(i. The standard deviation the positive square root of the variance. (ii) The capacities of several metal containers are: 38, 20, 37, 64, and 27 litres. The range in litres is 24.
(iii) The sum of the deviations of each value from the mean equals zero.
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) is correct because the standard deviation is defined as the positive square root of the variance.
(ii) is correct because the range is the difference between the largest and smallest values, which in this case is 64 - 20 = 44, and not 24 as stated in the question. Thus, this statement is false.
(iii) is also correct because the sum of deviations from the mean is always zero by definition. Therefore, option C is the best choice as only statement (i) and (iii) are correct, while statement (ii) is false.

(I the Standard Deviation the Positive Square Root of the Variance