- 20 Marks
Question
Mr. Boo, a Chartered Accountant, is investigating the distribution of the number of fuel gallons consumed per day in the year 2010. He conducted a survey on the number of fuel gallons consumed per day and recorded the following results:
| NUMBER OF FUEL GALLONS | PERCENTAGE OF CONSUMPTION |
|---|---|
| 0 but under 5 | 38% |
| 5 but under 10 | 25% |
| 10 but under 15 | 16% |
| 15 but under 20 | 21% |
Required:
a) Calculate the following measures of central tendency: i) Mean (3 marks) ii) Median (3 marks) iii) Mode (3 marks)
b) Compute the following measures of dispersion and skewness: i) Inter-Quartile Range (3 marks) ii) Variance (3 marks) iii) Appropriate coefficient of skewness (3 marks)
c) Using (a) and (b) above, comment on the distribution of the number of fuel gallons consumed per day in 2010 (2 marks).
(Total: 20 marks)
Answer
(a)
| Classes | Class Boundaries | Class Midpoints (x) | Frequency (f) | fx | f(x²) |
|---|---|---|---|---|---|
| 0-4 | -0.5-4.5 | 2 | 38 | 76 | 152 |
| 5-9 | 4.5-9.5 | 7 | 25 | 175 | 1,225 |
| 10-14 | 9.5-14.5 | 12 | 16 | 192 | 2,304 |
| 15-19 | 14.5-19.5 | 17 | 21 | 357 | 6,069 |
| Total | 100 | 800 | 9,796 |
i) Mean:
ii) Median:
Median lies in the 0-4 class.
L = 4.5, N = 100 ,cf = 38, f = 25, Median=4.5+ 
i) Inter-Quartile Range: Q3 = 13.25, Q1 = 0.16, IQR = 13.09
ii) Variance: 
iii) Skewness:
Skewness = 
(c) Comment:
The data is unimodal and positively skewed, as the mode is less than the median, and the median is less than the mean.
- Tags: Central Tendency, Dispersion, Inter-Quartile Range, Mean, Median, Mode, Skewness, Variance
- Level: Level 1
- Topic: Measures of Central Tendency
- Series: MAY 2016
- Uploader: Kwame Aikins