GMAT Math : Descriptive Statistics

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Example Question #3 : Mode

Determine the mode for the following set of numbers.

{6,2,5,5,8,4}

Possible Answers:

$\textup{None of the other answers is correct.}$

$\textup{All of the numerical answers provided are correct.}$

Correct answer:

Explanation:

The mode is the most frequent number, thus our answer is .

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Example Question #4 : Mode

Find the mode of the following set of numbers:

$\textup{4,6,7,7,8,10,28}$

Possible Answers:

Correct answer:

Explanation:

The mode is the most frequent number, thus the answer is .

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Example Question #10 : Calculating Mode

A = B > C > D > E

Give the mode of the set $\left \{ A, B, C, D, E \right \}$ .

Possible Answers:

$\frac{A + E }{2}$

$\frac{A +B+ C+D+E }{5}$

The set has no mode.

Correct answer:

Explanation:

The mode of a set, if it exists, is the value that occurs most frequently. The inequality

A = B > C > D > E

means that the set

$\left \{ A, B, C, D, E \right \}$

can be rewritten as

$\left \{ A,A, C, D, E \right \}$ .

The most frequently occurring value is , making this the mode.

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Example Question #101 : Descriptive Statistics

Find the mode of the following set of numbers.

$\textup{1,1,2,7,8,10,11}$

Possible Answers:

Correct answer:

Explanation:

The mode is the most frequent number. Thus, our answer is .

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Example Question #102 : Descriptive Statistics

A = B > C > D = E > F .

Give the mode of the set $\left \{ A, B, C, D, E,F\right \}$ .

Possible Answers:

$\textup{The set has no mode.}$

$\frac{C+D}{2}$

$A\textup{ and }D\textup{ are both modes.}$

$\frac{A +B+ C+D+E+F }{6}$

$\frac{A+F}{2}$

Correct answer:

$A\textup{ and }D\textup{ are both modes.}$

Explanation:

The mode of a set, if it exists, is the value that occurs most frequently. The inequality

A = B > C > D = E > F

means that the set

$\left \{ A, B, C, D, E,F\right \}$

can be rewritten as

$\left \{ A, A, C, D,D,F\right \}$

and occur as values twice each; the other values, and , are unique. Therefore, the set has two modes, and .

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Example Question #103 : Descriptive Statistics

A = B < C= D

Which of these values is not a mode of the set $\left\{ A, B, C, D \right \}$ ?

Possible Answers:

$\textup{None of the other choices is correct.}$

Correct answer:

$\textup{None of the other choices is correct.}$

Explanation:

The mode of a set is the value that occurs most frequently in that set. Since

A = B < C= D , it follows that

$\left\{ A, B, C, D \right \}$

can be rewritten as

$\left\{ A, A, C, C \right \}$ .

This makes and both modes, since both occur twice. Equivalently, since A = B and C= D , and are modes.

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Example Question #104 : Descriptive Statistics

True or false: is the arithmetic mean of the set $S = \left \{ A, B, C, D, E \right \}$ .

Statement 1: A < B < C < D< E

Statement 2: is the arithmetic mean of and .

Possible Answers:

EITHER STATEMENT ALONE provides sufficient information to answer the question.

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.

STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.

STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.

Correct answer:

BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.

Explanation:

Assume both statements to be true, and examine two cases.

Case 1: A = 1, B = 2, C = 3, D= 4, E= 5

$\mu = \frac{A+B+C+D+E}{5} = \frac{1+2+3+4+5}{5} = \frac{15}{5} = 3 = C$

A < B < C < D< E

The arithmetic mean of and is

$\frac{A+ E}{2} = \frac{1+5}{2} = \frac{6}{2} = 3 = C$

The conditions of both statements are satisfied.

The mean of the five numbers is their sum divided by 5:

$\mu = \frac{A+B+C+D+E}{5} = \frac{1+2+3+4+5}{5} = \frac{15}{5} = 3 = C$

Case 2: A = 0, B = 2, C = 3, D= 5, E= 6

A < B < C < D< E

The arithmetic mean of and is

$\frac{A+ E}{2} = \frac{0+6}{2} = \frac{6}{2} = 3 = C$

The conditions of both statements are satisfied.

But the mean of the five numbers is

$\mu = \frac{A+B+C+D+E}{5} = \frac{0+2+3+5+6}{5} = \frac{16}{5} = 3.2 \ne C$

Therefore, the mean may or may not be equal to .

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GMAT Math : Descriptive Statistics

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #3 : Mode

Example Question #4 : Mode

Example Question #10 : Calculating Mode

Example Question #101 : Descriptive Statistics

Example Question #102 : Descriptive Statistics

Example Question #103 : Descriptive Statistics

Example Question #104 : Descriptive Statistics

All GMAT Math Resources

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