Edexcel GCSE Statistics Paper 1 Higher June 2019 question paper 1ST0/1H

The diagram represents a children’s playground that has been divided into 20 squares of equal area.

In the playground there are some children and some play equipment only.

The number of children in each square at 11 am one Saturday is shown below.

Use the information above to complete this choropleth map.

Grace concludes that there is likely to be more play equipment in that part of the playground represented by the squares in the top left hand corner of the choropleth map than elsewhere in the playground.

Assess the validity of Grace’s conclusion with reference to the choropleth map.

The cumulative frequency diagram gives information about the heights, in metres, of a sample of 100 oak trees in Camden, London.

Using the cumulative frequency diagram, complete the table below for the heights of

The box plot shows information about the heights, in metres, of a sample of maple trees in Camden, London.

For the sample of oak trees the least height is 2.0 m the greatest height is 22.3 m

On the grid above, draw a box plot for the heights of the sample of oak trees.

Compare the two distributions of heights. Give three comparisons and interpret one of these comparisons.

The table gives information about the numbers of students from different types of schools who applied to Cambridge University in 2016

(Source: www.cam.ac.uk)

Richard is going to take a sample of 200 of these students stratified by gender.

Work out how many female students there should be in this sample.

Describe a situation when it would not be appropriate to take a sample stratified by gender.

Richard could have used a different category for his stratified sample.

What is this different category?

A student is to be chosen at random from the 9963 students.

F is the event that the student chosen is female.

I is the event that the student chosen is from an independent school.

M is the event that the student chosen is from a maintained school.

Explain why the event F and the event I are not mutually exclusive.

Find P(I or M).

Diana is a journalist working for a local newspaper.

She is writing a newspaper article about how house prices in the local area have changed.

Diana has house price data for 1996 and for 2016

She plans to include in her article the median house price for 1996 and the median house price for 2016

Mika thinks that Diana should also include in her article the interquartile range of house prices for 1996 and the interquartile range of house prices for 2016

Give one reason why including the interquartile ranges in the article would be appropriate.

Give one reason why including the interquartile ranges in the article would not be appropriate.

Chris is carrying out an experiment to see if left handed people have a better memory than right handed people. He has two groups of people with the same number of people in each group.

Group A contains left handed people only and group B contains right handed people only.

Each person is given 15 objects to memorise and then they are tested to see how many objects they remember.

The variables for the experiment are shown in the table.

For each variable, put a tick () in the correct column of the table to show the type of variable.

Chris is not sure whether to work out the mean or the median number of objects each group remembered.

Describe a situation for which it would be more appropriate to work out the median than the mean.

Chris worked out these summary statistics for the number of objects people in group A remembered.

Lower quartile = 5 Median = 7 Upper quartile = 8

Sanjit is a member of group A.

He remembered 14 objects.

Determine whether or not the number of objects Sanjit remembered is an outlier.

The table gives the crude birth rates and crude death rates, per 1000 people, for two Caribbean islands in the year 2015

(Source: www.data.worldbank.org)

Jamil concludes that the crude birth rate and the crude death rate for Saint Lucia show that the population of Saint Lucia increased in 2015

Explain how the data can be used to support Jamil’s conclusion.

Give a reason why the data might not support Jamil’s conclusion.

In 2015, the total population of Barbados was 284 217

Using the formula below, work out the number of births in Barbados in 2015

The standard population of Barbados and of Saint Lucia for three different age groups in 2015 is shown in the table.

Give an interpretation of the number 64 in the table.

Compare the crude death rate for Barbados with the crude death rate for Saint Lucia.

By referring to the information in the Standard population table, suggest a reason for your comparison.

The pie charts show information about the numbers of visitors to the UK for the given reasons in January 2017 and in July 2017

The pie charts do not show that there were more visitors to the UK on business in January 2017 than in July 2017 Explain why.

The number of visitors to the UK in January 2017 in order to visit friends or relatives is 1 080 733

Work out the number of visitors to the UK in January 2017 to have a holiday.

The table gives information about the total number of visitors to the UK in January 2017 and in July 2017

Ruth thinks there is a more appropriate way to draw pie charts now that she knows the information in the table.

Explain, giving reasons, how she should do this.

You must refer to the information in the table in your explanation.

The table shows some of the expected percentile weights (kg) for babies up to 6 months old, based on data collected from the World Health Organisation.

