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ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

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

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All ISEE Upper Level Quantitative Resources

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Example Questions

Example Question #571 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

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

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.

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 #13 : How To Find Median

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:

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 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 #14 : How To Find Median

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:

The mean of the set is greater than the median 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.

The median of the set is greater than the mean 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 #15 : How To Find Median

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:

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 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 #571 : 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 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.

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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Example Question #17 : How To Find Median

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

$\left \{ 15,28,14,11,10,5 \right \}$

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:

If there are an even number of values, the median is the average of the two middle values of a set of data. In this question in order to find the median we should first put the numbers in order:

$\left \{ 5,10,11,14,15,28 \right \}$

So the median is:

$Median=\frac{11+14}{2}=\frac{25}{2}=12.5$

The 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:

$Mean = \frac{5+10+11+14+15+28}{6}=\frac{83}{6}\approx 13.83$

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

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Example Question #18 : How To Find Median

In the following set of data the mean is . Find the median.

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

Possible Answers:

Correct answer:

Explanation:

First we need to find . We know that the mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

$Mean = \frac{2+4+N+8+10}{5}=\frac{24+N}{5}=10$

$\Rightarrow 24+N=50\Rightarrow N=50-24=26$

Now we have:

$\left \{ 2,4,26,8,10 \right \}$

If there are an odd number of values in a data set, the median is the middle value. First we need to put the numbers in order:

$\left \{ 2,4,8,10,26 \right \}$

So the median is .

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Example Question #16 : How To Find Median

In the following set of data the mean and the mode are equal. Find the median.

$\left \{ 1,3,3,3,N,4,8 \right \}$

Possible Answers:

Correct answer:

Explanation:

The mode of a set of data is the value which occurs most frequently which is in this problem (it is not dependent on in this problem). So the mean is also equal to .

We know that the mean of a set of data is given by the sum of the data, divided by the total number of values in the set. So we can write:

$Mean = \frac{1+3+3+3+N+4+8}{7}=\frac{22+N}{7}=3$

$\Rightarrow 22+N=21\Rightarrow N=21-22=-1$

So we have:

$\left \{ 1,3,3,3,-1,4,8 \right \}$

If there are an odd number of values in a data set, the median is the middle value. First we need to put the numbers in order:

$\left \{ -1,1,3,3,3,4,8 \right \}$

So the median is also .

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Example Question #91 : Data Analysis

Give the median of this data set:

20, 23, 25, 26, 28, 33, 100

Round to the nearest tenth, if applicable.

Possible Answers:

36.4

The data set has no median.

Correct answer:

Explanation:

The seven elements are already arranged in ascending order, so we need to look at the value occurring in the middle - that is, the fourth position. This element is 26.

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

A data set has six known quantities and two unknown positive quantities, as follows:

$\left \{ 15, 25, 25, 35, 35, 40, M, N \right \}$

It is known, however, that M + N = 70

Which is the greater quantity?

(A) The mean of the data set

(B) The median of the data set

Possible Answers:

(A) and (B) are equal

It is impossible to determine which is greater from the information given

(A) is greater

(B) is greater

Correct answer:

It is impossible to determine which is greater from the information given

Explanation:

If M + N = 70 , then the mean of the data set is the sum of the eight elements divided by eight:

$\left ( 15 + 25+ 25+ 35+ 35+40+ M + N \right ) \div 8$

$=\left ( 175+ 70 \right ) \div 8 = 245\div 8 = 30.625$

The median of the data set, however, depends on the values of and , as can be demonstrated using two cases.

Case 1: M = N = 35

The data set is then

$\left \{ 15, 25, 25, 35, 35, 35, 35, 40 \right \}$

and the median is the mean of the two middle values. Since both middle values are 35, the median is 35.

Case 2: M = 15 and N = 55

The data set is then

$\left \{ 15,15, 25, 25, 35, 35, 40,55 \right \}$

and the median is the mean of the two middle values. They are 25 and 35, so the median is $\left (25+35 \right ) \div 2 = 30$

In the first case, the median is greater than the mean; in the second case, the mean is greater than the median. Therefore, the information is insufficient.

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All ISEE Upper Level Quantitative Resources

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ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning

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

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #571 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #13 : How To Find Median

Example Question #14 : How To Find Median

Example Question #15 : How To Find Median

Example Question #571 : Isee Upper Level (Grades 9 12) Quantitative Reasoning

Example Question #17 : How To Find Median

Example Question #18 : How To Find Median

Example Question #16 : How To Find Median

Example Question #91 : Data Analysis

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

All ISEE Upper Level Quantitative Resources

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