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Solved problems for the chapter:

Mean, median and mode

View the theory »

Measures of central tendency for KS4

1. Arithmetic mean

1.1. Arithmetic mean of grouped data

2. Mode

2.1. Mode of grouped data

2.2. Bimodality

3. Median

4. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:mean%2C_median_and_mode/5375/

Example 1.

The table below gives information about the results in a school assignment:

assessment	frequency	relative frequency
1	4
2	8
3	11
4	10
5	7

Calculate the average score and complete the table with relative frequencies.

Example 2.

Ski jumper Mark jumped four times in training and reached the following distances: 94 m, 100 m, 94 m and 96 m.

Calculate the average length of his jumps
How many meters should he jump in the fifth jump for training to increase the average to 98 m?

The table shows the results of a written knowledge assessment.

Score	1	2	3	4	5
Number of students	6	9	6	11	8

Find the mode and median and calculate the arithmetic mean for the data in the table.

The table shows the temperatures at 1:00pm for each day of the week.

Day of the week	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday

Calculate the average temperature for the week. Round the result to one decimal place.

In a class competition, the following results were achieved in the 100 m run (in seconds):

Calculate the average time.
Calculate the percentage of the competitors who achieved a better time than average.

Student Nina scored an average of 65 points in six tests. What is the total number of points she scored in all the six tests?

The arithmetic mean of four numbers is 70. If the numbers 60 and 80 are among these four numbers, calculate the sum of the other two numbers?

In which of the data groups is the median equal to the mode?

33, 18, 19, 13, 18
26, 18, 26, 15, 28
32, 19, 28, 16, 19, 25, 19

Accommodation prices (in pounds) in ten hotels are given below:

Calculate the arithmetic mean, median and mode of accommodation prices from the given data.

10.

In a party consisting of 16 five-year-old children, 5 ten-year-old, two fathers, aged 45 and 48, and a seventy-year-old grandfather;

calculate the arithmetic mean, median, and mode of the age of the party participants;
find out which of these mean values best describes the situation and why?
without additional calculation, find changes in mean values if two five-year-old leave the party.

11.

An advertising agency buys new cars at the beginning of the year. Before buying, they check the numbers and ages of all the cars in the fleet. This year, they received the following data:

Age of cars (in years)	Number of cars
1	5
2	21
3	17
4	15
5	13
6	9

Calculate the arithmetic mean, median, and mode.

12.

A computer company recorded the number of system failure faults they had on a weekly basis and obtained the following data for 20 weeks:

3 3 3 1 3 2 4 6 6 3

4 3 4 3 3 0 4 3 3 5

Write a frequency table and calculate the mean, median and the mode of the number of faults experienced weekly.

13.

Ski jumper Peter achieved the following distances in the first four jumps during a training: 95 m, 101 m, 93 m and 95 m.

Calculate the average length of his jumps.
How many meters should he jump in the fifth training jump to increase the average to 98 m?