Antonia says,

“An estimate of the expected 30th percentile for a 3 month old boy is 5.8 kg”

Explain why this is not a good estimate.

Compare the expected 9th to the 91st interpercentile range for 5 month old girls with the expected 9th to the 91st interpercentile range for 5 month old boys. You must show your working.

Give an interpretation of your comparison in part (b).

According to an internet site, an estimate of the number of reindeer in a region of Ontario is 5000

(Source: www.ontario.ca

Giovani wants to verify this estimate.

He goes to the region of Ontario, captures a sample of 250 reindeer, attaches a tag to each reindeer and then releases the 250 reindeer back into the same region of Ontario.

Three days later, Giovani returns to the same region of Ontario and catches a sample of 98 reindeer.

He finds that 5 of these reindeer are tagged.

Giovani concludes that this information can be used to verify the estimate of 5000

Discuss the appropriateness of Giovani’s method and of his conclusion.

As part of your discussion you should show your calculations and state any assumptions made.

The table shows information about the amount of time that each member of a group of 46 teenagers spent on social media during one day.

Time spent on social media (t minutes)	Frequency
0 t 50	1
50 t 100	4
100 t 150	8
150 t 200	17
200 t 300	16

Use linear interpolation to find an estimate of the median time spent on social media by the 46 teenagers.

The average person will spend approximately 116 minutes on social media each day.

(Source: www.socialmediatoday.com)

Compare the amount of time spent on social media by the 46 teenagers with the amount of time spent on social media by the average person.

The table below gives the mean, the standard deviation and the median for the times spent on social media during one day by a sample of sixty year olds.

Calculate the skew of the times spent on social media by the sample of sixty year olds.

Interpret your answer to part (b).

Some students at a school walk home and some students go home by bus.

The times taken by the students at the school to walk home have a mean of 25 minutes and a standard deviation of 6 minutes.

The times taken to walk home can be modelled by a normal distribution.

Shanaya says,

“More than 80% of the students who walk home take between 19 and 37 minutes”

Use statistical calculations to assess Shanaya’s conclusion.

The diagram below shows a sketch of the distribution of the times taken by students to go home by bus.

Explain why it is not appropriate to use a normal distribution to model the times taken by students to go home by bus.

On the same grid, sketch a diagram showing the distribution of the times taken by students to walk home.

A is the event that a student walks to school, where P(A) = 0.6

B is the event that a student is driven to school, where P(B) = 0.3

Some students are driven some of the way to school and then they walk the rest of the way to school, where P(A and B) = 0.15

A student is picked at random from the students at the school.

Work out P(A or B).

Mr Singh collected data about the number of students in each of three classes in his school and the mean mark of each class in a science test.

The table gives some information about his data.

Mr Singh plans to use one of the following two methods to work out the mean mark of all the students in the three classes.

Method 1 Work out the mean of 63, 72 and 55

Method 2 Given that Mr Singh knows the value of n, work out the weighted mean mark for the three classes.

For each of these two methods, assess whether or not the method is an appropriate way to work out the mean mark of all the students in the three classes.

Method 1

Method 2

The weighted mean mark for the three classes is 64.1 correct to one decimal place.

Calculate the value of n.

The three classes have also taken a mathematics test.

Mr Singh thinks that there is a relationship between the science marks and the mathematics marks.

He draws a scatter diagram for each of the three classes.

For each diagram, he used the science mark, x, for each student in the class as the explanatory variable and the corresponding mathematics mark, m, as the response variable.

Mr Singh then used statistical software to find the equation of the regression line for the data in each scatter diagram.

Here are the equations.

Mr Singh thinks that he has made a mistake with one of the equations.

Compare the equations of the three regression lines and explain which one is most likely to be incorrect. Explain your answer in context.

Mr Singh decides to compare the science marks, x and the history marks, y, of class A.

He uses statistical software to draw this scatter diagram and the regression line.

Find an equation of the regression line of this scatter graph in the form y = a + bx

A company wants to investigate the number of sick days its employees have off work.

The company uses a questionnaire.

Here is one of the questions on the questionnaire.

Assess the appropriateness of the method the company uses.

All the company’s employees completed the question.

615 ticked box A.

102 ticked box B.

Show that an estimate of the number of employees who ticked box A because they answered yes to the question is 137