Examkin

Question

Difficulty: MediumMeasures of Central Tendency for Grouped Data

The frequency table below shows the distribution of daily petrol consumption (in litres) recorded by 4040 commercial minibus drivers:

Daily Petrol Consumption (litres)Frequency (ff)
10−1410 - 1466
15−1915 - 191010
20−2420 - 241212
25−2925 - 2988
30−3430 - 3444

What is the mean daily petrol consumption of the minibus drivers?

  1. A
    19.25 litres19.25\text{ litres}
  2. B
    22.00 litres22.00\text{ litres}
  3. 21.25 litres21.25\text{ litres}Answer
  4. D
    23.25 litres23.25\text{ litres}

Answer

The mean daily petrol consumption is 21.25 litres21.25\text{ litres}.
The mean of a grouped frequency distribution is computed by multiplying the midpoint of each class interval by its frequency, summing these products, and dividing by the total frequency. For the given distribution, ∑fx=850\sum fx = 850 and ∑f=40\sum f = 40, giving a mean of 21.25 litres21.25\text{ litres}.

Step-by-Step Solution

1
Calculate the class mark (midpoint) xx for each class interval.
Midpoints are: 1212 for 10−1410 - 14, 1717 for 15−1915 - 19, 2222 for 20−2420 - 24, 2727 for 25−2925 - 29, and 3232 for 30−3430 - 34.
For grouped data, each class interval is represented by its midpoint.
2
Multiply each midpoint xx by its corresponding frequency ff to find fxfx.
6×12=726 \times 12 = 72, 10×17=17010 \times 17 = 170, 12×22=26412 \times 22 = 264, 8×27=2168 \times 27 = 216, 4×32=1284 \times 32 = 128.
This yields the total sum contribution of each class.
3
Find total frequency ∑f\sum f and total sum of products ∑fx\sum fx.
∑f=6+10+12+8+4=40\sum f = 6 + 10 + 12 + 8 + 4 = 40 and ∑fx=72+170+264+216+128=850\sum fx = 72 + 170 + 264 + 216 + 128 = 850.
Required components for the grouped mean formula.
4
Calculate the mean xˉ=∑fx∑f\bar{x} = \frac{\sum fx}{\sum f}.
\bar{x} = \frac{850}{40} = 21.25\text{ litres}.
Applying the formula for the mean of grouped frequency distribution.

Key Concept

Grouped Mean Calculation using Midpoints
Estimated Time:1m 30s
Rate this question

Topics

Measures of Central Tendency for Grouped Data

More questions from this topic