Question

In this problem, we explore the effect on the standard deviation of adding the same constant to each data value in a data set. consider the following data set.
8, 16, 14, 8, 16

a) use the defining formula, the computation formula, or a calculator to compute s. (enter your answer to four decimal places.)

b) add 8 to each data value to get the new data set 16, 24, 22, 16, 24. compute s. (enter your answer to four decimal places.)

c) compare the results of parts (a) and (b). in general, how do you think the standard deviation of a data set changes if the same constant is added to each data value?

adding the same constant c to each data value results in the standard deviation remaining the same.

adding the same constant c to each data value results in the standard deviation increasing by c units.

adding the same constant c to each data value results in the standard deviation decreasing by c units.

there is no distinct pattern when the same constant is added to each data value in a set.

Answer 1

The standard deviation of both the data are the same which is 3.67 and adding the same constant c to each data value results in the standard deviation remaining the same.

What is the standard deviation?

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

We have a data set:

8, 16, 14, 8, 16

As we know the formula for standard deviation is:

$\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}$

Here σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observation in data set.

X = (8+16+14+8+16)/5 = 12.4

n = 5

After calculating the standard deviation will be:

σ = 3.67

Add 8 to each data value to get the new data set 16, 24, 22, 16, 24.

New standard deviation:

σ(new) = 3.67

The standard deviation of both the data are same we can say the standard deviation does not change when we add a constant to each data value.

Adding the same constant c to each data value results in the standard deviation remaining the same.

Thus, the standard deviation of both the data are the same which is 3.67 and adding the same constant c to each data value results in the standard deviation remaining the same.

Learn more about the standard deviation here:

brainly.com/question/12402189

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