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Find the sample variance and standard deviation for the following sample. Round the answers to two decimal places as needed.

15, 37, 23, 18, 17, 10

Please show work.

User Yrpalnoob
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2 Answers

4 votes

Answer:

sample variance is 90.40 and the sample standard deviation is 9.49

Step-by-step explanation:

User Gemma
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4 votes

Answer:

Step-by-step explanation:

To find the sample variance and standard deviation, we need to first find the mean of the sample, and then use that to calculate the variance and standard deviation.

The mean of the sample is:

(15 + 37 + 23 + 18 + 17 + 10) / 6 = 16

Next, we'll find the difference between each value and the mean, square those differences, and divide the sum of the squared differences by the sample size minus one (n - 1):

(15 - 16)^2 = 1

(37 - 16)^2 = 361

(23 - 16)^2 = 49

(18 - 16)^2 = 4

(17 - 16)^2 = 1

(10 - 16)^2 = 36

The sum of the squared differences is: 1 + 361 + 49 + 4 + 1 + 36 = 452

The sample variance is: 452 / (6 - 1) = 452 / 5 = 90.4

Finally, the sample standard deviation is the square root of the sample variance:

The sample standard deviation is: sqrt(90.4) = 9.49

So, the sample variance is 90.40 and the sample standard deviation is 9.49.

User Sathesh
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