# ISEE Upper Level Math : How to find median

## Example Questions

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### Example Question #21 : Data Analysis And Probability

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

Explanation:

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

Starting with this:

Rearrange to look like this:

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.

### Example Question #1 : How To Find Median

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

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 .

### 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?

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 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 .

### Example Question #22 : Data Analysis And Probability

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

Explanation:

There are 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 and largest values. So we can write:

So:

### Example Question #5 : Median

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

What is the median score?

Explanation:

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

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:

### Example Question #2 : Median

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

Find the median height.

Explanation:

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

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 value which is .

### Example Question #7 : Median

Find the median in the following set of data:

Explanation:

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

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 and values:

### Example Question #8 : Median

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

Explanation:

The data should first be ordered:

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 and values:

### Example Question #91 : Statistics

The heights of the members of a basketball team are inches. The mean of the heights is . Give the median of the heights.

Explanation:

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

Where:

is the mean of a data set, indicates the sum of the data values and is the number of data values. So we can write:

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

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

### Example Question #10 : Median

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

Explanation:

There are  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  and  largest values. So we can write:

So:

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