Averages, Ranges & Data (Edexcel GCSE Maths: Foundation): Exam Questions

A factory which produces bicycles is planning to make four different models; A, B, C, and D.

60 people are asked which of the four models they would be most likely to buy.

The table shows information about the results.

The factory is going to make 20 000 bicycles next year.

(i) Work out how many model C bicycles the factory should make next year.

[2]

(ii) Explain why your answer to part (i) may be inaccurate.

[1]

The table below shows the number of goals a team scored in 45 matches.

Find the median number of goals scored per game.

Daniel asked 50 students how many minutes they each took to get to school.

 Work out an estimate for the mean number of minutes taken by the 50 students.

The table shows the temperature, in °C, at midday on the first day of each month during one year in a city.

Calculate the mean of these temperatures.

............................................. °C

Helena has a set of cards.
She takes one card at random and records the number shown.
She does this 50 times.
The results are shown in the table.

Calculate the mean of her results.

Joel spins a fair five sides spinner numbered 2, 3, 4, 5, 6.

The table shows the results of his first 20 spins.

i) Write down the mode.

[1]

ii) Calculate the mean.

[3]

Joel wants to draw a pie chart to show the results in the table.

iiia) Show that the sector angle for the number 2 is 54°.

[1]

iiib) Find the sector angle for the number 6.

[2]

The table shows the number of bananas bought by the last 50 customers at a store.

i) Find the range.

[1]

ii) Work out the median.

[1]

iii) Calculate the mean.

[3]

The number of people in each of 150 cars entering the leisure centre car park is recorded.
The table shows the results.

i) Write down the mode.

[1]

ii) Calculate the mean.

[3]

The mean weight of 5 cantaloupes is 3.6 kg.

Kafui recorded the weight of one of the cantaloupes as 5kg.

Work out the mean weight of the other 4 cantaloupes.

Kafui made a mistake.

The cantaloupe was in fact 8kg, not 5kg.

How does this affect your answer to part (a)?

Here is a list of numbers.

Peter says the mode is 7.

Peter is not correct.

What is wrong with Peter's answer?

Work out the range of the numbers in the list.

Work out the mean of the numbers in the list.

A farmer has grown 960 sunflowers in a rectangular field. The farmer wants to take a sample of sunflowers to determine when they will be ready to harvest. He decides to take a sample of 24 sunflowers, selecting them from one corner of the field.

State the population.

State one potential issue with the sample method that the farmer intends on using.

Suggest one improvement to the sample to improve the reliability of the data.

A stable records the number of carrots that each of 5 horses eats per week.

5, 7, 3, 4, 6

Calculate the mean number of carrots eaten per week by these 5 horses.

Another horse joins the stable. The mean number of carrots eaten by a horse per week is now 5.5 carrots. How many carrots does the new horse eat each week?

Charlene is the record keeper for her school's netball team.

At the end of 9 games, the team's mean score was 35 goals per game.
At the end of 10 games, the team's mean score was 1 goal higher.

Charlene's mother says,

"The team must have scored 45 goals in their 10th game."

Is her mother right?
You must show how you get your answer.

Eve works in a shop that sells trousers.

The table shows information about the leg lengths of 40 customers who bought trousers from the shop in July.

Calculate an estimate for the mean leg length.

Trousers are made in lengths Short, Regular, Long, and Extra Long.

Eve needs to order more trousers in August.

The modal size of trousers sold is Regular.

Eve is going to order of the trousers in size Regular.

The manager of the shop tells Eve she should not order so many Regular trousers.

Who is correct, Eve or the manager?

You must give a reason for your answer.

Ken wants to find investigate the opinion of students in his school, which has 5 year groups.

The table gives information about the number of students in each year group in Ken's school.

 (i) State the population in this situation.

[1]

(ii) State one reason why Ken should consider surveying a sample.

[1]

(iii) State one reason why Ken should consider surveying the population.

[1]

(iv) Ken decides to take a survey of 30 students.

Calculate how many students from Fifth year should be in his sample for it to be representative of the population.

[3]

The table shows information about the number of hours that 110 children spent playing video games last week.

Jamie is trying to calculate an estimate for the mean number of hours that the 110 children played video games for last week.

His working is shown below.

Mean = 

Jamie has made 1 mistake in his calculation.

Describe the mistake and correct it to find the correct estimated value of the mean.

The table gives information about the weights, in kg, of 36 packages being loaded on to a delivery truck.

(i) Calculate an estimate for the mean weight of the packages.

[4]

(ii) Explain why your answer to part (i) will only be an estimate.

[1]

(iii) On a different delivery truck, there are 50 packages.

Using the data in the table, estimate the number of these packages that weigh between 0 and 10 kg.

[2]

Ning has a spinner numbered 1 to 6.
She spins it 50 times and her results are shown in the table.

i) Write down the mode.

[1]

ii) Find the median.

[1]

iii) Work out the mean.

[3]

The mean of seven numbers is 16.

Six of these numbers are 12, 20, 19, 10, 21 and 13.

Find the seventh number.

Six students bring an apple to school one day.
The list shows the mass of each apple, correct to the nearest gram.

Find

ia) the mode,

.............................................. g [1]

ib) the range,

.............................................. g [1]

ic) the median.

.............................................. g [2]

ii) Another student, Toni, also brings an apple to school.
The mean mass of the 7 apples is 89g.

Work out the mass of Toni’s apple.

.............................................. g [3]

The mean of three numbers is 150.

The numbers are 361, and  .

Find the value of .

= ................................................... 

Five numbers have a mean of 9.4 .
Four of the numbers are 3, 5, 10 and 12.

Work out the range of the five numbers.

The number of examinations that each of 196 candidates takes is recorded in the table.

i) Write down the range.

[1]

ii) Find the median.

[1]

iii) Calculate the mean.

[3]

iv) A candidate is selected at random.

Find the probability that the candidate takes fewer than 8 examinations.

[2]

The table shows information about the heights of plants.

Find the class interval that contains the median.

Here are two sets of numbers, A and B.

Set A = {}

Set B = {}

mean of Set A : mean of Set B = 3:8

Work out the value of .