Measures of Central Tendency (Edexcel GCSE Statistics: Foundation): Exam Questions

The table shows information about houses for sale in Oxford.

(Source: adapted from rightmove.co.uk (opens in a new tab))

An estate agent says the mode of the number of bedrooms for these houses is 3.

Explain how she knows this.

The estate agent wants to investigate the prices of these houses.

She takes a stratified sample of 60 houses according to the number of bedrooms.

Work out the number of houses in her sample for each number of bedrooms.

Describe how to select the 60 houses in the sample.

Diane recorded the number of hours that she watched television each day last week.

Draw a line graph for this data.

Label each axis.

Calculate the mean number of hours.

Find the median.

Noah recorded the number of hours that he watched television each day last week.

He calculated the mean and the median of his results.

Use your answers to part (b) and part (c) to compare the average amount of television watched by Diane and by Noah last week.

Tomoyo found the weight, in grams, of each of 100 cherries.

Circle the two words from the list that best describe the data Tomoyo found.

quantitative    qualitative    discrete    continuous    bivariate    ordinal    categorical

Tomoyo grouped the weights and she then drew this diagram for her results.

The incomplete frequency table shows some information about her results.

(i) Complete the frequency column in the table.

(2)

(ii) Calculate an estimate of the mean weight of the 100 cherries.

........................ g

(3)

A basketball team played 9 matches at the start of a season.

The total number of points they scored in each match is listed below.

Here are some words used to describe data.

grouped    discrete    categorical    continuous

Select a word from the list to complete the sentence.

The total number of points scored in a match is an example of ___________ data.

Work out the median score for these 9 matches.

Give one advantage of using the median to summarise this data.

Work out the range of points for these 9 matches.

The median and range for the final 9 matches of the season are shown in the table below.

Use your answers to part (b) and part (d) to compare the performance of the basketball team in the first 9 matches with the performance in the final 9 matches.

Give two comparisons and interpret both in context.

A fjord is a deep and narrow part of a sea with steep land on three sides.

Emily is investigating the length of fjords in Norway. She collects some data from the internet and puts the data into a grouped frequency table.

The grouped frequency table below shows information about the results she collected.

(Source: https://en.wikipedia.org/wiki/List_of_Norwegian_fjords (opens in a new tab))

Work out the number of fjords that have a length of at least 100km.

(i) Calculate an estimate of the mean length of these fjords.
Give your answer to 1 decimal place.

......................... km (3)

(ii) Explain why your answer to part (b)(i) is only an estimate.

(1)

(iii) How could Emily have improved the accuracy of her answer to part (b)(i)?

(1)

Emily plans to use a frequency polygon to represent the lengths of the fjords.

Discuss whether or not a frequency polygon would be an appropriate diagram to use.

Jenny is investigating how many days per week people use a gym.

She asks the 40 people in her fitness group how often they use the gym each week. Jenny draws this bar chart for her data.

One of these people is chosen at random.

Find the probability that this person uses the gym exactly 2 days per week.

What is the modal number of days to use the gym each week?

Jenny thinks that there are a lot of people in her fitness group who are exercising less than 2 days per week as there is a total of 10 people who used the gym on 0 days or 1 day per week.

Explain why Jenny might not be correct.

Ben is researching information about the number of British swimming medals won at the Olympics.

Here are his results, giving the number of British swimming medals won at the Olympics from 1900 to 2016

(Source: www.teamgb.com (opens in a new tab))

Fill in the tally chart for Ben’s results and complete the frequency column.

Suggest a suitable diagram that could be used for Ben’s results.

Write down the mode or modes.

Work out the median.

Ben wants to use an average to summarise the data.

Which of the mode or the median would be more appropriate?
Give a reason for your answer.

Tachi collects data on the heights, in metres, of a sample of Egyptian pyramids.

Here is her data.

(Source: www.rankred.com (opens in a new tab))

Tachi picks one of these pyramids at random.

Find the probability that this pyramid will have a height of more than 100 m.

The mean height of a sample of Mexican pyramids is 53.5 m.

Tachi says, "On average these Egyptian pyramids are twice as high as the Mexican pyramids."

Is Tachi correct?
You must show working to support your answer.

The range of heights for the Mexican pyramids is 45m.
The lowest height of the Mexican pyramids is 30m.

Work out the greatest height of the Mexican pyramids.

............................. m

David asked 15 of his friends about the number of pets they each have. Here is the data he collected.

0   0   0   0   0   1   1   2   2   2   4   4   4   4   8

Choose the word in the list below that describes this type of data.

Write down the modal number of pets.

Find the median number of pets.

State which average, the mode or the median, best represents these data. Give a reason for your answer.

Find the interquartile range of the number of pets.

Wanda asked some of her friends about the number of pets they each have.

The table below is a summary of the data she collected.

Compare the distribution of the numbers of pets for David with the distribution of the numbers of pets for Wanda.

Give two comparisons and interpret each of your comparisons.

Wanda recorded the highest number of pets as 15

She says that this must be an outlier and concludes that it should be removed from her data.

(i) Give one reason why Wanda’s conclusion may be appropriate.

[1]

(ii) Give one reason why Wanda’s conclusion may not be appropriate.

[1]

Kyle is investigating the heights and the weights of professional basketball players.

He found the weight, in kilograms, of some professional basketball players from 1950 to 1959

Choose the word in the list below that describes weight, in kilograms, as a type of data.

The incomplete histogram and incomplete grouped frequency table give information about the weights, in kilograms, of the professional basketball players from 1950 to 1959

Use the information in the histogram to complete the table.

Use the information in the table to complete the histogram.

Kyle also drew a histogram for the weights of professional basketball players from 2000 to 2009
This histogram was negatively skewed.

Interpret the negative skew of the weights of professional basketball players from 2000 to 2009

Kyle also collected data about the heights of professional basketball players from 1950 to 1959 and the heights of professional basketball players from 2000 to 2009

The grouped frequency table below gives information about the heights of professional basketball players from 2000 to 2009

The estimate of the mean height for professional basketball players from 1950 to 1959 is calculated to be 190.9cm to one decimal place.

(i) Calculate an estimate of the mean height of basketball players from 2000 to 2009

....................................................... cm

[3]

(ii) Comment on how the mean height of professional basketball players has changed between the two sets of data.

[1]

Rose is investigating the number of brothers and sisters that students in her secondary school have.

To investigate this she asks 10 students in Year 8 and 10 students in Year 11 how many brothers and sisters they each have.

Assess Rose’s method for her data collection.

The vertical line graph shows the data that she collected.

How many students have 2 or more brothers and sisters?

Write down the mode.

Rose uses her vertical line graph to conclude that no student in her school has 5 or more brothers or sisters.

Assess whether or not Rose’s conclusion is appropriate.

Connie is going to write a report on the difference in total rainfall between London and Aberdeen in 2019

She collects secondary data to investigate this.

What should Connie include in her report?

Describe one way that she could obtain this secondary data.

The table shows the total rainfall, in cm, for each month in 2019 in London.

(Source: en.climate-data.org (opens in a new tab))

The mean monthly rainfall in Aberdeen in 2019 is 6.2cm.

Connie considers the data in the table and concludes that the mean monthly rainfall for Aberdeen in 2019 is greater than the mean monthly rainfall in London in 2019

Is Connie correct? You must show how you get your answer.