The sum of deviations of the individual data elements from their mean is a. always equal to zero. b. always greater than zero. c. always less than zero. d. sometimes greater than and sometimes less than zero, depending on the data elements.

Question

Mathematics

Ian Armstrong

2 September, 06:11

The sum of deviations of the individual data elements from their mean is a. always equal to zero. b. always greater than zero. c. always less than zero. d. sometimes greater than and sometimes less than zero, depending on the data elements.

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Answers (1)

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Skyla Chandler · Answer 1

a. always equal to zero.

Step-by-step explanation:

The mean is the sum of the values of all elements in a data-set divided by the size of the data-set.

For the sum of deviations, we sum (if positive) or subtract (if negative) all the elements with the mean.

Doing this, the result will always be 0.

Simple example:

Data set: {5,7}

Mean: 6

(5 - 6) + (7 - 6) = - 1 + 1 = 0

So the correct answer is:

a. always equal to zero.