# Common Core: 6th Grade Math : Find Measures of Center, Variability, and Patterns in Data: CCSS.Math.Content.6.SP.B.5c

## Example Questions

### Example Question #6 : Range

What is the range of the following data set?

Explanation:

The range of a data set is equal to the difference between the largest and the smallest numbers.

### Example Question #7 : Range

Find the range of this set of numbers:

Explanation:

First order the numbers from least to greatest:

Then subtract the smallest number from the largest number:

### Example Question #84 : How To 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 #1 : How To Find Range

Given the following set of numbers, find the range.

Explanation:

In order to find the range for a set of data, take the largest number and subtract the smallest number.

In this case, the largest number is  and the smallest number is

Remember that when we subtract a negative, we are actually adding the absolute value of the numbers:

Therefore:

is the same as

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

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 #12 : How To Find Median

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 #13 : How To Find Median

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 remain unchanged

The median will increase by

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 #10 : How To Find Median

In Jane's previous six basketball games, she made the following number of baskets:

What is the median number of baskets she made?

Explanation:

The first step to finding the median is to reorder the number of baskets that Jane scored from smallest to largest. This gives us:

The median number is the number in the middle of the set. Given that there are two middle numbers (4 and 6), the average of these numbers will be the median.

The average of 4 and 6 is:

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

What is the mean of the values , , ,