A dataset of employee salaries has a standard deviation of 6. If every salary in the datas… — GRE General Test

A dataset of employee salaries has a standard deviation of $6$ . If every salary in the dataset is multiplied by $3$ and then increased by $10$ , what is the standard deviation of the resulting dataset?

A
$6$
$18$ Answer
C
$28$
D
$16$
E
$54$

Answer

The standard deviation of the resulting dataset is

18

Multiplying each data point by

3

increases the spread around the mean by a factor of

3

, changing the standard deviation from

6

18

. Adding

10

to each value shifts all values by the same amount, which leaves the distance between data points and the mean unchanged. Thus, the standard deviation remains

18

Step-by-Step Solution

Evaluate the effect of multiplying each value in the dataset by a positive constant

c = 3

The standard deviation is scaled by

3

, giving a new standard deviation of

6 \times 3 = 18

Scaling every data value by a constant factor

c

multiplies the measures of dispersion (such as standard deviation, range, and IQR) by

|c|

Evaluate the effect of adding a constant

k = 10

to each value in the dataset.

The standard deviation remains

18

Adding a constant to every data value shifts the entire distribution along the number line without changing the relative distances between values or the overall spread.

Key Concept

Linear Transformations on Standard Deviation

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

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