New

New

Year 11

•

Higher

# Interquartile range

I can calculate the IQR and interpret what this means.

New

New

Year 11

•

Higher

# Interquartile range

I can calculate the IQR and interpret what this means.

## Lesson details

### Key learning points

- The interquartile range tells us how spread out the middle 50% of the data is
- This can be seen visually with a box plot
- Box plots and cumulative frequency graphs can be compared
- This comparison involves the median and interquartile range

### Common misconception

Not referring to the context of the question when comparing the data.

Highlight that just saying the median or the interquartile is bigger is of little use unless you know what the data was about.

### Keywords

Interquartile range - Interquartile range is calculated by finding Q3 − Q1. This is because it is the range from the first to the third quartile.

Give pupils the opportunity to verbalise what the median and interquartile range tell us, ensuring that the context is carefully referred to. Check that pupils understand the difference between measure of spread and a measure of central tendency.

Teacher tip

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Video

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## Starter quiz

Download starter quiz

### 6 Questions

Q1.

Anything below the __________ represents 75% of the data.

lowest value

lower quartile

median

Correct answer: upper quartile

upper quartile

highest value

Q2.

Anything below the lower quartile represents what percentage of the data?

Correct Answer: 25%, 25

25%, 25

Q3.

What is the range of the middle 50% of data?

Correct Answer: 19 cm, 19

19 cm, 19

Q4.

A wider box indicates data that is consistent.

Correct Answer: less

less

Q5.

Which class did better on average?

Correct Answer: A, a

A, a

Q6.

Which class' scores were more consistent?

Correct Answer: B

B

## Exit quiz

Download exit quiz

### 6 Questions

Q1.

Which of the following describe the interquartile range?

Highest value $$-$$ lowest value

Correct answer: Width of the box on a box plot

Width of the box on a box plot

Correct answer: The difference between the upper and lower quartiles

The difference between the upper and lower quartiles

Correct answer: $$Q_3-Q_1$$

$$Q_3-Q_1$$

Q2.

What is the interquartile range of the data represented on this box plot?

Correct Answer: 16 cm, 16

16 cm, 16

Q3.

Calculate the interquartile range from this cumulative frequency graph.

Correct Answer: 8

8

Q4.

What is the interquartile range of this set of data? 17, 13, 19, 21, 13, 14.

Correct Answer: 6

6

Q5.

This table shows information about the heights of some year 7 and 11 pupils. Compare their heights by selecting the most useful statement.

The Y11 median and interquartile range are higher than Y7.

On average the Y11 are taller and their heights are more consistent.

Correct answer: On average the Y11 are taller and their heights are less consistent.

On average the Y11 are taller and their heights are less consistent.

The Y11 median was higher, but the interquartile range is lower than Y7.

Q6.

This table shows information about the times some children and adults take to complete a puzzle. Compare their times by selecting the most useful statement.

On average the children did better and their times are more consistent.

Correct answer: On average the children did better and their times are less consistent.

On average the children did better and their times are less consistent.

The children's median was lower and their interquartile range was higher.

On average the adults did better and their times are less consistent.

The adults' median was better and their interquartile range was lower.