GMAT Math : Descriptive Statistics

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Example Questions

Example Question #1 : Arithmetic Mean

The average of 10, 25, and 70 is 10 more than the average of 15, 30, and x. What is the missing number?

Possible Answers:

$15$ $\displaystyle 15$

$35$ $\displaystyle 35$

$20$ $\displaystyle 20$

$30$ $\displaystyle 30$

$25$ $\displaystyle 25$

Correct answer:

$30$ $\displaystyle 30$

Explanation:

The average of 10, 25, and 70 is 35: $\frac{10+25+70}{3}=35$ $\displaystyle \frac{10+25+70}{3}=35$

So the average of 15, 30, and the unknown number is 25 or, 10 less than the average of 10, 25, and 70 (= 35)

so $\frac{15+30+x}{3}=25$ $\displaystyle \frac{15+30+x}{3}=25$

$15+30+x=75$ $\displaystyle 15+30+x=75$

$45+x=75$ $\displaystyle 45+x=75$

$x=30$ $\displaystyle x=30$

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Example Question #5 : Arithmetic Mean

What is the average of 2x, 3x + 2, and 7x +4?

Possible Answers:

4x + 2

not enough information

3x + 4

Correct answer:

4x + 2

Explanation:

$average = \frac{sum}{terms} = \frac{2x + 3x + 2 + 7x + 4}{3} = \frac{12x + 6}{3} = 4x +2$ $\displaystyle average = \frac{sum}{terms} = \frac{2x + 3x + 2 + 7x + 4}{3} = \frac{12x + 6}{3} = 4x +2$

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Example Question #2 : Arithmetic Mean

The average high temperature for the week is 85. The first six days of the week have high temperatures of 89, 76, 92, 90, 80, and 84, respectively. What is the high temperature on the seventh day of the week?

Possible Answers:

$\displaystyle 86$

$\displaystyle 85$

$\displaystyle 83$

$\displaystyle 84$

$\displaystyle 82$

Correct answer:

$\displaystyle 84$

Explanation:

$average = \frac{sum}{days}$ $\displaystyle average = \frac{sum}{days}$

$85=\frac{89+76+92+90+80+84+x}{7}=\frac{511+x}{7}$ $\displaystyle 85=\frac{89+76+92+90+80+84+x}{7}=\frac{511+x}{7}$

$\displaystyle 595=511+x$

x=84 $\displaystyle x=84$

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Example Question #6 : Arithmetic Mean

Jimmy's grade in his finance class is based on six equally-weighted tests. If Jimmy scored 98, 64, 82, 90, 70, and 88 on the six tests, what was his grade in the class?

Possible Answers:

$\displaystyle 82$

$\displaystyle 80$

$\displaystyle 86$

$\displaystyle 88$

$\displaystyle 84$

Correct answer:

$\displaystyle 82$

Explanation:

$avg=\frac{98+64+82+90+70+88}{6}=\frac{492}{6}=82$ $\displaystyle avg=\frac{98+64+82+90+70+88}{6}=\frac{492}{6}=82$

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Example Question #21 : Descriptive Statistics

Sandra's grade in economics depends on seven tests - five hourly tests, a midterm, and a final exam. The midterm counts twice as much as an hourly test; the final, three times as much.

Sandra's grades on the five hourly tests are 84, 86, 76, 89, and 93; her grade on the midterm was 72. What score out of 100 must she achieve on the final exam so that her average score at the end of the term is at least 80?

Possible Answers:

$\displaystyle 80$

$\displaystyle 84$

$\displaystyle 76$

She cannot achieve this average this term

$\displaystyle 92$

Correct answer:

$\displaystyle 76$

Explanation:

This is a weighted mean, with the hourly tests assigned a weight of 1, the midterm assigned a weight of 2, and the final assigned a weight of 3. The total of the weights will be

$\displaystyle 5 (1) + 2 + 3 = 10$.

If we let $\displaystyle N$ be Sandra's final exam score, Sandra's final weighted average will be

$\small \frac{84 + 86 + 76+ 89+ 93 + 72 \cdot 2 + N \cdot 3}{10}$ $\displaystyle \small \frac{84 + 86 + 76+ 89+ 93 + 72 \cdot 2 + N \cdot 3}{10}$

$\small = \frac{84 + 86 + 76+ 89+ 93 + 144 + 3N}{10}$ $\displaystyle \small = \frac{84 + 86 + 76+ 89+ 93 + 144 + 3N}{10}$

$\small = \frac{572 + 3N}{10}$ $\displaystyle \small = \frac{572 + 3N}{10}$

For Sandra to get a final average of 80, then we set the above equal to 80 and calculate $\displaystyle N$:

$\small \frac{572 + 3N}{10} = 80$ $\displaystyle \small \frac{572 + 3N}{10} = 80$

$\small 572 + 3N = 800$ $\displaystyle \small 572 + 3N = 800$

$\small 3N = 228$ $\displaystyle \small 3N = 228$

$\small N = 76$ $\displaystyle \small N = 76$

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Example Question #2031 : Problem Solving Questions

Consider the following set of numbers:

85, 87, 87, 82, 89

What is the mean?

Possible Answers:

$\displaystyle 87$

$\displaystyle 82$

$\displaystyle 86$

$\displaystyle 85$

Correct answer:

$\displaystyle 86$

Explanation:

$mean=\frac{85+87+87+82+89}{5}=86$ $\displaystyle mean=\frac{85+87+87+82+89}{5}=86$

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Example Question #481 : Arithmetic

Consider the following set of numbers:

85, 87, 87, 82, 89

What is the median?

Possible Answers:

$\displaystyle 85$

$\displaystyle 87$

$\displaystyle 82$

$\displaystyle 86$

Correct answer:

$\displaystyle 87$

Explanation:

Reorder the values in numerical order:82, 85, 87, 87, 89

The median is the center number, 87.

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Example Question #22 : Descriptive Statistics

$\displaystyle 28,30,31,35,41$

Find the mean of the sample data set.

Possible Answers:

$\displaystyle 30$

$\displaystyle 31$

$\displaystyle 32$

$\displaystyle 34$

$\displaystyle 33$

Correct answer:

$\displaystyle 33$

Explanation:

The mean of a sample data set is the sum of all of the values divided by the total number of values. In this case:

$\frac{28+30+31+35+41}{5}=\frac{165}{5}=33$ $\displaystyle \frac{28+30+31+35+41}{5}=\frac{165}{5}=33$

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Example Question #23 : Descriptive Statistics

The average of the following 6 digits is 75. What is a possible value of $\displaystyle x$?

80, 78, 78, 70, 71, $\displaystyle x$

Possible Answers:

$\displaystyle 73$

$\displaystyle 76$

$\displaystyle 74$

$\displaystyle 75$

Correct answer:

$\displaystyle 73$

Explanation:

$\displaystyle (75)(6)=450$

Therefore, the sum of all 6 digits must equal 450.

$\displaystyle 450=80+78+78+70+71+x$

$\displaystyle 450=377+x$

Subtract 377 from both sides.

x=73 $\displaystyle x=73$

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Example Question #484 : Arithmetic

When assigning a score for the term, a professor takes the mean of all of a student's test scores except for his or her lowest score.

On the first five exams, Donna has achieved the following scores: 76, 84, 80, 65, 91. There is one more exam in the course. Assuming that 100 is the maximum possible score, what is the range of possible final averages she can achieve (nearest tenth, if applicable)?

Possible Answers:

Minimum 66; maximum 99.2

Minimum 79.2; maximum 86.2

Minimum 66; maximum 71.8

Minimum 80, maximum 84

Minimum 79.2; maximum 99.2

Correct answer:

Minimum 79.2; maximum 86.2

Explanation:

The worst-case scenario is that she will score 65 or less, in which case her score will be the mean of the scores she has already achieved.

$\frac{76+ 84+80+65+ 91}{5} = 79.2$ $\displaystyle \frac{76+ 84+80+65+ 91}{5} = 79.2$

The best-case scenario is that she will score 100, in which case the 65 will be dropped and her score will be the mean of the other five scores.

$\frac{76+ 84+80+ 91+100}{5} = 86.2$ $\displaystyle \frac{76+ 84+80+ 91+100}{5} = 86.2$

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GMAT Math : Descriptive Statistics

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #1 : Arithmetic Mean

Example Question #5 : Arithmetic Mean

Example Question #2 : Arithmetic Mean

Example Question #6 : Arithmetic Mean

Example Question #21 : Descriptive Statistics

Example Question #2031 : Problem Solving Questions

Example Question #481 : Arithmetic

Example Question #22 : Descriptive Statistics

Example Question #23 : Descriptive Statistics

Example Question #484 : Arithmetic

All GMAT Math Resources

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