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# Lesson Worksheet: Grouped Frequency Tables: Estimating the Median Mathematics

In this worksheet, we will practice estimating the median for data presented in a grouped frequency table using cumulative frequency graphs.

**Q1: **

The following frequency table represents the final exam grades for grade 3 students.

Grade | 0–20 | 20–40 | 40–60 | 60–80 | 80–100 |
---|---|---|---|---|---|

Frequency | 2 | 2 | 5 | 15 | 10 |

What is the frequency of the class containing the median?

**Q2: **

The following frequency table represents the ages of members of a health club.

Age (Years) | 15–20 | 20–25 | 25–30 | 30–35 | 35–40 | 40–45 |
---|---|---|---|---|---|---|

Frequency | 2 | 3 | 14 | 15 | 1 | 10 |

What is the total number of members?

In which age group does the median exist?

- A30–35
- B20–25
- C25–30
- D15–20
- E35–40

**Q3: **

The following frequency table represents the time records for 26 racers, to the nearest second.

Time Records (s) | 50–55 | 55–60 | 60–65 | 65–70 |
---|---|---|---|---|

Frequency | 2 | 6 | 14 | 4 |

Estimate the median of the data, approximate to the nearest integer.

**Q4: **

The following frequency table represents the number of clients visiting a shop during opening hours for a certain day.

Time | 1:00 pm–2:30 pm | 2:30 pm–4:00 pm | 4:00 pm–5:30 pm | 5:30 pm–7:00 pm | 7:00 pm–8:30 pm | 8:30 pm–10:00 pm |
---|---|---|---|---|---|---|

Number of Clients | 2 | 2 | 5 | 6 | 3 | 2 |

Which interval contains the median?

- A5:30 pm–7:00 pm
- B8:30 pm–10:00 pm
- C4:00 pm–5:30 pm
- D2:30 pm–4:00 pm
- E7:00 pm–8:30 pm

**Q5: **

Find the missing value in the following table if you know that the estimated value of the median is 42.4.

Class Limits | 10–<20 | 20–<30 | 30–<40 | 40–<50 | 50–<60 | 60–<70 |
---|---|---|---|---|---|---|

Frequency | 315 | 445 | 275 | 290 | 615 |

**Q6: **

Given that is the lower boundary point of the median class and is the class width of the median class, which of the following formulas is used in order to estimate the median of the grouped data?

- A
- B
- C
- D
- E

**Q7: **

The following table gives the frequency distribution of the percentage of calls received each day in a call center in a month.

Days | 1–8 | 8–15 | 15–22 | 22–29 |
---|---|---|---|---|

Percent |

Calculate the estimated median to the nearest hundredth.

**Q8: **

Find the missing value in the following table if you know that the estimated value of the median is 11.25.

Class Limits | 1–6 | 6–11 | 11–16 | 16–21 | 21–26 |
---|---|---|---|---|---|

Frequency | 45 | 50 | 60 | 20 |

**Q9: **

Considering the following cumulative frequency graph, find an estimate for the median of the data.

**Q10: **

The following graph shows the time a group of students spent studying mathematics last semester.

Find an estimate of the median of the data approximated to the nearest hundredth.