In this worksheet, we will practice choosing and evaluating the appropriate measure of the central tendency of a given data.

**Q1: **

Shown are the exam scores of 10 students.

76 | 63 | 77 | 71 | 81 |

0 | 54 | 93 | 47 | 82 |

Calculate the mean score.

Calculate the median of the scores.

Explain which of these measures of central tendency better represents a typical score in the exam.

- AThe median, because the mean is skewed too low due to the score of 0
- BThe mean, because the median is skewed too low due to the score of 0
- CThe median, because the mean is skewed too high due to the score of 93
- DThe mean, because the median is skewed too high due to the score of 93

**Q2: **

A data set has 20 different values: 18 of the values are between 10 and 20 but 2 of the values are greater than 40. Which measure of central tendency would better represent a typical value of the data set?

- AThe mode, because it is a robust statistic
- BThe mean, because it considers all the data values
- CThe median, because it is less affected by outliers

**Q3: **

The following table shows the greatest distances thrown by the finalists in the discus competition of the 2016 Rio Olympics for both men and women.

Distance | ||
---|---|---|

Men (m) | Women (m) | |

Gold | 68.37 | 69.21 |

Silver | 67.55 | 66.73 |

Bronze | 67.05 | 65.34 |

4 | 66.58 | 64.90 |

5 | 65.10 | 64.37 |

6 | 64.95 | 63.13 |

7 | 64.50 | 63.11 |

8 | 63.72 | 63.06 |

The following summary statistics have been calculated.

Men | Women | |
---|---|---|

Mean | 65.98 | 64.98 |

Median | 65.84 | 64.64 |

Why is there a greater difference between the mean and the median for women than there is for men?

- AThe men’s results are more variable.
- BThe competitors in gold medal position significantly outperformed the rest of the field.
- CThe women’s results are generally lower than the men’s.
- DFor women, there is one very high result in comparison to the rest of the data which increases the mean but not the median.
- EThe farthest throw by a woman was longer than the farthest throw by a man.

**Q4: **

A group of girl scouts is selling boxes of cookies to raise money for charity. The line plot shows how many boxes of cookies they sold. State whether the mean would be a good measure of central tendency for the data or not. Explain your answer.

- AYes, the mean closely represents the middle of the data.
- BNo, the mean is skewed too high because of the data point 36.

**Q5: **

Which measure of centrality is less sensitive to outliers in comparing the two data sets shown?

Data Set 1 | 25 | 22 | 28 | 51 | 26 | 28 | 29 | 32 |
---|---|---|---|---|---|---|---|---|

Data Set 2 | 21 | 27 | 19 | 26 | 24 | 23 | 28 | 25 |

- A mode
- B mean
- C standard deviation
- D median
- E range

**Q6: **

Which of the following is NOT an example of a measure of centre?

- A mode
- B mean
- C median
- Dinterquartile range