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Data Distributions SAC

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Data Distributions SAC

Two Australian community teams recorded the points they scored in eight matches. Use the data below to analyse and compare their distributions. Show working for calculations and include units where appropriate.

Team

Points in each match

Kookaburras

12, 15, 16, 16, 18, 20, 22, 25

Wallabies

14, 14, 17, 18, 18, 19, 21, 31

Part A: Describe the data

Use the match scores in the table for Questions 1–4.

1.Which team has the higher mean score? Calculate both means to support your choice.

2.Find the median score for each team. What do the medians suggest about a typical match score?

3.State the mode or modes for each team. What does this tell you about how often those scores occurred?

4.Calculate the range for each team. Which team has the larger range, and by how many points?

Part B: Spread and unusual scores

For quartiles, use the median-of-halves method: split each ordered set into a lower four and an upper four, then find the median of each half.

5.Find Q1, Q3 and the interquartile range (IQR) for each team.

6.Use the 1.5 × IQR rule to check whether either team has an outlier. Show the relevant upper fence and explain your conclusion.

7.Draw parallel box plots for the two teams on the same scale. Include a number line from 10 to 35, labelled in steps of 5. For the Wallabies, show the outlier as a separate point.

Part C: Interpret and compare

Use the statistics you calculated to explain what the results might mean for the teams.

8.Which team has the smaller IQR? What does this indicate about the spread of the middle half of its scores?

9.The Wallabies' mean is 19 and their median is 18. Explain how the score of 31 affects the mean and the likely shape of their distribution.

10.A supporter says, “The Wallabies were clearly more consistent because their IQR is smaller.” Is this conclusion fully supported by the data? Compare both the IQRs and ranges in your response.

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More Maths Worksheets

Data Distributions SAC

Data Distributions SAC

Part A: Describe the data

Part B: Spread and unusual scores

Part C: Interpret and compare

3 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

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