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ISEE Upper Level Quantitative : Data Analysis

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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All ISEE Upper Level Quantitative Resources

8 Diagnostic Tests 234 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #564 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

A data set has twelve elements; the mean and the median of the set are both 50.

A new data set is formed by increasing each element by 5. Which is the greater quantity?

(a) The mean of the new data set

(b) The median of the new data set

Possible Answers:

It is impossible to tell from the information given

(b) is greater

(a) is greater

(a) and (b) are equal

Correct answer:

(a) and (b) are equal

Explanation:

(a) Since each element of the old set is increased by 5, the sum of the elements is increased by $5 \times 12 = 60$ . This increases the mean by $60 \div 12 = 5$ , to 55.

(b) The median of the old set is the mean of the sixth- and seventh-highest elements. Since each element of the old set is increased by 5, these elements remain the sixth- and seventh-highest elements; their sum is increased by 10, and their mean is increased by 5, to 55.

The mean and the median of the new set are equal.

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Example Question #1 : How To Find Median

Which is the greater quantity?

(a) The median of the data set $\left \{ \frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6} \right \}$

(b) $\frac{3}{4}$

Possible Answers:

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

Correct answer:

(a) and (b) are equal

Explanation:

The median of a data set with five elements is its third-greatest element, which here is $\frac{3}{4}$ .

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Example Question #1 : Median

Which is the greater quantity?

(a) The median of the data set $\left \{ 1, \frac{1}{2}, \frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6}, \frac{1}{7}\right \}$

(b) $\frac{1}{4}$

Possible Answers:

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

(a) is greater

Correct answer:

(a) and (b) are equal

Explanation:

The median of a data set with seven elements is its fourth-greatest element, which here is $\frac{1}{4}$ .

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Example Question #1 : How To Find Median

A data set has nine elements. Four of the elements are greater than 50; four are less than 50.

Which is the greater quantity?

(a) The median of the data set

(b) 50

Possible Answers:

(b) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

(a) is greater.

Correct answer:

(a) and (b) are equal.

Explanation:

If four of the elements are greater than 50 and four are less than 50, then the fifth-highest element, which is the median of a nine-element set, must be 50.

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Example Question #11 : Median

Consider the data set $\left \{ -1, 2, -3, 4, -5, 6, -7\right \}$

Which is the greater quantity?

(a) The median of the data set

(b) The mean of the data set

Possible Answers:

(b) is greater

It is impossible to tell from the information given

(a) and (b) are equal

(a) is greater

Correct answer:

(b) is greater

Explanation:

(a) Arrange the elements in ascending order:

$\left \{ -7, -5, -3, -1, 2,4,6 \right \}$

The median is the middle element, which is .

(b) Add the elements and divide by 7:

$[ (-7) + (-5) + (-3) + (-1) + 2 + 4 + 6 ] \div 7 = -4 \div 7 = - \frac{4}{7}$

$- \frac{4}{7} > -1$ , so the mean is greater.

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Example Question #11 : How To Find Median

In the following set of numbers compare the mean and the median of the set:

$\left \{ 7,3,2,-1,14 \right \}$

Possible Answers:

The mean of the set is greater than the median of the set.

It is not possible to tell from the information given

The median of the set is greater than the mean of the set.

The mean of the set is equal to the median of the set.

Correct answer:

The mean of the set is greater than the median of the set.

Explanation:

The median is the middle value of a set of data containing an odd number of values. In this question in order to find the median we should first put the numbers in order:

$\left \{ -1,2,3,7,14 \right \}$

So the median is .

Mean of a data set $x_{1},x_{2}, ..., x_{n}$ is the sum of the data set values divided by the number of data:

$Mean=\frac{x_{1}+x_{2}+...+x_{n}}{n}$

So we have:

$Mean = \frac{-1+2+3+7+14}{5}=\frac{25}{5}=5$

So the mean of the set is greater than the median of that.

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Example Question #572 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

In the following set of numbers compare the mean and the median of the set:

$\left \{ 28,25,31,34,37,43,40 \right \}$

Possible Answers:

The mean of the set is equal to the median of the set.

