Measures of Dispersion (Edexcel GCSE Statistics: Foundation): Exam Questions

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.

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]

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]

The cumulative frequency step polygon shows information about the number of goals scored in each of 28 matches played by the German women’s national football team.

(Source: www.worldfootball.net/teams/deutschland‑frauen‑team/)

Give a reason why a cumulative frequency step polygon is used to represent this information rather than a cumulative frequency curve.

Find the mode of the number of goals scored.

Find the number of these matches where

(i) exactly 6 goals were scored,

[1]

(ii) more than 6 goals were scored.

[2]

In 24 matches fewer than n goals were scored.

Find the value of n

Klara tries to calculate the interquartile range of the number of goals scored.

She gets an answer of 14

Explain how you know that her answer is incorrect.