Activities

1. What does it mean if data has a gap?

2. What does it mean if data has a cluster?

3. Using the dot plot below, identify the following statements as true or false.
   1. There is a gap in the data.
   2. There is a peak in the data.
   3. The dot plot has a line of symmetry.
      
      

4. How would you describe the shape of the histograms below?  Skewed right, skewed left, or symmetrical?  Explain.
   a.
   b.
   
   

5. Create a list of data that would create a dot plot that would be skewed to the left.  Explain your answer.

Answer Key/Rubric

1. Data has a gap if there is a part of data that is missing or if there is a large break in the values.

2. Data has a cluster if a large amount of the values are in the same general spot on a graph. 

3. Answers as follows:

a. False

b. True

c. False

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

            a. The histogram is skewed to the right.

• Right skewed data is bunched up toward the left and with a "tail" stretching toward the right.

            b. The histogram is symmetrical. 

• A histogram is symmetrical when you draw a vertical line down the center of it and the two sides are identical in shape and size.
• A histogram is perfectly symmetric if its right half is a mirror image of its left half.
• Histograms that are not symmetric are referred to as skewed.

5. Students’ data sets will vary.
   
   Properties of left skewed data include, but are not limited to:

• Data has a long “tail” to the left.
• The mean and the median are both less than the mode
• Example table: