The frequency table below shows the fuel efficiency, measured in \text{km/L}, for a fleet … — JAMB UTME

The frequency table below shows the fuel efficiency, measured in $\text{km/L}$ , for a fleet of $50$ delivery vans operated by a logistics company:

Fuel Efficiency (km/L)	Frequency ( $f$ )
10 – 14	8
15 – 19	12
20 – 24	20
25 – 29	10

What is the mean fuel efficiency of the fleet, in $\text{km/L}$ ?

Answer: 20.2 km/L

Answer

The mean fuel efficiency of the fleet is 20.2 km/L.

The estimated mean is found by calculating the midpoint of each class interval, multiplying each midpoint by its class frequency, summing these products to get 1010, and dividing by the total frequency of 50, resulting in 20.2 km/L.

Step-by-Step Solution

Determine the midpoint (x) for each class interval.

Midpoints are 12 for 10–14, 17 for 15–19, 22 for 20–24, and 27 for 25��29.

For grouped frequency data, each class interval is represented by its midpoint x = (lower limit + upper limit) / 2.

Compute the product of frequency and midpoint (f * x) for each interval.

Products: (8 * 12) = 96, (12 * 17) = 204, (20 * 22) = 440, (10 * 27) = 270.

To calculate the total contribution of values from each class interval.

Sum all products (sum of f * x) and divide by the total number of delivery vans (sum of f).

sum of f * x = 96 + 204 + 440 + 270 = 1010. sum of f = 50. Mean = 1010 / 50 = 20.2.

The formula for the estimated mean of grouped data is mean = (sum of f * x) / (sum of f).

Key Concept

Measures of Central Tendency for Grouped Data (Grouped Mean)

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