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mathematics UK Year 10 Mathematics (KS4)

Solved problems for the chapter:

Mean Median Mode and Range

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_median_mode_and_range/3678/

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 chart below shows the number of baskets scored by the top scorer of a basketball tournament in six matches.

What is the average number of baskets scored by the top scorer in six matches? Calculate and write the answer.

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.

The figure below shows the prices of a barrel of oil on the world market. Prices are in pounds.

Read the prices and write them in the spreadsheet. Calculate the average oil price from Jan. 12 to Jan.19.
Calculate the maximum price increase between consecutive days. Write it down as a percentage.
Calculate savings on purchase of 20,000 barrels of oil if purchase is made Jan. 12 instead of Jan. 14.

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.

Jane paid the monthly amounts listed in the following table for using a mobile phone last year:

Month	Amount (in Pounds)
January
February
March
April
May
June
July
August
September
October
November
December

Calculate the average monthly amount of Jane's payments on mobile phone. How many months did she pay a higher amount than the average monthly amount?
Jane had 220 pounds monthly scholarships. Calculate what percentage of the scholarship she spent on mobile phone used last year.
The pie chart shows the shares of the annual amount that Jane paid last year for SMS, Subscription and Calls. How much did Jane pay for each service last year?

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?

10.

Tina earned 218.40 pounds in July with her student work, Lea 98.20 pounds, and Meta 101.60 pounds. In August, Tina earned a fifth less, Lea increased her earnings by 15%, and Meta earned the same amount as in July.

Calculate the missing values and fill in the table.

Tina Lea Meta
Earnings in July (in Pounds)
Earnings in August (in Pounds)
Calculate the average earnings of the girls in July and in August. Calculate by how many pounds the average August earnings of the girls were lower than the average earnings in July.
Meta invested her entire earnings in a bank that pays interest at the annual interest rate of 2.5% with an annual accrual of interest. Calculate how many more pounds she will have in four years.

11.

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?

12.

300,000 people live in an American city. One color-blind person was listed in a sample of hundred people. How many color-blind (statistically) people are expected to live in the city?

13.

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

14.

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

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

15.

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.

16.

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.

17.

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.

18.

A family weighed the amount of trash they dumped into a brown bio-waste container. The mass of garbage for the last 6 months is shown in the chart below:

Which month did they throw away the most garbage?
How many kilograms of garbage did they throw away in the month when they threw away the most garbage?
Calculate the arithmetic mean of the mass of discarded garbage for the six months.

19.

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?

	Tina	Lea	Meta
Earnings in July (in Pounds)
Earnings in August (in Pounds)