Tabulation, Diagrams & Representation (Edexcel GCSE Statistics: Higher)

The population pyramid shown below gives information about the percentages of the population of Australia who are male and who are female in 2022.

Each percentage is given correct to one decimal place.

(Source: populationpyramid.net)

Write down the percentage of the population who are male in the age group 85-89.

Work out the percentage of the population who are female in the age group 15-24.

In 2022, the number of females aged 0-4 in Australia was 736 085

(Source: Australian Bureau of Statistics)

Using the information above and from the population pyramid, explain why the percentage of the population that are female and in the age group 0-4 is given as 2.8% on the population pyramid.

You must show your working.

Suraya is carrying out research into the ages of people in Australia.

She uses the information from the population pyramid to claim,

"In Australia in 2022 the number of males who were younger than 15 was smaller than the number of males who were aged 65 or older"

Explain whether or not Suraya's claim is correct.

Hermione investigated the weights of adult male and adult female polar bears.

Using secondary data, she recorded the weight, in kg, of each female in a sample of 20 adult female polar bears and the weight, in kg, of each male in a sample of 20 adult male polar bears.

She drew the box plot below for the recorded weights of the 20 adult male polar bears.

The table below gives information about the recorded weights of the 20 adult female polar bears.

Using the data from the table, draw on the grid above a box plot for the recorded weights of the adult female polar bears.

Liliana is investigating the profits of a market stall trader.

Liliana found out data on the actual profits of each of 349 items sold by the market stall trader in the previous week.

The histogram below was drawn using Liliana's data.

A negative profit for a sale means that a loss was made.

In the previous week, 21 items were sold at a loss.

Find out how many items did not make a profit of more than £10.

Liliana decides that an item that makes a profit of £10 or more is considered a 'high profit' item.

Liliana says that more than 1 in 4 items that the market stall trader sells is a 'high profit' item.

Determine whether or not Liliana is correct.

You should comment on the reliability of your conclusion.

The movie genre preferences of students from two different schools were investigated.

The students from each school were asked to select their preferred genre of movie from the following options: comedy, action, horror and romance.

The comparative pie charts below show information about the number of students in each school that preferred the different movie genres.

The pie charts are drawn accurately and the angles for the comedy genre in each are given.

The radius of the pie chart for school B is greater than the radius of the pie chart for school A.

Explain what can be deduced from this information.

40 students in school A preferred comedy movies.

Given that the radius of the larger pie chart is 3 cm and the radius of the smaller chart is 2 cm, work out the number of students from school B that also preferred comedy movies.

The cumulative frequency graph gives information about the height, in metres, of 52 giant redwood trees.

(i) Find an estimate of the 25th percentile of this information.

[2]

(ii) Interpret this value in context.

[1]

Half of the giant redwood trees have a height between 66 metres and metres.

Work out an estimate for the value of .

The cumulative frequency step polygon shows information about the numbers of daily complaints received by a company over 100 days.

Explain why a cumulative frequency step polygon is more appropriate for this data rather than a cumulative frequency diagram.

Using the cumulative frequency step polygon, find, for the number of daily complaints,

(i) the median,

[1]

(ii) the interquartile range,

[2]

(iii) the mode.

[1]

Write down the largest number of daily complaints.

Find the number of days that received more than 9 complaints.

A school of 2000 students held an election for Head Student. The bar chart shows the results of the vote.

Ed says:

"Dubheasa received at least twice as many votes as any other candidate!"

Do you agree with this statement?
Give a reason for your answer.

Explain why the bar chart could be considered to be misleading.

Francis wants to show the proportion of the votes that each candidate received.

What type of statistical diagram could Francis draw?

A survey is taken for a primary school class to check which vegetables they like before their Christmas lunch is cooked.

The Venn diagram below shows the number of children who like parsnips and the number of children who like Brussels sprouts .

Use the Venn diagram to fill in all the values in the two-way table below.

The frequency polygon below has been drawn using grouped data about the heights of a sample of plants, measured in centimetres.

The groups for the data each have the same width.

Alan looks at the frequency polygon and suggests that the most common height of plant is 12.5 cm.

Comment on Alan's suggestion.

Alan's friend Charlie calculates the range of the heights of the plants using the frequency polygon as follows

27.5 - 2.5 = 25 cm

(i) Explain why Charlie is incorrect.

[1]

(ii) Find the maximum range of heights of the plants.

[1]

(iii) Find the minimum range of heights of the plants.

[1]

The cumulative frequency graph shows information about the daily humidity, in %, in Bournemouth for the 30 days of September of 2024.

(Source: WeatherOnline)

Find the percentage of days for which the humidity was greater than 70%

For Bournemouth in September 2024, the maximum daily humidity was 100% and the minimum daily humidity was 50%.

Show that the minimum daily humidity is not an outlier.

The box plot below shows information about the daily humidity (%) in Carlisle for each day of September 2024.

On the grid above, draw a box plot for the daily humidity in September 2024 for Bournemouth.

Compare the distributions of daily humidity in September 2024 for Carlisle and Bournemouth.

The pie charts show information about the numbers of children who trained in different sports activities at a summer activity camp in 2023 and 2024.

The pie charts do not show that there were more children who attended the summer activity camp in 2024 than in 2023.

Explain why.

The number of children who attended the summer activity camp in 2024 to train in football was 252.

Work out the number of children that attended the summer activity camp in 2024 who trained in athletics.

The table gives information about the total number of children to attend the summer activity camp in 2023 and 2024.

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

Explain, giving reasons, how he should do this, and why it is more appropriate.

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

Felicia believes that the weights of African elephants at birth are normally distributed.

She collects information about the weights, in kg, of 23 African elephant newborn calves.

She draws the histogram below, showing the distribution of the weights.

Felicia also calculates that the mean of the weights is 99.39 kg and the standard deviation is 7.08 kg.

Calculate an estimate for the proportion of these 23 African elephant newborn calves whose weight is within 1 standard deviation of the mean.

Give your answer correct to 2 significant figures.