# ISEE Middle Level Quantitative : How to find median

## Example Questions

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

Brandon is training for a marathon.  Each day after school he runs for two hours.  Over the course of two weeks, he runs the following distances:

What is the median distance that Brandon runs?

There is no median.

Explanation:

In order to find the median, we must first put the data in numerical order from least to greatest:

Next, we must find the number that is in the middle, but since there are fourteen numbers, there is no number that falls exactly in the center.  When this happens, we add the two middle numbers together and divide by two.  In this case, our middle numbers are and .

Brandon's median distance is .

### Example Question #2 : How To Find Median

Which is the greater quantity?

(A) The median of the data set

(B) The median of the data set

(A) and (B) are equal

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

(B) is greater

(A) is greater

(A) and (B) are equal

Explanation:

Each data set has five elements; the median is the element in the middle after the elements are arranged in ascending sequence, which both are. In each case, the median will be the third-highest element. Since in both data sets, this element is 100, the medians are equal.

### Example Question #3 : How To Find Median

Give the median of the data set

Explanation:

The median of a data set with an even number of elements is the mean of the two elements in the middle when they are arranged in ascending order. The data set has six elements, so the median is the mean of the third-highest and third-lowest elements:

### Example Question #4 : How To Find Median

The median of the weights of the nine students in the history club is 150 pounds. What is the sum of their weights?

(A) 1,350 pounds

(B) The sum of the weights of the students

(A) and (B) are equal

(B) is greater

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

(A) is greater

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

Explanation:

It is impossible to tell which is greater.

For example, if all nine students weight 150 pounds, their median weight is 150, and their total weight is equal  pounds.

If, however, their weights are

then the median of their weights - the middle value - is still 150 pounds, but the sum of their weights is

### Example Question #5 : How To Find Median

Consider the data set

Which of the following elements replaces the box to make 50 the median of the data set?

None of the other responses are correct.

None of the other responses are correct.

Explanation:

The median of eleven elements is the element in the middle when arranged in ascending order - that is, the sixth-lowest element. If the box is replaced with a 40, the data set becomes

making 40 the sixth element.

If the box is replaced with a value less than 40, then the lowest five values are 20, 30, 30, 40, and the new element, and the sixth element is 40.

If the box is replaced with a value greater than 40, then the lowest five values are 20, 30, 30, 40, 40, and the sixth element is 40.

No matter what, the median is 40.

### Example Question #6 : How To Find Median

The six students in the science club weigh 145 pounds, 172 pounds, 166 pounds, 159 pounds, 153 pounds, and 201 pounds. Give the median of their weights.

Explanation:

In ascending order, their weights are:

The median is the average of the two numbers in the middle of the set, which are 159 and 166:

The median weight is 162.5 pounds.

### Example Question #7 : How To Find Median

Consider the data set .

Which of the following elements, when plugged in for the square, make 40 the median of the data set?

All of the other responses are correct.

All of the other responses are correct.

Explanation:

The median of eleven elements is the element in the middle, assuming the numbers are arranged in order.

If the box is replaced with a 40, the data set becomes

,

making 40 the sixth element.

If the box is replaced with a value less than 40, then the lowest five values are 20, 30, 30, 40, and the median is 40.

If the box is replaced with a value greater than 40, then the lowest five values are 20, 30, 30, 40, 40, and the median is 40.

No matter what, the median is 40.

### Example Question #8 : How To Find Median

The six students in the science club weigh  pounds,  pounds,  pounds,  pounds,  pounds, and  pounds. Give the median of their weights.