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Cookie Fundraiser Data Set 1The data displayed below are a perfectly symmetrical data set, centered about the mean.
| Number of Boxes of Cookies Sold |
|---|
| 0 |
| 1 |
| 1 |
| 3 |
| 5 |
| 5 |
| 6 |
Here are the one-variable statistics for this data:
The mean of this data is 3 boxes, with a standard deviation of 2.2 boxes. This means that, on average, each data value is about 2.2 away from the mean of 3.
Now, consider this data. Notice the last two values in the table are larger.
| Number of Boxes of Cookies Sold |
|---|
| 0 |
| 1 |
| 1 |
| 3 |
| 5 |
| 15 |
| 26 |
Here are the one-variable statistics for this data:
The data have now become skewed right. The mean of the data has shifted up to 7.29 boxes, with a standard deviation of 8.99 boxes. This means that, on average, each data value is about 8.99 away from the mean of 7.29.
Compare the two box and whisker plots.
The second data set is skewed right. The data are much more variable (spread out). This is supported by the larger standard deviation of 8.99 boxes.
Standard deviation can be used as a measure of a data set’s variability. Data that have a large standard deviation are spread out and inconsistent.