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GRE Subject Test: Math : Variance

Study concepts, example questions & explanations for GRE Subject Test: Math

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Example Questions

Example Question #33 : Other Topics

Find the variance of the scores 18, 4, 9, 6, 11, and 20.

Possible Answers:

41.78 $\displaystyle 41.78$

34.56 $\displaystyle 34.56$

28.33 $\displaystyle 28.33$

43.09 $\displaystyle 43.09$

35.91 $\displaystyle 35.91$

Correct answer:

34.56 $\displaystyle 34.56$

Explanation:

First find the mean of the scores by adding them up and dividing by the number of scores.

$\displaystyle 18+4+9+6+11+20=68$

$\frac{68}{7}=11.33$ $\displaystyle \frac{68}{7}=11.33$

Subtract the mean of 11.33 from each of the scores.

$\displaystyle 18-11.33=6.67$

$\displaystyle 4-11.33=-7.33$

$\displaystyle 9-11.33=-2.33$

$\displaystyle 6-11.33=-5.33$

$\displaystyle 11-11.33=-0.33$

$\displaystyle 20-11.33=8.67$

Now, square the results.

$6.67^{2}=44.49$ $\displaystyle 6.67^{2}=44.49$

$(-7.33)^{2}=53.73$ $\displaystyle (-7.33)^{2}=53.73$

$(-2.33)^{2}=5.43$ $\displaystyle (-2.33)^{2}=5.43$

$(-5.33)^{2}=28.41$ $\displaystyle (-5.33)^{2}=28.41$

$(-0.33)^{2}=0.11$ $\displaystyle (-0.33)^{2}=0.11$

$8.67^{2}=75.17$ $\displaystyle 8.67^{2}=75.17$

Now we need the average of these values to get the variance. First, add up these values.

$\displaystyle 44.49+53.73+5.43+28.41+0.11+75.17=207.34$

Now divide by 6 which is the number of scores.

$\frac{207.34}{6}=34.56$ $\displaystyle \frac{207.34}{6}=34.56$

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Example Question #1 : Variance

$What\ is\ the\ standard\ deviation\ for\ a\ set\ of\ data\ with\ a\ variance\ of\ 16?$ $\displaystyle What\ is\ the\ standard\ deviation\ for\ a\ set\ of\ data\ with\ a\ variance\ of\ 16?$

Possible Answers:

256 $\displaystyle 256$

$\displaystyle 16$

$\displaystyle 4$

$\displaystyle 8$

Correct answer:

$\displaystyle 4$

Explanation:

$The\ relationship\ between\ standard\ deviation\ and\ variance\ is\ listed\ below:$ $\displaystyle The\ relationship\ between\ standard\ deviation\ and\ variance\ is\ listed\ below:$

$(standard\ deviation)^2=variance$ $\displaystyle (standard\ deviation)^2=variance$

$standard\ deviation=\sqrt{variance}$ $\displaystyle standard\ deviation=\sqrt{variance}$

$In\ this\ question\ variance=16$ $\displaystyle In\ this\ question\ variance=16$

$This\ means\ that\ standard\ deviation=\sqrt{16}=4$ $\displaystyle This\ means\ that\ standard\ deviation=\sqrt{16}=4$

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GRE Subject Test: Math : Variance

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #33 : Other Topics

Example Question #1 : Variance

All GRE Subject Test: Math Resources

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