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Lesson Worksheet: Grouped Frequency Tables: Estimating the Mean Mathematics

In this worksheet, we will practice estimating the mean using grouped frequency tables.

Q1:

A number of teenagers were surveyed on how many days a month they exercise. The results are given below. Complete the table by finding the midpoints of each group.

Days0–5–10–15–20–25–
Frequency378641
Midpoint (Days)7.517.5
  • A2.5, 12.5, 22.5, 30
  • B5, 12.5, 22.5, 27.5
  • C2.5, 12.5, 22.5, 27.5
  • D2.5, 12.5, 22.5, 25
  • E2.5, 15, 22.5, 27.5

Q2:

In an extract of a book, the number of words per sentence was counted. Find the missing numbers in the following table.

Number of WordsFrequencyMidpointFrequency × Midpoint
1–715460
8–1420
15–214518810
22–2847251,175
29–352332736
36–421039390
  • A14, 280
  • B8, 160
  • C12, 240
  • D10, 200
  • E11, 220

Use the previous table to calculate an estimate for the mean number of words. Give your answer to two decimal places.

Q3:

In order to estimate the mean from given grouped data, which of the following is true?

  • AWe calculate the upper limit of each class and then use the following rule: sum of (×)÷eachupperlimitclassfrequencysumoffrequencies.
  • BWe calculate the lower limit of each class and then use the following rule: sum of (×)÷eachlowerlimitclassfrequencysumoflowerpoints.
  • CWe calculate the midpoint of each class and then use the following rule: sum of (×)÷eachmidpointclassfrequencysumofmidpoints.
  • DWe calculate the midpoint of each class and then use the following rule: sum of (×)÷eachmidpointclassfrequencysumoffrequencies.
  • EWe calculate the lower limit of each class and then use the following rule: sum of (×)÷eachlowerlimitclassfrequencysumoffrequencies.

Q4:

The frequency table shows the distribution of daily wages of 50 workers in a factory. Estimate the mean wage received.

Wages 25– 35– 45– 55– 65– Total
Frequency 7 9 15 10 9 50

Q5:

The frequency distribution shows the weights of 30 children. Estimate the mean weight recorded.

Weight (kg) 6– 10– 14– 18– 22– 26– 30– Total
Number of Children 6 5 5 3 6 3 2 30

Q6:

The following table shows the salaries (𝑠) of employees in a certain company, given in Egyptian pounds (LE).

Salary (𝑠, LE)1,0003,0005,0007,000
Number of Employees58 3 5

Estimate the mean salary (in LE), giving your answer approximated to two decimal places.

Q7:

The following table shows sample data organized in a frequency distribution.

Class (𝑥) 0- 3- 6- 9- 12-
Frequency5 4 1047

Estimate the value of the mean, giving your answer to 1 decimal place.

Q8:

The following table shows sample data organized in a frequency distribution.

Class 0– 4– 8– 12– 16–
Frequency510 4 4

If the estimated mean is 10, find the missing frequency in the table.

Q9:

The frequency table shows the distribution of marks that 50 students attained in an exam. Find the mean mark.

Mark 10– 20– 30– 40– 50– Total
Frequency 9 8 11 13 9 50

Q10:

The following table represents the time taken by 35 people to travel to work.

Time (Minutes) 5– 10– 15– 20–
Frequency 10 15 7 3

Calculate an estimation for the mean number of minutes people take to travel to work. Round your answer to two decimal places.

This lesson includes 22 additional questions and 221 additional question variations for subscribers.

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