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.

 Days Frequency Midpoint (Days) 0– 5– 10– 15– 20– 25– 3 7 8 6 4 1 ⋯ 7.5 ⋯ 17.5 ⋯ ⋯
• 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 .
• BWe calculate the lower limit of each class and then use the following rule: sum of .
• CWe calculate the midpoint of each class and then use the following rule: sum of .
• DWe calculate the midpoint of each class and then use the following rule: sum of .
• EWe calculate the lower limit of each class and then use the following rule: sum of .

Q4:

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

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

Q5:

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

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

Q6:

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

 Salary (𝑠, LE) Number of Employees 1,000– 3,000– 5,000– 7,000– 5 8 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) Frequency 0- 3- 6- 9- 12- 5 4 10 4 7

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 Frequency 0– 4– 8– 12– 16– 5 ⋯ 10 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 Frequency 10– 20– 30– 40– 50– Total 9 8 11 13 9 50

Q10:

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

 Time (Minutes) Frequency 5– 10– 15– 20– 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.

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