Sets?? I Think

[patricialec]

Hello there
I could use help in the following:

x is the standard deviation of the set of numbers {a,b,c,d,e}. For each of the following sets, indicate which sets who have a standard deviation equal to x.

{a+2,b+2,c+2,d+2,e+2}
{a-2,b-2,c-2,d-2,e-2}
{2a,2b,2c,2d,2e}

How would I go about solving this? I appreciate any help. :twisted:

 

[soroban]

Hello, patricialec!

I believe we're supposed to think through these problems.

Informally speaking, the standard deviation is the "spread" of a set of numbers.

\(\displaystyle x\text{ is the standard deviation of the set of numbers: }\:\{a,b,c,d,e\}.\)

\(\displaystyle \text{For each of the following sets, indicate which sets who have a standard deviation equal to }x.\)

\(\displaystyle (1)\;\{a\!+\!2,\:b\!+\!2,\:c\!+\!2,\:d\!+\!2,\:e\!+\!2\}\)

\(\displaystyle \text{Adding 2 to each score does }not\text{ change the spread of the numbers.}\)
,. . \(\displaystyle \text{This set has a standard deviation equal to }x.\)

\(\displaystyle (2)\;\{a\!-\!2,\:b\!-\!2,\:c\!-\!2,\:d\!-\!2,\:e\!-\!2\}\)

\(\displaystyle \text{Subtracting 2 from each score does }not\text{ change the spread of the numbers.}\)
. . \(\displaystyle \text{This set has a standard deviation equal to }x.\)

\(\displaystyle (3)\;\{2a,2b,2c,2d,2e\}\)

\(\displaystyle \text{Doubling each score }does\text{ change the spread of the numbers.}\)
. . \(\displaystyle \text{(They are spread twice as far apart.)}\)

\(\displaystyle \text{This set has a standard deviation equal to }2x.\)

 

[patricialec]

THank you so much.... :wink: