What does the box in a box plot represent?

The interquartile range (IQR), the middle 50% of the data between the lower and upper quartiles.

What do the whiskers on a box plot represent?

The lowest 25% of the data (left whisker) and the highest 25% (right whisker). They join the box to the minimum and maximum values.

Is the median always in the middle of the box?

No. The median line is inside the box but may not be centrally placed. It depends on the distribution of the middle 50%.

When are box plots particularly useful?

When data contains extreme values or outliers. They split data into quartiles so we can see low, middle, and high points without extreme values distorting the view.

How do you compare two box plots?

Two pairs of comments: 1) Compare medians (average) and explain in context. 2) Compare IQRs (spread) and explain in context. Smaller IQR means more consistent.

What does a smaller IQR indicate?

More consistent data. The middle 50% is less spread out.

How do you calculate IQR from a box plot?

IQR = upper quartile - lower quartile. Read these values from the box edges.

What statistics can you calculate from a box plot?

Range (highest - lowest) and IQR (upper quartile - lower quartile). You can also read the median and quartiles directly.

Box Plots | AQA GCSE Maths

Q: What are the five values needed to draw a box plot?

Lowest data value, lower quartile, median, upper quartile, highest data value.

Box Plots

Summary

Box plots (box-and-whisker diagrams) display the five-number summary: lowest value, lower quartile, median, upper quartile, highest value. They split data into quartiles and are useful when data contains extreme values. The box shows the interquartile range (middle 50%); whiskers show the lowest and highest 25%. Compare box plots by commenting on median (average) and IQR (spread).

1. What are Box Plots?

Box plots are also known as box-and-whisker diagrams.

They are used when we want to split data into quartiles.

Useful when data contains extreme values (e.g. car prices: many family cars, few expensive sports cars).

Box plots let us see what happens at low, middle, and high points and consider extreme values.

2. The Five Values Needed

Lowest data value.

Lower quartile (Q1, 25th percentile).

Median (Q2, 50th percentile).

Upper quartile (Q3, 75th percentile).

Highest data value.

These five values are marked by short vertical lines on graph paper.

3. Drawing a Box Plot

Plot all five points as short vertical lines.

The middle three values (lower quartile, median, upper quartile) form a box with the median line inside.

The median will not necessarily be in the middle of the box.

The box represents the interquartile range (IQR), the middle 50% of the data.

The lowest and highest values are joined to the box by horizontal lines called whiskers.

Whiskers represent the lowest 25% and highest 25% of the data.

4. Reading from a Box Plot

You can read off the five values from a given box plot.

Calculate range = highest - lowest.

Calculate IQR = upper quartile - lower quartile.

IQR measures spread of the middle 50%; a smaller IQR means more consistent data.

5. Comparing Box Plots

6. Worked Example

Box Plots

Summary

1. What are Box Plots?

Box plots are also known as box-and-whisker diagrams.

They are used when we want to split data into quartiles.

Useful when data contains extreme values (e.g. car prices: many family cars, few expensive sports cars).

Box plots let us see what happens at low, middle, and high points and consider extreme values.

2. The Five Values Needed

Lowest data value.

Lower quartile (Q1, 25th percentile).

Median (Q2, 50th percentile).

Upper quartile (Q3, 75th percentile).

Highest data value.

These five values are marked by short vertical lines on graph paper.

3. Drawing a Box Plot

Plot all five points as short vertical lines.

The middle three values (lower quartile, median, upper quartile) form a box with the median line inside.

The median will not necessarily be in the middle of the box.

The box represents the interquartile range (IQR), the middle 50% of the data.

The lowest and highest values are joined to the box by horizontal lines called whiskers.

Whiskers represent the lowest 25% and highest 25% of the data.

4. Reading from a Box Plot

You can read off the five values from a given box plot.

Calculate range = highest - lowest.

Calculate IQR = upper quartile - lower quartile.

IQR measures spread of the middle 50%; a smaller IQR means more consistent data.

5. Comparing Box Plots

Aim for two pairs of comments: one about average (median), one about spread (IQR or range).

First pair: Compare medians. E.g. median for boys (12) is greater than for girls (8). Then explain in context: boys were on average 4 seconds slower.

Second pair: Compare IQRs. E.g. IQR for boys (6) is lower than for girls (9). Then explain: boys times were less spread out, more consistent.

Remember: smaller range or IQR means more consistent data.

6. Worked Example

Union Athletic: median 4, lower quartile 2, upper quartile 7.5, lowest 1, highest 10.

Draw: plot five vertical lines, draw box around middle three, whiskers to outer two.

Compare with Albion Rovers: Union Athletic has higher median (4 vs 3), so on average scored more goals. Union Athletic has higher IQR (5.5 vs 3.5), so Albion Rovers were more consistent.