Activities

1. Find the mean, median, mode, and range of the values in the table. Round all answers to the nearest tenth if needed.
   
2. Find the inter quartile range for the values in the table.
   
3. Calculate the mean of the data on the dot plot.
   
4. What is the Interquartile range of the box and whisker graph?
   

5. Explain how to find the mean absolute deviation of the following numbers:
   
   

6. Identify the outlier in the data below.  What effect does the outlier have on the mean and median? Which measure of center is affected more by this outlier, the mean or the median? Justify your reasoning by calculating the mean and median both with and without the outlier.
   

Answer Key/Rubric

1. Mean = 22.9

Median = 20

Mode = no mode

Range = 34

2. IQR = Q3 – Q1

IQR = 16 – 7

IQR = 9

3. 5

4. 7

5. Explanations may include, but are not limited to:

• Calculate the mean of the data:
  
• Find the distance of each value from the mean:
  
• Find the mean of the those values:
  
• Mean = 9; Mean deviation = 3

6. Acceptable answers may include, but are not limited to:

• Outlier is the week the student earned $20
• Outliers have a greater affect on the mean because it draws the mean toward it, pulling it away from the best representation of all the data
• The mean will decrease because you are taking out a high value, it will have more of a significant change in amount than the median
• The median may or may not change depending on the data set you have.  Taking away one high value will not change the median drastically.  If you have a set of data with many repeating values near the median taking out an outlier may not change the value at all.
• With Outlier:

Mean = $8.00

Median = $6.00

• Without Outlier:

New mean = $5.60

New median = $5.00