Question

pls help me to answer this​

Answer 1

Answers:

• Variance = 3
• Standard Deviation = Exactly $\sqrt{3}$ which approximates to 1.73205

I'm using the population version of each item.

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Explanation:

I'll assume your teacher wants the population variance and population standard deviation.

The first task is to add the values up

-2 + 1 + (-1) + 2 + (-3) + 0 + 2 + 1 = 0

Divide that sum over the number of values in the set (n = 8)

0/8 = 0

The mean is 0.

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The next step is to subtract the mean from each value. Luckily the mean is 0 so it won't change any of the values from the given data set.

But if you really wanted, you could have -2-0 = -2, 1-0 = 1, and so on.

Afterward, square each result

• (-2)^2 = 4
• 1^2 = 1
• (-1)^2 = 1
• 2^2 = 4
• (-3)^2 = 9
• 0^2 = 0
• 2^2 = 4
• 1^2 = 1

Adding these squares gets us

4+1+1+4+9+0+4+1 = 24

This is the Sum of the Squared Errors (SSE). Each error is the distance or difference a value is from the mean. The "squared" part should be fairly self explanatory, as well as the "sum" part also.

Divide this SSE value by the sample size n = 8

SSE/n = 24/8 = 3

This is the population variance. To get the sample variance, divide the SSE over n-1 instead of n.

Apply the square root to the variance to get the standard deviation.

So the standard deviation is exactly $\sqrt{3}$ which approximates to roughly 1.73205

Both variance and standard deviation are a measure how spread out a data set is.