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ISEE Upper Level Math : How to find median

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Example Question #1 : How To Find Median

The following are the scores from a math test in a given classroom. What is the median score?

$\small \left \{ 70,89,67,77,92,83,68,75\right \}$

Possible Answers:

77.625

84.5

Correct answer:

Explanation:

To find the median you need to arrange the values in numerical order.

Starting with this:

Rearrange to look like this:

$\small \small \left \{ 67,68,70,75,77,83,89,92\right \}$

If there are an odd number of values, the median is the middle value. In this case there are 8 values so the median is the average (or mean) of the two middle values.

$\small (75+77)\div2=76$

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Example Question #1 : Median

The median of nine consecutive integers is 604. What is the greatest integer?

Possible Answers:

607

612

610

613

608

Correct answer:

608

Explanation:

The median of nine (an odd number) integers is the one in the middle when the numbers are arranged in ascending order; in this case, it is the fifth lowest. Since the nine integers are consecutive, the greatest integer is four more than the median, or 604 + 4 = 608 .

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Example Question #1 : How To Find Median

The median of consecutive integers in a set of data is . What is the smallest integer in the set of data?

Possible Answers:

Correct answer:

Explanation:

We know that the numbers should be arranged in ascending order to find the median. When the number of values is odd, the median is the single middle value. In this question we have consecutive integers with the median of . So the median is the 6th number in the rearranged data set. Since the integers are consecutive, the smallest integer is five less than the median or it is equal to 28-5=23 .

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Example Question #4 : How To Find Median

What is the median of the frequency distribution shown in the table:

$\begin{matrix} Data \ Value & Frequency \\ 12 & 4\\ 14& 7\\ 15& 3\\ 18& 2 \end{matrix}$

Possible Answers:

Correct answer:

Explanation:

There are 4+7+3+2=16 data values altogether. When the number of values is even, the median is the mean of the two middle values. So in this problem the median is the mean of the 8th and 9th largest values. So we can write:

$8th\ largest \ value=14$

$9th\ largest \ value=14$

So:

$Median=\frac{14+14}{2}=14$

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Example Question #5 : How To Find Median

Scores from a math test in a given classroom are as follows:

$\left \{ 80, 84, 86, 66, 57, 69, 92, 90 \right \}$

What is the median score?

Possible Answers:

Correct answer:

Explanation:

In order to find the median the data must first be ordered. So we have:

$\left \{ 57,66,69,80,84,86,90,92 \right \}$

In this problem the number of values is even. We know that when the number of values is even, the median is the mean of the two middle values. So we get:

$Median=\frac{80+84}{2}=82$

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Example Question #1 : How To Find Median

Heights of a group of students in a high school are as follows (heights are given in ):

$\left \{ 176,180,181,182,168,174,169,188,165 \right \}$

Find the median height.

Possible Answers:

180cm

174cm

178cm

176 cm

172cm

Correct answer:

176 cm

Explanation:

In order to find the median the data must first be ordered. So we have:

$\left \{ 165,168,169,174,176,180,181,182,188 \right \}$

When the number of values is odd, the median is the single middle value. In this problem we have nine values. So the median is th 5th value which is 176cm .

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Example Question #1 : How To Find Median

Find the median in the following set of data:

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

Possible Answers:

Correct answer:

Explanation:

In order to find the median, the data must first be ordered. So we should write:

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

When the number of values is even, the median is the mean of the two middle values. In this problem we have values, so the median would be the mean of the 5th and 6th values:

$Median=\frac{3+3}{2}=3$

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Example Question #8 : How To Find Median

If is a real number, find the median in the following set of data in terms of .

$\left \{ t,t+4,t+2,t+5,t+1,t+8 \right \}$

Possible Answers:

t+4

t+1

t+3

t-2

t+2

Correct answer:

t+3

Explanation:

The data should first be ordered:

$\left \{ t, t+1, t+2, t+4, t+5, t+8 \right \}$

When the number of values is even, the median is the mean of the two middle values. So in this problem we need to find the mean of the 3th and 4th values:

$Median=\frac{(t+2)+(t+4)}{2}=\frac{2t+6}{2}=t+3$

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Example Question #9 : How To Find Median

The heights of the members of a basketball team are 64,78,76,80,82,83,75,x inches. The mean of the heights is $78\ in$ . Give the median of the heights.

Possible Answers:

$80\ in$

$79\ in$

$83\ in$

$81\ in$

$82\ in$

Correct answer:

$79\ in$

Explanation:

The mean is the sum of the data values divided by the number of values or as a formula we have:

$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}$

Where:

$\bar{x}$ is the mean of a data set, $\sum$ indicates the sum of the data values $x_{i}$ and is the number of data values. So we can write:

$\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_{i}=\frac{(64+78+76+80+82+83+75+x)}{8}$

$\Rightarrow \bar{x}=\frac{538+x}{8}=78\Rightarrow 538+x=78\times 8$

$\Rightarrow 538+x=624\Rightarrow x=624-538=86\ in$

In order to find the median, the data must first be ordered:

$\left \{ 64,75,76,78,80,82,83,86 \right \}$

Since the number of values is even, the median is the mean of the two middle values. So we get:

$Median=\frac{78+80}{2}=79\ in$

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Example Question #10 : How To Find Median

Give the median of the frequency distribution shown in the following table:

$\begin{matrix} Data \ Value & Frequency \\ 120 & 7\\ 142& 3\\ 160& 4\\ 174& 6 \end{matrix}$

Possible Answers:

138

144

142

151

150

Correct answer:

151

Explanation:

There are 7+3+4+6=20 data values altogether. When the number of values is even, the median is the mean of the two middle values. So in this problem the median is the mean of the 10th and 11th largest values. So we can write:

$10th\ largest \ value=142$

$11th\ largest \ value=160$

So:

$Median=\frac{142+160}{2}=151$

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ISEE Upper Level Math : How to find median

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #1 : How To Find Median

Example Question #1 : Median

Example Question #1 : How To Find Median

Example Question #4 : How To Find Median

Example Question #5 : How To Find Median

Example Question #1 : How To Find Median

Example Question #1 : How To Find Median

Example Question #8 : How To Find Median

Example Question #9 : How To Find Median

Example Question #10 : How To Find Median

All ISEE Upper Level Math Resources

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