Box Plots (Edexcel GCSE Statistics)

Box Plots

What is a box plot?

• A box plot is a graph that clearly shows key statistics from a data set

  • It shows the median, quartiles, minimum and maximum values and outliers

  • It does not show any other individual data items

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

• The middle 50% of the data will be represented by the 'box' section of the graph

  • and the lower and upper 25% of the data will be represented by each of the 'whiskers'

• Any outliers are represented with a cross on the outside of the whiskers

  • If there is an outlier then the whisker will end at the value before the outlier

• Only one axis is used when graphing a box plot

  • It is still important to make sure the axis

    • has a clear, even scale

    • and is labelled with units

• If you are given a box plot

  • You can read off the five values

    • minimum value, lower quartile, median, upper quartile and maximum value

  • And then calculate other statistics

    • like the range

    • or the interquartile range (IQR)

When are box plots used?

• Box plots are used when we are interested in splitting data up into quartiles

• Often, data will contain extreme values

  • Consider the cost of a car

    • There are far more family cars than there are expensive sports cars

  • If you had 50 data values about the prices of cars

    • and 49 of them were family cars but 1 was a sports car

    • the sports car’s value would not 'fit in' with the rest of the data

• Using quartiles and drawing a box plot allows us to split the data

  • We can see what is happening at the low, middle and high points

  • and consider any possible extreme values

How do I draw a box plot?

• You need to know five values to draw a box plot

  • Lowest data value

    • or lowest value that is not an outlier

  • Lower quartile

  • Median

  • Upper quartile

  • Highest data value

    • or highest value that is not an outlier

• Box plots are drawn accurately (usually on graph paper)

• The five points are marked by short vertical lines

  • The middle three values then 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 (middle 50% of the data)

  • The lowest data value and highest data value are joined to the box by horizontal lines

    • These are the 'whiskers'

    • They represent the lowest 25% of the data and the highest 25% of the data

  • Any outliers should be represented by crosses

    • These will be beyond the ends of the whiskers

How do I compare box plots?

• Box plots are often used for comparing two sets of data

  • Both box plots will be drawn one above the other on the same scale on the x-axis

• It is easy to see the main shape of the distribution of the data from a box plot

• If you are asked to compare box plots aim for two pairs of comments

  • The first pair of comments should mention average - i.e. the median

    • The first comment should compare the value of the medians
      e.g. the median for non-club members (12) is greater than the median for club members (8)

    • The second comment should explain it in the context of the question
      e.g. the non-club members were, on average, 4 seconds slower than the club members

  • The second pair of comments should mention spread - i.e. the interquartile range (or range)

    • The first comment should compare the value of the IQRs
      e.g. the IQR for club members (6) is lower than the IQR for non-club members (9)

    • The second comment should explain it in the context of the question
      e.g. the club members' times were less spread out than the non-club members, the club members were more consistent