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GRE Subject Test: Math : Probability & Statistics

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

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All GRE Subject Test: Math Resources

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Example Questions

Example Question #31 : Probability & Statistics

What is the mean of: $\{2,4,6,0,3,11\}$ ?

Possible Answers:

$4. \overline {33}$

4.33

4.4

4.3

Correct answer:

$4. \overline {33}$

Explanation:

Find the sum of all the numbers in the set:

2+4+6+0+3+11=26
Count how many numbers are in the set...

There are six numbers...

Divide the sum of the set by how many numbers to find the mean...

$\frac {26}{6}=4.\overline {33}$

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Example Question #32 : Probability & Statistics

What is the mean of

$\{1,2,3,4,5,6,7,8,9\}$ ?

Possible Answers:

5.5

None

5.25

$5.\overline {5}$

Correct answer:

Explanation:

Find the sum of all the numbers in the set:

$\large 1+2+3+4+5+6+7+8+9=45$

Count how many numbers are in the set...

There are $\large 9$ numbers..

To find the mean, divide the sum by how many numbers...

$\large \frac {45}{9}=5$

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Example Question #33 : Probability & Statistics

What is the mean of: $\{2,3,5,7,11,13,17,19,23,29,31,37,41,43\}$ ?

Possible Answers:

20.0714

$20 \frac{1}{7}$

$20 \frac{1}{14}$

Correct answer:

$20 \frac{1}{14}$

Explanation:

Step 1: To find the mean, we need to first find the sum of the numbers in the set.

$2+3+5+7+11+13+17+\\19+23+29+31+37+41+43=281$

Step 2: Count how many numbers are in the set...

There are numbers in the set.

Step 3: To find the mean, divide the sum of the numbers in the set by how many numbers there are in the set...

$\frac {281}{14}=20\frac {1}{14}\approx 20.07\overline{142857}$

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Example Question #533 : Gre Subject Test: Math

The average test score was an , the scores were as followed 98,75,88,84,91 , and . Find

Possible Answers:

Correct answer:

Explanation:

Use the mean equation:

$\frac{(x_1+x_2+x_3+x_4+x_5+x_6)}{6} = Average$

Enter in the numbers

$\frac{(98+75+88+84+91+x)}{6} = 87$

Simplify

$\frac{436+x}{6} = 87$

Multiply each side by

436+x = 522

Subtract 436 from both sides

x=86

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Example Question #1 : Variance

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

Possible Answers:

43.09

34.56

35.91

41.78

28.33

Correct answer:

34.56

Explanation:

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

18+4+9+6+11+20=68

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

Subtract the mean of 11.33 from each of the scores.

18-11.33=6.67

4-11.33=-7.33

9-11.33=-2.33

6-11.33=-5.33

11-11.33=-0.33

20-11.33=8.67

Now, square the results.

$6.67^{2}=44.49$

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

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

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

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

$8.67^{2}=75.17$

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

44.49+53.73+5.43+28.41+0.11+75.17=207.34

Now divide by 6 which is the number of scores.

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

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Example Question #2 : Variance

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

Possible Answers:

256

Correct answer:

Explanation:

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

$(standard\ deviation)^2=variance$

$standard\ deviation=\sqrt{variance}$

$In\ this\ question\ variance=16$

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

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Example Question #31 : Statistics

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

Possible Answers:

5.14

3.49

6.8

6.3

2.61

Correct answer:

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

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

Next, square those values

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

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

$1^{2}=1$

$2^{2}=4$

$3^{2}=9$

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

16+4+1+4+9=34

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

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

$\sqrt{6.8$ =2.61

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Example Question #31 : Statistics

What is the range of the set of numbers: 7,6,4,3,5,2,5,7,5,23,111,88,26 ?

Possible Answers:

113

109

115

102

Correct answer:

109

Explanation:

Step 1: Arrange the numbers in the set from smallest to largest:

After we arrange, we get: 2,3,4,6,6,6,7,8,8,23,26,88,111 .

Step 2: To find the range, subtract the largest number from the smallest number.

Range=111-2=109

The range of the data set is 109 .

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Example Question #32 : Statistics

What is the range of the numbers: 2,3,7,9,14,11,100,99,62

Possible Answers:

100

Correct answer:

Explanation:

Step 1: Re-write all numbers in order from smallest to largest

2,3,7,9,11,14,62,99,100 .

Step 2: Subtract the largest number and smallest number

100-2=98

The range is .

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Example Question #33 : Probability & Statistics

What is the range of the set: { 2,4,6,5,7,9,11,31,13,-2 }

Possible Answers:

Correct answer:

Explanation:

Step 1: Arrange the numbers from smallest to largest:

We get: -2,2,4,5,6,7,9,11,13,31

Step 2: Find the range.. To find this, subtract the biggest number from the smallest number

Range=31-(-2)=31+2=33

The range is

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GRE Subject Test: Math : Probability & Statistics

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

All GRE Subject Test: Math Resources

Example Questions

Example Question #31 : Probability & Statistics

Example Question #32 : Probability & Statistics

Example Question #33 : Probability & Statistics

Example Question #533 : Gre Subject Test: Math

Example Question #1 : Variance

Example Question #2 : Variance

Example Question #31 : Statistics

Example Question #31 : Statistics

Example Question #32 : Statistics

Example Question #33 : Probability & Statistics

All GRE Subject Test: Math Resources

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