Mathematics, 07.06.2020 04:01 sydneydavis57

The standard deviation of a set of numbers is 22.2. What would the standard deviation be if each one of the numbers in the set was decreased by 4?

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Answer from: ezelle

There would be no change in the standard deviation if each one of the numbers in the set was decreased by 4.

Step-by-step explanation:

We are given that the standard deviation of a set of numbers is 22.2.

And we have to check that what would be the standard deviation, if each one of the numbers in the set was decreased by 4.

For concluding this, we will take a simple example;

Suppose that there are three set of numbers : 6, 8 and 10

Firstly, we will calculate the standard deviation for these numbers;

X $X - \bar X$ $(X-\bar X)^{2}$

6 6 - 8 = -2 4

8 8 - 8 = 0 0

10 10 - 8 = 2 4

Here, the Mean of the three numbers is given by;

Mean, $\bar X$ = $\frac{6+8+10}{3}$ = 8

Now, standard deviation formula is given by;

Standard deviation, s = $\sqrt{\frac{(\sum X - \bar X)^{2} }{n-1} }$

= $\sqrt{\frac{8 }{3-1} }$ = 2

Now, we will decrease each of the three numbers by 4, we get ;

X $X - \bar X$ $(X-\bar X)^{2}$

2 2 - 4 = -2 4

4 4 - 4 = 0 0

6 6 - 4 = 2 4

Here, the Mean of the three numbers is given by;

Mean, $\bar X$ = $\frac{2+4+6}{3}$ = 4

Now, standard deviation formula is given by;

Standard deviation, s = $\sqrt{\frac{(\sum X - \bar X)^{2} }{n-1} }$

= $\sqrt{\frac{8 }{3-1} }$ = 2

From this, we observe that even after decreasing each number by 4, the standard deviation remains same.

SO, we can conclude that if each one of the numbers in the set was decreased by 4 , the standard deviation of a set of numbers will be 22.2 only.

Answer from: Quest

because that’s us why

Answer from: Quest

you can use a^2+ b^2=c^2

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The standard deviation of a set of numbers is 22.2. What would the standard deviation be if each one...

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