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Sagot :
Answer:
8.19
Step-by-step explanation:
Adding 5 points to each score in the sample has no effect on the standard deviation. The standard deviation remains the same and constant.
Therefore, the standard deviation for the new sample is 8.19
You can use the fact that standard deviation is a measure of variation.
The standard deviation of the new sample will be same as the old standard deviation, which is 8.19
What does standard deviation measure?
Standard deviation measures how much the data points vary or disperse from the mean of the data.
The standard deviation is calculated as:
[tex]\sigma = \sqrt{\dfrac{\sum (\overline{x} - x_i)}{n}[/tex]
How to know the standard deviation of the new sample if each score was increased by 5 points?
Since each score was increased by 5 points, we have the mean increased by 5 point too
[tex]\overline{x} = \dfrac{1}{n}\sum(x_i) \\\\x_i -> x_i + 5\\\\\overline{x} = \dfrac{1}{n}\sum(x_i + 5) = \dfrac{5n}{n} + \dfrac{1}{n}\sum(x_i) = 5 + \dfrac{1}{n}\sum(x_i)[/tex]
Putting new mean and new values in the standard deviation formula, we get:
[tex]\sigma = \sqrt{\dfrac{\sum (\overline{x} + 5 - x_i - 5)^2}{n}} = \sqrt{\dfrac{\sum (\overline{x} - x_i)}{n}\\[/tex]
Thus, standard deviation won't change and will stay same as before.
Thus,
The standard deviation of the new sample will be same as the old standard deviation, which is 8.19
Learn more about standard deviation here;
https://brainly.com/question/5916717
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