Edexcel GCSE Statistics Paper 1 Higher November 2020 question paper 1ST0/1H

A presenter wants to get feedback on a lecture that she gave.

There were 467 students at the lecture.

The presenter plans to give a questionnaire to a sample of 50 of these students.

One of the questions on the questionnaire is

Circle the word from the list that best describes the type of data that this question collects.

ordinal bivariate continuous grouped

Describe how the presenter can use a list of random numbers to select a simple random sample of 50 students.

The map below gives information about the percentage change in the number of police officers in each of the 42 different police force regions of England and Wales between 2014 and 2015

Write down the percentage change in the number of police officers in region 17

In how many of the 42 regions did the number of police officers increase?

Sadiq thinks that the map shows that there was a decrease in the overall number of police officers in England and Wales between 2014 and 2015

Explain why Sadiq may not be correct.

Write down the statistical name for the type of map used in this question.

The composite bar chart shows information about the number of new car registrations for the first quarter of 2018 in the UK and in Italy for each fuel type.

(Source: European Automobile Manufacturers Association)

In total, there were more new car registrations in the UK than in Italy.

Work out an estimate for how many more.

Explain why the answer to part (a) is an estimate.

For each fuel type, compare the number of new car registrations in the UK with the number of new car registrations in Italy.

The table below shows the number of alternative fuel new car registrations in the UK for the first quarter of each year from 2015 to 2017

Michael says that the information in the table shows that the total number of alternative fuel new car registrations in the UK for 2015 to 2017 increased each year.

Explain why Michael’s conclusion may not be valid.

It was reported that 3% of the old style £1 coins are fake.

All the other old style £1 coins are genuine.

Shreya has two old style £1 coins.

She does not know if each coin is genuine or fake.

Complete the probability tree diagram.

Show that the probability that both of Shreya’s coins are genuine is 0.9409

Shreya claims that the probability that exactly one of her two coins is fake is less than 6%

Determine whether or not Shreya is correct.

The table shows information from a survey about train passengers’ satisfaction with 10 categories of train facilities in spring 2018

In which of the 10 categories was

the ‘% satisfied or good’ the least?

the ‘% dissatisfied or poor’ the greatest?

How many people said ‘satisfied or good’ for punctuality?

Michelle claims that the percentages for ‘Cleanliness of the inside’ are the most reliable for these 10 categories.

Using the information in the table, suggest why she might think this.

The cumulative frequency graph shows information about the maximum daily temperature, in °C, in Bingley for the 30 days of June 2018

Find the 90th percentile.

Interpret your 90th percentile in context.

For Bingley in June 2018, the lowest maximum daily temperature was 13 °C and the greatest maximum daily temperature was 28 °C.

Show that the greatest maximum daily temperature in June is not an outlier.

The box plot below shows information about the maximum daily temperature, in °C, in Aultbea for each day of June 2018

On the grid above, draw a box plot for the maximum daily temperatures in June 2018 for Bingley.

Compare the distributions of maximum daily temperatures in June 2018 for Aultbea and for Bingley.

Reeta read a report that said that these days more 18 to 24 year olds find out what is happening in the news from social media than find out by watching TV. She decided to investigate how the 12 000 students at her university find out what is happening in the news. Reeta wrote the following as a hypothesis: Do more students get their news from social media than from other sources?

Comment on whether it is appropriate to use this as a hypothesis.

Reeta planned to use a sample of the students at her university stratified by gender and by age.

Explain why this method of sampling would be appropriate.

Reeta found that she could not get a list of all the students at her university to use for her stratified sample. Instead she decided she would question students in the university cafeteria. Here is the data collection sheet Reeta plans to use.

Discuss whether Reeta’s data collection sheet is appropriate for her to use. You should consider how Reeta might use the responses and describe any problems she may have when she uses the data collection sheet.

Reeta’s friend George is at a different university with 18 000 students.

George carried out a similar investigation at his university so that he and Reeta could compare their results.

They each questioned the same percentage of students at the university they each attend.

They decided to compare their results by using comparative pie charts.

Explain why comparative pie charts would be appropriate.

Reeta used a circle with diameter 10 cm for her pie chart.

Calculate the diameter of the circle that George used for his pie chart.

Discuss two things that Reeta and George should have considered in planning their investigations to help improve the reliability and validity of their comparisons.

The table shows information about the performance of students in a Maths examination and in a Statistics examination.

Freya scored 62 marks in her Statistics examination.

Show that Freya’s standardised score for Statistics is 0.5

Freya’s Maths examination mark was 59 giving her a standardised score for Maths of 0.7

She thinks she did better in the Statistics examination than in the Maths examination.

Explain whether or not Freya is correct.

Freya also took a French examination. She says that her mark in this examination is below average.

Explain how Freya’s standardised score for French can be used to confirm this.

Tamiki wants to estimate the number of pigeons in a park.

He catches a sample of 48 pigeons in the park, tags each pigeon and then releases it.

A week later, Tamiki catches a sample of 20 pigeons in the park.

He uses the Petersen capture recapture formula to estimate that there are 240 pigeons in the park.

Work out how many of the 20 pigeons in Tamiki’s sample had tags.

Comment on the reliability of Tamiki’s estimate by considering the assumptions that he needed to make in order to use the Petersen capture recapture formula.

The table gives the price index number for the average rail fare in Great Britain for each of six years, with 2012 as base year.

The table also gives some of the chain base index numbers for the same information.

(Source: Office of Rail and Road)

Find, correct to 2 decimal places, the chain base index number for 2017

Chris wanted to know the percentage increase in the cost of the average rail fare in Great Britain between 2016 and 2017

Here is his working.

Explain whether or not Chris is correct.

The geometric mean of the chain base index numbers for 2013 to 2017 is 102.18

Interpret this geometric mean in the context of the average rail fare in Great Britain.

Describe the trend in visitor numbers to the museum over these three years.

For which quarter each year does the museum have the fewest visitors?

David has drawn a right-angled triangle on the graph from 2015 Quarter 1 to 2016 Quarter 4 so that he can calculate the gradient of the trend line, correct to one decimal place.

Here is his calculation.

Interpret, in context, the gradient of 1.4

David used the trend line and mean seasonal variation (or average seasonal effect) to predict the number of visitors to the museum for Quarter 2 of 2018

Comment on the validity of a prediction found in this way.

The actual number of visitors to the museum in Quarter 2 of 2018 was 203 100

Determine how close David’s prediction was to 203 100

In a town music competition, 6 groups competed against each other.

The table shows the marks awarded to each group by the invited independent judge.

The table also shows what the Mayor thought the rank order of the groups should be. (Best group is given rank 1)

Using suitable calculations, investigate how much agreement there is between the judge and the Mayor.

You may use the blank columns in the table for your working.

Fruitees sweets come in different flavours.

There are 8 sweets in a pack of mixed flavours and the flavours for each pack are chosen at random.

The mean number of strawberry flavour Fruitees in a pack of 8 sweets is 2

Ed suggests that the number of strawberry flavour Fruitees in a pack of 8 sweets can be modelled by a binomial distribution.

By considering the conditions that make a binomial distribution a suitable model, explain why Ed’s suggestion is appropriate.

One sweet is selected at random from a pack of Fruitees.

Find the probability that the flavour of this sweet is strawberry.

Ed buys a pack of Fruitees.

Find the probability that there will be exactly 3 strawberry flavour Fruitees in the pack.