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GRE Subject Test: Math : Standard Deviation

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Example Questions

Example Question #531 : Gre Subject Test: Math

What is the standard deviation of the numbers 3, 5, 8, 9, and 10?

Possible Answers:

5.14 $\displaystyle 5.14$

6.8 $\displaystyle 6.8$

3.49 $\displaystyle 3.49$

2.61 $\displaystyle 2.61$

6.3 $\displaystyle 6.3$

Correct answer:

2.61 $\displaystyle 2.61$

Explanation:

The first step with standard deviation is to find the average or mean of the numbers. Add 3+5+8+9+10 together to get 35. Divide that by the number of scores, which is 5, to get a mean of 7.

Now, subtract the mean from each of the numbers

$\\3-7=-4 \\5-7=-2 \\8-7=1 \\9-7=2 \\10-7=3$ $\displaystyle \\3-7=-4 \\5-7=-2 \\8-7=1 \\9-7=2 \\10-7=3$

Next, square those values

$(-4)^{2}=16$ $\displaystyle (-4)^{2}=16$

$(-2)^{2}=4$ $\displaystyle (-2)^{2}=4$

$1^{2}=1$ $\displaystyle 1^{2}=1$

$2^{2}=4$ $\displaystyle 2^{2}=4$

$3^{2}=9$ $\displaystyle 3^{2}=9$

Now find the mean of these squared differences by adding the values and then dividing by the amount of numbers, 5 in this case.

$\displaystyle 16+4+1+4+9=34$

$\frac{34}{5}=6.8$ $\displaystyle \frac{34}{5}=6.8$

Finally, take the square root of this number to get the standard deviation.

$\sqrt{6.8$ $\displaystyle \sqrt{6.8$ =2.61 $\displaystyle =2.61$

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GRE Subject Test: Math : Standard Deviation

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Example Question #531 : Gre Subject Test: Math

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