# SSAT Middle Level Math : How to find median

## Example Questions

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### Example Question #11 : How To Find Median

Shelly took five tests and quizzes this semester in school. If her grades were , , , , and , what is her median test score?

Explanation:

First, order the test scores from least to greatest:

Identify the middle test score:

Answer: Shelley's median test score is 92.

### Example Question #12 : How To Find Median

Find the median of the following test scores from Andy's class;

Explanation:

To find the median of a set, you must order all the scores from lowest to highest.

Then you must find the middle number.

Since this set is even, you have two middle numbers which are  and .

You must average the two which gives you .

### Example Question #86 : Data Analysis

Horatio's soccer team has scored the below number of goals in their last eight games, what is the median number of goals that have been scored?

Explanation:

First we must put the numbers  in order from least to greatest.

After the numbers are in order, if it is an odd number of numbers we chose the middle number - that is the median.

In this case, we have an even number of numbers, so we must take the average of the middle two numbers which is given below:

So the median is !

### Example Question #87 : Data Analysis

Horatio's soccer team has scored the below number of goals in their last  games:

Horatio calculates the median to be  for this set of data. He then goes back and finds that the game where he thought they scored 9 goals; his team actually scored  goals - how will this change the median if he replaces the  with  in the data set?

The median will increase by

The median will remain unchanged

The median will increase by

The median will increase by

The median will remain unchanged

Explanation:

When finding the median we must first reorganize the numbers from least to greatest, here is what the numbers are before and after they were organized.

Given:

After Organized from least to greatest:

In order to find the Median for an even number of numbers (we have  numbers in this set) we take the average of the middle two numbers.

Here we would add  which is , we then divide by two to find the mean which is

If we were to change the  to an , this does not impact the middle two numbers, they will remain  and  which means the Median will remain

The middle two numbers are still  and

The Median will remain unchanged.

### Example Question #1 : Find Median

Subtract the median from the mode in this set of numbers:

Explanation:

First, order the numbers from least to greatest:

Find the median—the middle number:

Now, find the mode—the most recurring number:

Finally, subtract the median from the mode:

### Example Question #14 : How To Find Median

Subtract the range from the median in this set of numbers:

Explanation:

First, order the numbers from least to greatest:

In order to find the range, subtract the smallest number from the greatest:

Now, find the median by identifying the middle number:

Finally, subtract the range from the median:

### Example Question #85 : Data Analysis

Given the following data sets of data, identify how the median would change if an additional data point of  was added to the new set?

Data Set:

New Data Set:

Explanation:

First, we need to find the median for the first data set:

We must put the numbers in order from least to greatest:

Since there is an even number of items in the data set, we will take the average of the middle two numbers to find the median.

The median for this data set is:

Next, we must find the new median for the new data set:

Again, we must put the numbers in order from least to greatest:

Since there is an odd number of items, we can choose the middle number to be the median.

In this case, the middle number is , which means the new median is:

Therefore, we know that the median will decrease by .

### Example Question #15 : How To Find Median

Use the following data set to answer the question:

Find the median.

Explanation:

To find the median of a data set, we will arrange the numbers in ascending order, then we will find the number located in the middle of the set.

So, given the set

we will first arrange them in ascending (from smallest to largest) order.  We get

Now, we will locate the number in the middle of the set.

We can see that it is 5.

Therefore, the median of the data set is 5.

### Example Question #16 : How To Find Median

Give the median of the data set: