CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion
Which statement about the standard deviation is correct?
The standard deviation is never negative and equals zero only when all observations are identical. It is the positive square root of the average squared deviation from the mean. It is independent of a change of origin but is affected by a change of scale.
- AIt is never negative and is zero only when all observations are equalCorrect
- BIt can be negative when most deviations are below the mean
- CIt is unaffected by a change of scale
- DIt is always smaller than the mean deviation
Explanation
SD is the positive root of the mean squared deviation, so it is non-negative, and it is zero only if every value equals the mean. It is independent of origin but changes with scale. It is not smaller than mean deviation; in fact it is at least as large as the mean deviation about the mean.
Did you get it right without looking?
One question tells you little. A timed set on Measures of Central Tendency and Dispersion shows your real accuracy, how long you take and where you lose marks.
More Measures of Central Tendency and Dispersion questions
- The weights (in kg) of six employees in an office are: 65, 72, 68, 72, 70, 73. Which of the following statements is correct?
- For a distribution, the mean is 60 and the variance is 144. What is the coefficient of variation?
- For a distribution, the quartile deviation is 10 and the coefficient of quartile deviation is 0.25. What is the value of the third quartile?
- What is the standard deviation of the first seven natural numbers 1, 2, 3, 4, 5, 6, 7?
- Which of the following is a correct statement about the mode?
- The following 11 observations are already arranged in ascending order: 12, 15, 18, 22, 25, 28, 30, 35, 40, 45, 50. Using the position formul…