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.

Grade0–2020–4040–6060–8080–100
Frequency2251510

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)15–2020–2525–3030–3535–4040–45
Frequency231415110

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)50–5555–6060–6565–70
Frequency 2 6144

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.

Time1:00 pm–2:30 pm2:30 pm–4:00 pm4:00 pm–5:30 pm5:30 pm–7:00 pm7:00 pm–8:30 pm8:30 pm–10:00 pm
Number of Clients225632

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 Limits10–<2020–<3030–<4040–<5050–<6060–<70
Frequency315445275290615

Q6:

Given that 𝐿 is the lower boundary point of the median class and 𝑊 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?

  • A𝐿+𝑓×𝑊precumulativefrequency
  • B𝐿+𝑓×𝑊precumulativefrequency
  • C𝐿++𝑓×𝑊precumulativefrequency
  • D𝐿+𝑛𝑓×𝑊precumulativefrequency
  • E𝐿𝑓×𝑊precumulativefrequency

Q7:

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

Days1–88–1515–2222–29
Percent25%30%35%10%

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 Limits1–66–1111–1616–2121–26
Frequency45506020

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.

This lesson includes 9 additional questions and 136 additional question variations for subscribers.

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