# Calculating standard deviation.

#### allsmiles An example of the calculation for the population standard deviation of a set of data is shown. Approximate the population standard deviation for the set { 4 , 5 , 7 , 5 , 6 , 3}, to the nearest tenth.

1.3 is it the Correct Answer
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#### harish21 An example of the calculation for the population standard deviation of a set of data is shown. Approximate the population standard deviation for the set { 4 , 5 , 7 , 5 , 6 , 3}, to the nearest tenth.

1.3 is it the Correct Answer
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1.3 is correct An example of the calculation for the population standard deviation of a set of data is shown. Approximate the population standard deviation for the set { 4 , 5 , 7 , 5 , 6 , 3}, to the nearest tenth.

1.3 is it the Correct Answer
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Hi allsmiles,

just follow the procedure as detailed.

1. Calculate the mean of the six numbers.
2. Calculate the deviations of the six numbers from the mean.
3. Square all the deviations
4. Sum all the squares of the deviations
5. Find the average square by dividing by 6
6. Take the square root

$$\displaystyle \mu=\frac{4+5+7+5+6+3}{6}=\frac{30}{6}=5$$

The deviations are 4-5, 5-5, 7-5, 5-5, 6-5, 3-5

Hence, square these, find the average of the squares and take the square root.

I get $$\displaystyle \sqrt{1.67}=1.2922$$, then just round it off, but go through the workings.

#### masters

MHF Helper An example of the calculation for the population standard deviation of a set of data is shown. Approximate the population standard deviation for the set { 4 , 5 , 7 , 5 , 6 , 3}, to the nearest tenth.

1.3 is it the Correct Answer
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Hi allsmiles,

$$\displaystyle \mu=5$$

From the table, you can conclude:

$$\displaystyle \sigma=\sqrt{\frac{10}{6}}\approx 1.3$$