Stats Rock
Using Pet Rocks to Find the Mean, Median and
Interquartile Range (IQR)
Data Set
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.
Mean and Median
The Mean, Median and Mode Toads
Click to watch!
Mean of a Data Set
This data set represents the number of hours spent doing
homework by 6th grade students. Given the data set
(3,5,6,4,2,0,1,4 ) we will find its mean, median, and interquartile
range (IQR).
 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
 Step 2: Now we count the number of pieces of data in our
data set. We have 8 pieces of data.
 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.
Let’s Practice Finding the Mean
 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
 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
hundredths place. 15.67
Median of a Data Set
Using the same data set about the number of hours spent by 6th
graders doing homework (3,5,6,4,2,0,1,4), we will find its median.
 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)
 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.
Let’s Practice Finding the Median
 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.
 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.
Interquartile Range (IQR)
The interquartile range (IQR) is a measure of variability
in our data set.
 The data points in our data set are divided into 4
quartiles. The IQR is the difference between the third
quartile Q3 and the first quartile Q1.
 The IQR will contain the middle 50% of the data points
in your data set.
More About the Interquartile Range
(IQR)
Q1
25%
Q2
25%
Q3
25%
The middle 50% of
your data is the IQR
The interquartile range (IQR) is = Q3 – Q1.
25%
How to find the Interquartile Range
Let’s see how to find the Interquartile Range
 How to Find An Interquartile Range
Click to watch!
Let’s Practice Finding the IQR
 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
 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