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BlackZzzverrR [31]
2 years ago
7

Compute the standard deviation of the following set of data to the nearest whole number:

Mathematics
1 answer:
Klio2033 [76]2 years ago
3 0

Answer:

Step-by-step explanation:

The standard deviation is the square root of the variance, and the variance is found by using the mean. So we will do that first. I will use the population variance as opposed to the sample variance since our set of numbers is small.

The mean: 8 + 12 + 15 + 17 + 18 = 70 and divide that by 5 to get

\bar{x}=14 and use this to find the variance in the formula:

s^2=\frac{\sum(x_i-\bar{x})^2}{n} it is a bit difficult to enter that formula in correctly, but here's how it works mathematically:

s^2=\frac{(8-14)^2+(12-14)^2+(15-14)^2+(17-14)^2+(18-14)^2}{5}

Squaring this ensures us that we don't end up with zero, which would be useless.

s^2=\frac{36+4+1+9+16}{5} so

s^2=13.2 which means that the standard deviation is

s = 3.633

(If you do it with n-1 = 4 in the denominator of the variance, you get a standard deviation of 4.062)

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