# Lesson Worksheet: Measuring Central Tendency and Range Mathematics

In this worksheet, we will practice finding the mean, median, mode, and range of a data set.

**Q1: **

The ages of the people at a gathering were 49, 27, 37, 44, 34, 36, 19, 24, 23, 40, 20, 21, and 43. When one more person joined the gathering the mean age became 31. How old was the person who joined?

**Q2: **

The table shows the hours trained per month for two athletes. Find the mean number of hour trained for athlete (B).

Athlete (A) | 64 | 54 | 53 | 75 | 54 | 56 | 73 | 46 | 75 | 47 | 53 | 70 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Athlete (B) | 52 | 67 | 73 | 74 | 70 | 69 | 57 | 64 | 48 | 73 | 68 | 65 |

**Q3: **

Calculate the mean of the values in the table.

17 | 25 | 13 | 22 | 15 | 17 | 24 | 21 | 23 | 14 | 19 | 22 | 19 | 16 | 18 |

**Q4: **

Fawaz wants to find out the average age of people who go swimming on a Saturday morning. He records the following data on a particular Saturday morning: 5, 12, 24, 19, 64, 38, 71, 13, 14, 41, 3.

Calculate the mean of the data giving your answer accurate to one decimal place.

Calculate the median of the data.

Calculate the mode of the data.

- A27.6
- B3
- C71
- D19
- EThere is no mode.

Calculate the range of the data.

**Q5: **

Determine the mean, median, and mode for the given data.

Name | Ali | Osama | Kayan | Fahd | Abdullah | Hoor | Abeer | Faisal |
---|---|---|---|---|---|---|---|---|

Age | 18 | 9 | 15 | 18 | 10 | 7 | 14 | 5 |

- Amean12, median12, mode15.
- Bmean14, median10, mode18.
- Cmean12, median14, mode18.
- Dmean12, median12, mode18.

**Q6: **

The table shows the total precipitation in Arches National Park in January of each year. Calculate the mean January precipitation over the entire period shown in the table.

Year | 1 997 | 1 998 | 1 999 | 2 000 | 2 001 | 2 002 | 2 003 | 2 004 |
---|---|---|---|---|---|---|---|---|

Precipitation (in) | 1.09 | 0.013 | 0.54 | 0.80 | 0.89 | 0.24 | 0.11 | 0.16 |

**Q7: **

The table shows the salaries, in thousands of dollars, of ten employees in a company.

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|

22 | 24 | 30 | 19 | 95 | 31 | 25 | 96 | 20 | 23 |

Calculate the mean salary in dollars.

Calculate the median salary in dollars.

Which of these two measures of central tendency more accurately reflects the **majority** of the data?

- AThe median
- BThe mean

**Q8: **

The scores earned on a math test are 86, 80, 76, 68, 73, 85, 74, 70, 71, and 70. Find the mean, median, and mode for the set of data.

- AMean, median, mode
- BMean, median, mode
- CMean, median, mode
- DMean, median, mode
- EMean, median, mode

**Q9: **

Given that the median is 67, the range is 44, and the data is ordered from least to greatest, find the missing values in the data set .

- A72, 76
- B72, 87
- C70, 87
- D74, 87
- E62, 76

**Q10: **

Which of the following sets of data has a median of 45, a range of 57, and a mode of 45?

- A25, 67, 19, 45, 45, 77
- B26, 67, 20, 45, 44, 77
- C26, 26, 45, 77, 20, 76
- D26, 67, 20, 20, 20, 45
- E67, 45, 26, 77, 20, 45