by-Step Solution

1
Multiply each profit level by its corresponding frequency to get the total profit contribution per group
f⋅xf \cdot x values are 30, 75, 140, 75, and 60
Each profit value must be weighted by how many enterprises earned that amount
2
Sum all weighted profit values to find total combined profit
∑fx=380\sum fx = 380
The sum of f⋅xf \cdot x gives the grand total daily profit for all surveyed enterprises
3
Sum all frequencies to obtain total count of enterprises
∑f=20\sum f = 20
The mean requires dividing total profit by total sample size
4
Divide total weighted profit by total number of enterprises
xˉ=38020=19\bar{x} = \frac{380}{20} = 19
Formula for discrete grouped mean is xˉ=∑fx∑f\bar{x} = \frac{\sum fx}{\sum f}

Key Concept

Calculation of Mean from a Discrete Frequency Distribution
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Topics

Measures of Central Tendency

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