It is not possible to tell from the information given

The median of the set is greater than the mean of the set.

The mean of the set is greater than the median of the set.

Correct answer:

The mean of the set is equal to the median of the set.

Explanation:

The median is the middle value of a set of data containing an odd number of values. In this question in order to find the median we should first put the numbers in order:

$\left \{ 25,28,31,34,37,40,43 \right \}$

So the median is .

Mean of a data set $x_{1},x_{2}, ..., x_{n}$ is the sum of the data set values divided by the number of data:

$Mean=\frac{x_{1}+x_{2}+...+x_{n}}{n}$

So the mean of the set is equal to the median of the set.

$Mean = \frac{25+28+31+34+37+40+43}{7}=\frac{238}{7}=34$

So the mean of the set is greater than the median of that.

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Example Question #573 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Consider the following set of data:

$\left \{ 0,0.0001,0.001,0.01,0.1 \right \}$

$A=Median\ of\ the\ set$

$B=Mean\ of\ the\ set$

Compare and

Possible Answers:

It is not possible to tell from the information given.

The median of the set is greater than the mean of the set.

The mean of the set is equal to the median of the set.

The mean of the set is greater than the median of the set.

Correct answer:

The mean of the set is greater than the median of the set.

Explanation:

The median is the middle value of a set of data containing an odd number of values. In this question in order to find the median we should first put the numbers in order:

$\left \{ 0, 0.1, 0.01, 0.001, 0.0001 \right \}$

So the median is 0.01 .

Mean of a data set $x_{1},x_{2}, ..., x_{n}$ is the sum of the data set values divided by the number of data:

$Mean=\frac{x_{1}+x_{2}+...+x_{n}}{n}$

So the mean of the set is equal to the median of the set.

$Mean = \frac{0+0.1+0.01+0.001+0.0001}{5}=\frac{0.1111}{5}=0.02222\approx 0.02$

So the mean of the set is greater than the median of that.

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Example Question #574 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

In the following set of numbers compare the mean and the median of the set:

$\left \{ 1,3,4,115,120,185,224 \right \}$

Possible Answers:

It is not possible to tell from the information given.

The mean of the set is equal to the median of the set.

The mean of the set is greater than the median of the set.

The median of the set is greater than the mean of the set.

Correct answer:

The median of the set is greater than the mean of the set.

Explanation:

The median is the middle value of a set of data containing an odd number of values which is 115 in this problem.

Mean of a data set $x_{1},x_{2}, ..., x_{n}$ is the sum of the data set values divided by the number of data:

$Mean=\frac{x_{1}+x_{2}+...+x_{n}}{n}$

So the mean of the set is equal to the median of the set.

$Mean = \frac{1+3+4+115+120+185+224}{7}=\frac{652}{7}\approx 93.14$

So the median of the set is greater than the mean of that.

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Example Question #575 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

In the following set of numbers compare the mean and the median of the set:

$\left \{ 1,2,4,8,10 \right \}$

Possible Answers:

The mean of the set is greater than the median of the set.

The median of the set is greater than the mean of the set.

The mean of the set is equal to the median of the set.

It is not possible to tell from the information given

Correct answer:

The mean of the set is greater than the median of the set.

Explanation:

The median is the middle value of a set of data containing an odd number of values which is in this set of numbers.

Mean of a data set $x_{1},x_{2}, ..., x_{n}$ is the sum of the data set values divided by the number of data:

$Mean=\frac{x_{1}+x_{2}+...+x_{n}}{n}$

So we have:

$Mean = \frac{1+2+4+8+10}{5}=\frac{25}{5}=5$

So the mean of the set is greater than the median of the set.

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ISEE Upper Level Quantitative : Data Analysis

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #564 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #1 : How To Find Median

Example Question #1 : Median

Example Question #1 : How To Find Median

Example Question #11 : Median

Example Question #11 : How To Find Median

Example Question #572 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #573 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #574 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #575 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

All ISEE Upper Level Quantitative Resources

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