(i. If a distribution is highly skewed, the mean (measure of central tendency) should be avoided. (ii) A characteristic of the population is called a statistic.
(iii) A sample revealed that the ages of musicians playing in small local combos are 36, 29, 37, 32, 36 and 75. The median is the most appropriate measure of central tendency to represent the ages of the musicians.
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

(i) True, because in a highly skewed distribution, the mean can be misleading as it is affected by extreme values. The median is a better measure of central tendency in such cases.(ii) False, a characteristic of the population is called a parameter, while a statistic is a characteristic of a sample.(iii) True, given the presence of an outlier (age 75), the median (which would be the average of 36 and 37 in this case) provides a better representation of the central tendency of the ages than the mean, which would be skewed by the outlier.

(I If a Distribution Is Highly Skewed, the Mean (Measure