# Lesson Worksheet: Outliers of a Data Set Mathematics • 8th Grade

In this worksheet, we will practice identifying outliers from a data set.

**Q1: **

The table below shows the number of messages exchanged on the smart phones of 14 students over a single month. The data have also been plotted in a dot plot.

Are there any outliers in this data set? If so, specify the value or values of these outliers.

- AThere is one outlier in the data: 9,754.
- BThere is one outlier in the data: 4,542.
- CThere are two outliers in the data: 2,830 and 9,754.
- DThere is one outlier in the data: 2,830.
- EThere are no outliers in the data.

**Q4: **

The data in the table below is the average recorded speed, in miles per hour, of the first serve of the top 10 tennis players in the world.

Average Speeds of the First Serve of the Top Ten Tennis Players (mph) | ||||
---|---|---|---|---|

126 | 115 | 99 | 136 | 105 |

138 | 121 | 1,025 | 118 | 124 |

Calculate the mean first-serve speed in miles per hour approximated to 1 decimal place.

Recalculate the mean first-serve speed without the data point 1,025 mph, approximated to 1 decimal place.

By comparing the means you found in the first two parts of the question, make a conclusion about the validity of the 1,025 mph data point.

- AThe recorded speed of 1,025 mph is very important for calculating the mean of the first-serve speed, and we can not remove it from the data set.
- BThe inclusion or omission of the data point 1,025 mph drastically alters the mean of the data set because it is an extreme outlier. Physical intuition tells us that this recorded speed is probably an error.

**Q7: **

The table below shows the height (in centimeters) of 10 boys of the same age.

97 | 100 | 130 | 90 | 95 |

102 | 70 | 92 | 91 | 85 |

Using the standard deviation rule, identify the outlier (or outliers) approximated to one decimal place, if any.

**Q8: **

The table below shows the income (in thousands of British pounds) of 12 households from a neighborhood.

4.7 | 18.3 | 19.2 | 20.2 | 24.5 | 27.5 |

29.7 | 35.4 | 35.7 | 36.1 | 38.4 | 50.1 |

Using the 2-standard deviation rule, identify the outlier (or outliers), if any.

Using the 1.5 IQR rule, identify the outlier (or outliers), if any.

- A50 100 pounds
- B4 700 pounds
- CNone
- D4 700 pounds and 50 100 pounds