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The heights​ (in inches) of 10 adult males are listed below. Find the sample standard deviation. Round to the nearest hundredth

70, 72, 71, 70, 69, 73, 69, 68, 70, 71
.

1 Answer

5 votes

Answer: 1.49

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Step-by-step explanation:

Many calculators will do this calculation in basically one step.

If you do not have a calculator, then you can search out "sample standard deviation calculator". Make sure you do NOT use the population standard deviation. That's slightly different from the sample version. Be careful not to mix the two concepts.

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Despite the fact a calculator can do this in one step, I'll show you what's going on behind the scenes. Each of the calculations in this section can be done by hand using pencil and paper (some parts you'll need a bit of time/patience). To slightly speed things along, I think a calculator with basic functions should be allowed. Those basic functions would be: add, subtract, multiply, divide, and square root. Square roots can be calculated by hand, but I'm digressing a bit.

Anyways, the first task is to compute the mean. We add up the values and then divide by the sample size n = 10.

mean = (sum of values)/(number of values)

mean = (70+72+71+70+69+73+69+68+70+71)/10

mean = 703/10

mean = 70.3

This value is exact without any rounding done to it.

Next, we subtract the mean from each data value. A spreadsheet is recommended to keep track of everything.

70 - 70.3 = -0.3

72 - 70.3 = 1.7

71 - 70.3 = 0.7

70 - 70.3 = -0.3

69 - 70.3 = -1.3

73 - 70.3 = 2.7

69 - 70.3 = -1.3

68 - 70.3 = -2.3

70 - 70.3 = -0.3

71 - 70.3 = 0.7

Square each difference.

(-0.3)^2 = 0.09

(1.7)^2 = 2.89

(0.7)^2 = 0.49

(-0.3)^2 = 0.09

(-1.3)^2 = 1.69

(2.7)^2 = 7.29

(-1.3)^2 = 1.69

(-2.3)^2 = 5.29

(-0.3)^2 = 0.09

(0.7)^2 = 0.49

Add up those squares.

0.09+2.89+0.49+0.09+1.69+7.29+1.69+5.29+0.09+0.49 = 20.1

The sum of squares is 20.1

Next, we divide by n-1 = 10-1 = 9 to get the sample variance.

20.1/9 = 20.1/9 = 2.233333 approximately

Apply the square root to get the sample standard deviation.

sqrt(2.233333) = 1.494434 approximately

Rounding to the nearest hundredth, aka 2 decimal places, gets us the final answer 1.49

Once again, you can use a calculator to make all of this work happen in the background in one quick step. However, it still might be handy to see what's going on behind the scenes.

User Reddy SK
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