Stats Rock

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.

Data Set

The Mean, Median and Mode ToadsClick to watch!

Mean and Median

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.

Mean of a Data Set

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.

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.

Let’s Practice Finding the Mean

15.83

15.67

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.

Median of a Data Set

Find the median of the data set representing the number of guests at a birthday party. (25,30,15,10,5,10,31)

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)

Let’s Practice Finding the Median

Order the data set (5,10,10,15,25,30,31) . The median is the middle number, which is 15.

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. 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.

Interquartile Range (IQR)

More About the Interquartile Range (IQR)

25%

25%

25%

25%

Q1 Q2 Q3

The interquartile range (IQR) is = Q3 – Q1.

The middle 50% of your data is the IQR

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

Click to watch!

How to find the Interquartile Range

Find the IQR of the data set representing the number of guests at a birthday party. (25,30,15,10,5,10,31)

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)

Let’s Practice Finding the IQR

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

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