Activities

1. If a set of data does not have any outliers what is the best measure of center?

2. If you add more values to a set of data will it increase the range?

3. The following set of data has 2 modes.  Explain why the two modes describe the set of data better than using the mean or median.
4. At a doctor’s office the weight of some 6-year-old patients were recorded in a chart. What is the outlier in this data and what does it represent? What affect does the outlier have on the mean?
   

5. Looking at the box and whisker plot below find the range and interquartile range.  Which one do you think better describes the variation in the data?  Explain your answer.
   
6. Using the data regarding shirt prices below, which of the following would best describe the variation of the entire set of the data?  Choose from mode, range, interquartile range, or upper quartile.  Explain your answer.
   

Answer Key/Rubric

1. If there are no outliers in a set of data using the mean is a good representation of the data’s measure of center.  When you have an outlier that is extremely low or high it can lower or raise the mean.

2. No, adding values to a set of data will not increase the range, unless those values are smaller than the minimum or larger than the maximum.

3. Possible explanations may include, but are not limited to:

• The mean (7) and median (7) don’t show that the data has two sets of clusters.
• The mean and median don’t show that there is a gap in the data.
• Using the modes describes the data well because it represents all the values in the data set.

4. Outlier: 75

Outlier represents the child that is larger than most children at 6 years old.

The outlier makes the mean greater than it would be without it and not the best representation of the data.

5. Range = 16

Interquartile Range = 6

The interquartile range describes the variation in the data better than the range. 

Acceptable reasons may include, but are not limited to:

• The range includes the outlier which makes it seem like the data varies more than it actually does
• The interquartile range does not include the outlier so it gives a better description of the variation of the data. 

6. The range is the best measure to show the variation of the shirt prices.

       Reasons might include, but are not limited to:

• This data does not have any outliers so the range is not representing a variation that is misleading.
• Mode is a measure of center not variation