(i. The research director of a large oil company conducted a study of the buying habits of consumers with respect to the amount of gasoline purchased at full-service pumps. The arithmetic mean amount is 11.5 gallons and the median amount is 11.95 litres. The standard deviation of the sample is 4.5 litres. The Pearson's coefficient of skewness can be calculated to be +0.20. (ii) The Pearson's coefficient of skewness (Sk) measures the amount of skewness and may range from -3.0 to +3.0. It is computed by subtracting the median from the mean, multiplying the result by 3 and dividing by standard deviation.
(iii) A study has been made of the number of hours a light bulb will operate before it burns out. If the variance of this distribution were computed, it would be measured in hours squared
A) (i), (ii) and (iii) are all correct statements
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements, but not (i).
E) (i), (ii) and (iii) are all false statements.

Question

Quizplus · Accepted Answer

(ii) is correct because it accurately describes how Pearson's coefficient of skewness is calculated, which involves the difference between the mean and median, multiplied by 3, and then divided by the standard deviation. (iii) is correct because variance is indeed measured in the square of the unit of the original data, so for time measured in hours, variance would be in hours squared. (i) is incorrect because it mixes units (gallons and litres) without conversion, making the calculation of Pearson's coefficient of skewness as stated impossible or incorrect without first converting the units to be consistent.

(I the Research Director of a Large Oil Company Conducted