CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion
A distribution has mean 40, median 40 and mode 40. Which conclusion about its skewness is correct?
When mean, median and mode are all equal, Pearson's coefficient (Mean − Mode)/SD is zero whatever the standard deviation is. The distribution is therefore symmetrical with no skewness.
- AIt is positively skewed
- BIt is negatively skewed
- CIt is symmetrical, with zero skewnessCorrect
- DSkewness cannot be determined without the standard deviation
Explanation
Pearson's coefficient = (Mean − Mode)/SD = 0/SD = 0 for any positive SD. Equal mean, median and mode is the hallmark of a symmetrical distribution. The SD only scales the coefficient and cannot change zero.
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