Using Pet Rocks to Find the Mean, Median and
Interquartile Range (IQR)

A data set is a collection of data. It can be the ages of your classmates, the number of pets you own, or the weight of your pet rock.

The Mean, Median and Mode Toads
Click to watch!

This data set represents the number of hours spent doing homework by 6 th grade students. Given the data set
(3,5,6,4,2,0,1,4 ) we will find its mean, median, and interquartile range (IQR).
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Step 1: In order to find the mean (also called average) of a data set you first add all the pieces of data together. So we do the following: 3+5+6+4+2+0+1+4= 25
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Step 2: Now we count the number of pieces of data in our data set. We have 8 pieces of data.
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Step 3: Finally we divide the sum of the pieces of data by the number of pieces of data. So, 25 ÷ 8 = 3.125
We will round our decimal answers to the nearest hundredths
place. Our mean is 3.13.

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Find the mean of the data set representing the number of guests at a birthday party. (25,30,15,10,5,10) Round your answer to the nearest hundredths place. 15.83
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Find the mean of the data set representing the number of presents you received at your last birthday party.
( 20 ,50,3,10,1,10) Round your answer to the nearest

Using the same data set about the number of hours spent by 6 th graders doing homework (3,5,6,4,2,0,1,4), we will find its median.
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Step 1: Place the data set in order from smallest to largest value
(including all the repeating values). Place them in order just like
they appear on the number line. So our data set now looks like
(0,1,2,3,4,4,5,6)
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Step 2: Now look for the middle number in the data set. Since we have an even number of data points, the median will be found between numbers 3 and 4. In this case the median is found by adding the two numbers (3+4) and dividing by 2. This gives us 3.5 as the median. Note: In the case where you have an odd number of data points in the data set, the median is just the middle number. For example, in the data set (1, 5, 11,12,14) the median is
11.

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Find the median of the data set representing the number of guests at a birthday party.
(25,30,15,10,5,10,31)
Order the data set (5,10,10,15,25,30,31) . The median is the middle number, which is 15.
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Find the median of the data set representing the number of presents you received at your last birthday party.
( 20 ,50,3,10,1,11)
Order the data set (1,3,10,11,20,50). The median will be the number between 10 and 11. So, 10 + 11 = 21 ÷2 = 10.5. The median is 10.5.

The interquartile range (IQR) is a measure of variability in our data set.
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The data points in our data set are divided into 4 quartiles. The IQR is the difference between the third quartile Q 3 and the first quartile Q 1.
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The IQR will contain the middle 50% of the data points in your data set.

25%
Q1 Q2 Q3
25% 25% 25%
The middle 50% of your data is the IQR
The interquartile range (IQR) is = Q3 – Q1.

Let’s see how to find the Interquartile Range
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How to Find An Interquartile Range
Click to watch!

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Find the IQR of the data set representing the number of guests at a birthday party. (25,30,15,10,5,10,31)
First order the data set (5,10,10,15,25,30,31). Find the median of the data set = 15. Find the Q3 = 30. Find Q1 =10.
IQR = Q3 – Q1 = 20
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Find the median of the data set representing the number of presents you received at your last birthday party. ( 20 ,50,3,10,1,11)
First order the data set (1,3,10,11,20,50). Find the median of the data set = 10.5. Find the Q3 = 20. Find Q1 =3.
IQR = Q3 – Q1 = 17