Question

The sum of the deviations of each data value from this measure of central location will always be zero. A. Median B. Standard deviation C. Mean D. Mode

Answer 1

Answer:

C. Mean

Explanation:

Mean = (∑$x_{i}$)/N

Median = central values when data is sorted

Mode = most repeated value

Standard deviation = $\sqrt{sum(x_{i}-mean)^{2}/N}$

In standard deviation, formula you may see that deviation is being calculated from the mean (central location). But here we take square of the value before adding all of them.

But if we just take $sum(x - mean)$, it would be equal to zero.

EXAMPLE

Take 4, 9, 5 as data

mean = (4+9+5)/3 = 18/3 = 6

sum of deviations from mean = (4-6)+(9-6)+(5-6) = (-2)+(3)+(-1) = 0

Answer 2

Answer:

(C). Mean

Explanation:

Given a set of number data;

(A) The median is the number in that data that appears midway when the number data is sorted in ascending or descending order. And sum of the deviations from the median (if it even exists), will not always give zero.

(B) The standard deviation of the set of number data is found by taking the square root of the average of the square of the mean deviation of each number in the set.

(C) The mean of the set is the average of the set of numbers. The sum of the deviations of each number from the mean will always give zero. For example, given the following set of numbers: 3, 6, 2, 4, 10;

i. the mean of the set is (3 + 6 + 2 + 4 + 10) / 5 = 5

ii. the deviation of each element of the set from the mean is;

3 => 3 - 5 = -2

6 => 6 - 5 = 1

2 => 2 - 5 = -3

4 => 4 - 5 = -1

10 => 10 - 5 = 5

The sum of these deviations will give zero(0) i.e

-2 + 1 + -3 + -1 + 5 = 0

(D) The mode of the set is the number that has the highest frequency i.e the number that appears most. The sum of deviations from mode will not always give zero (0)

Therefore, the correct answer is C.