A dataset consists of five identical integers: 12, 12, 12, 12, and 12. What is the standar… — GMAT

A dataset consists of five identical integers: $12, 12, 12, 12,$ and $12$ . What is the standard deviation of this dataset?

$0$ Answer
B
$12$
C
$-12$
D
$144$
E
$2\sqrt{3}$

Answer

0

The correct value is

0

. Standard deviation measures how spread out the numbers in a dataset are around the mean. Since every value in the set is

12

, the mean is

12

and every value lies exactly on the mean (distance of

0

). Thus, the standard deviation is

0

Step-by-Step Solution

Calculate the arithmetic mean of the dataset

Mean

\mu = \frac{12 + 12 + 12 + 12 + 12}{5} = 12

The mean is needed to measure individual deviations.

Calculate the deviation of each data point from the mean

Deviations are

12 - 12 = 0

for all five elements

Standard deviation measures the average distance of data points from the mean.

Compute the standard deviation

Standard Deviation

SD = \sqrt{\frac{0^2 + 0^2 + 0^2 + 0^2 + 0^2}{5}} = 0

When all data points are identical, the spread around the mean is zero.

Key Concept

Standard deviation measures the dispersion or spread of a set of numbers around its mean. If all elements in a set are identical, there is no variation, so both the range and the standard deviation are equal to 0.

Question

Answer

Step-by-Step Solution

Key Concept

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