Comparing and describing distributions.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Comparing and describing distributions

Further statistics

Lesson 6 of 6

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up

Further statistics

Lesson 6 of 6

Answer each one, then check.

1

Name a measure of average.

2

Name a measure of spread.

3

What is an outlier?

4

Does an outlier affect the median much?

5

Does an outlier affect the mean much?

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up - Answers

Further statistics

Lesson 6 of 6

1

Name a measure of average.

Mean, median or mode

2

Name a measure of spread.

Range or interquartile range

3

What is an outlier?

A value far from the others

4

Does an outlier affect the median much?

No

5

Does an outlier affect the mean much?

Yes

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

Further statistics

Lesson 6 of 6

1

Compare two distributions using an average and a measure of spread.

2

Choose the best average and spread.

3

Describe skew.

4

Write comparisons in context.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Further statistics

Lesson 6 of 6

COMPARING

To compare distributions, compare one average and one measure of spread, using numbers and context.

A higher average means the values are generally bigger. A larger spread means the values are less consistent.

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The Shape of a Distribution

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Lesson 6 of 6

The tail shows the direction of the skew.

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Choosing Averages and Spreads

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Lesson 6 of 6

AVERAGES

• Mean uses every value, but is affected by outliers.

• Median is not affected by outliers.

• Mode is the most common value.

SPREADS

• Range uses the largest and smallest values only.

• IQR is the spread of the middle 50%.

• IQR is not affected by outliers.

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Comparing Two Data Sets

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Lesson 6 of 6

Boys: median 12.4 s, IQR 1.2 s. Girls: median 13.1 s, IQR 2.0 s. Compare the times for the 100 m sprint.

1

Average

Boys' median 12.4 is lower than girls' 13.1

2

Meaning

On average the boys were faster

3

Spread

Boys' IQR 1.2 is smaller than girls' 2.0

4

Meaning

The boys' times were more consistent

ANSWER

On average the boys were faster (median 12.4 s against 13.1 s) and their times were more consistent (IQR 1.2 s against 2.0 s).

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Comparing Cumulative Frequency Curves

Further statistics

Lesson 6 of 6

Two cumulative frequency curves show the times of Group A and Group B (60 people each). Group A: median 28, IQR 16. Group B: median 22, IQR 17. Compare the groups.

1

Median

B's median is lower

2

Spread

The IQRs are very close

3

Conclusion

Group B were quicker on average, with a similar spread

ANSWER

Group B were quicker on average (median 22 against 28) and both groups had a similar spread (IQR 17 against 16).

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Describing Skew

Further statistics

Lesson 6 of 6

The mean is 30 and the median is 25. Describe the skew.

1

Compare

The mean is greater than the median

2

Shape

The tail is to the right

ANSWER

The distribution has positive skew.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Writing Good Comparisons

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Lesson 6 of 6

A full-mark answer has four parts.

An average

Compare medians or means, quoting numbers.

A spread

Compare IQRs or ranges, quoting numbers.

Context

Write in terms of the situation.

A conclusion

For example "so Group B were faster and more consistent".

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Key Terms

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Lesson 6 of 6

Distribution

How values are spread across a data set.

Skew

A lack of symmetry; the tail shows the direction.

Symmetrical

The same on both sides of the middle.

Outlier

A value much larger or smaller than the rest.

Consistent

Little variation.

In context

Written using the real situation.

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Further statistics

Lesson 6 of 6

YOUR TASK

Write the Comparison

12 minutes

Set A: mean 24, range 10. Set B: mean 21, range 25. Write a comparison of the two sets.

1

Compare averages.

2

Compare spreads.

WHAT A GOOD ANSWER SHOWS

On average Set A has higher values (mean 24 against 21) and Set A is more consistent (range 10 against 25).

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Can I...?

Further statistics

Lesson 6 of 6

Compare two medians.

Compare two IQRs.

Compare means and ranges.

Read a cumulative frequency graph.

Describe skew.

Write in context.

Use numbers.

Explain the choice of average.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Compare one average and one spread.

Median and IQR are best if there are outliers.

Positive skew: long tail to the right, mean above median.

Give numbers and a conclusion.

EXAM FOCUS

The cumulative frequency graph shows the times taken by two groups. Compare the times. (4 marks)

Compare an average and a spread, and use the words of the question.

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