Using Summary Statistics (Edexcel GCSE Statistics: Foundation): Exam Questions

The incomplete multiple bar chart shows information about the numbers of UK films first shown in 2013 and in 2014 for some types of film.

9 UK action films were first shown in 2013

7 UK action films were first shown in 2014

Complete the multiple bar chart.

The number of UK films first shown in 2013 was 17 for two types of film.

Which two types of film?

Work out the total number of drama films that were first shown in these two years.

Compare the numbers of UK films of the different types that were first shown in 2013 with those first shown in 2014

Explain why it would not be appropriate to display the information from the multiple bar chart in a time series graph.

The table shows information about the ages, when elected, of French presidents and UK prime ministers for the years 1850 to 2015

(Source: Wikipedia)

Compare and interpret the spread of ages of French presidents with UK prime ministers for the years 1850 to 2015

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.

Claire collected data on the weights of the England football team and the weights of the England rugby team from the internet.

She calculated the mean and range of the weights of each team. Her results are shown in this table.

(Sources: thefa.com (opens in a new tab) and englandrugby.com (opens in a new tab))

State two possible problems with obtaining data from the internet

Use the information in the table to compare the distribution of weights of the England football team with the weights of the England rugby team. Interpret your comparison.

Suggest a possible problem with collecting primary data in this situation.

27 adults were each asked to count the number of times they could bounce a ball on a bat.

Here are the results.

Complete the stem and leaf diagram for this information.

Work out the interquartile range of the results.

The median of the results for 27 children is 9.

The interquartile range of the results for these children is 6.

Alex thinks these results show that adults are better than children at bouncing a ball on a bat.

Do you agree with Alex?
You must give reasons for your answer.

The tables show information about the number of episodes and viewing figures for two television programs, Emmerdale and Eastenders, for the years 2015 to 2018

(i) In which of these years did Eastenders have its greatest number of episodes?

(1)

(ii) What was the highest viewing figure for Emmerdale between 2015 and 2018?

................... million

(1)

Explain why the viewing figures in the table may not be accurate.

Compare the number of episodes for Emmerdale in 2016 with the number of episodes for Eastenders in 2016
Give a reason for your answer.

The incomplete graph shows the highest viewing figures for Emmerdale and for Eastenders between 2015 and 2018

Use the values for the highest viewing figures for Emmerdale from the table to complete the graph.

Describe the trend for the highest viewing figures for Eastenders between 2015 and 2018

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.

The time taken, in minutes, for some runners to complete a 5 km run was recorded. The incomplete histogram and incomplete grouped frequency table give information about the times taken, in minutes, for these runners to complete the 5 km run.

(Source: www.parkrun.org.uk (opens in a new tab))

Use the information in the histogram to complete the table.

Estimate the number of runners that took less than or equal to 23 minutes to complete the race.

Identify and interpret the skew shown on the histogram.

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.

Ana collected information about the Scottish Football Championship results for the 2021/2022 season.

The composite bar chart gives some information about the number of points scored by nine of the teams.

Points are scored from wins or draws.

Raith Rovers scored 36 points from wins and 14 points from draws.

Complete the composite bar chart for Raith Rovers.

What does the overall height of each bar represent?

Compare the points scored by Dunfermline Athletic with the points scored by Queen of the South.

Some researchers investigated the hand span, in centimetres, of adult pianists by their level – international, national and amateur.

The box plots below give information about the hand spans for national level and amateur level pianists.

Circle the word in the list below that describes hand span, in centimetres, as a type of data.

qualitative     ordinal     continuous     bivariate

The table gives information about the hand spans of the international level pianists.

Using the information in the table, draw on the grid above a box plot for the hand spans of the international level pianists.

Compare the three distributions of hand spans.
Give three comparisons and interpret two of your comparisons.

Pavel owns a music shop.
He wants to investigate the keyboard sizes used by pianists with different hand spans.
He collects data about the hand spans of the pianists who use his shop.

The table gives information about the number of these pianists with hand spans in each of four size categories.

Pavel plans to sample 20 of these pianists stratified by hand span size.

Explain how Pavel can obtain his stratified sample.
You should include details of any calculations he should use.

The table shows the average heights, to the nearest cm, of Adult Males and Adult Females who were born in the year 1996 in some countries of the world.

Write down the average height of Adult Males in Italy.

Write down the country in the table in which the Adult Females have the greatest average height.

Afzal thinks that the country in the table with the greatest difference in average heights between Adult Males and Adult Females is Italy.

Is Afzal correct?
Give a reason for your answer.

Using the table, compare the average height of Adult Males in Australia, with the average height of Adult Males in Zimbabwe.

Afzal suggests drawing a time series graph to represent the data in the table.

Explain whether or not this is an appropriate graph to use.

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]

Norbert asked each of the students in his class to name their favourite fruit from Apple, Banana, Orange or Pear.

The results are shown below.

Fill in the tally chart for this information and complete the frequency column.

How many students are in the class?

Find the probability that this student’s favourite fruit is Orange.

Compare the number of students whose favourite fruit is Apple to the number of students whose favourite fruit is Pear.

Norbert decides to find the favourite fruit that is the mode.

Explain why the mode is an appropriate average for Norbert to find for this type of data.

Give one advantage of the tally chart over the raw data.

Norbert wants to draw a diagram to represent his results.

Choose the type of diagram from the list below that is most suitable for him to draw.

Sam used the internet to collect the times, in minutes, it took for 50 cyclists to compete in a hill climb competition. He used a group frequency table to record the results he collected.

(i) Give one advantage of using grouped data rather than raw data.

[1]

(ii) Give one disadvantage of using grouped data rather than raw data.

[1]

Sam used this grouped frequency table to show the results for the hill climb.

(Source: cyclinguphill.com (opens in a new tab))

Before Sam collected the data he did not know what the longest time would be. The longest time in the hill climb was 28.3 minutes.

Explain why this table cannot be used to show the data for all 50 riders.

Sam drew this frequency polygon for the hill climb results.

Sam decided not to include the value of 28.3 minutes on his frequency polygon.

Suggest a reason why Sam’s decision might be appropriate.

(i) Describe the skew of the distribution

[1]

(ii) Interpret the skew of the distribution in context.

[1]

Logan is investigating the heights of male adult giraffes and the heights of female adult giraffes.

He records the height, in metres, of each of a sample of male adult giraffes and the height, in metres, of each of a sample of female adult giraffes.

He draws the box plot below for the recorded heights of the male adult giraffes.

The table gives information about the recorded heights of the female adult giraffes.

Logan makes the following two conclusions.

1. Male adult giraffes are generally taller than female adult giraffes.

2. The heights of the female adult giraffes are more consistent than the heights of the male adult giraffes.

Assess Logan’s two conclusions.
You should show clearly the values of any statistics you use in your answer.