Box-Plots Aqa Higher

Box plots

What are box plots and when should they be used?

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

• They 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 around 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

  • Lower quartile

  • Median

  • Upper quartile

  • Highest data value

• Usually on graph paper, box plots are drawn accurately with the five points 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 often called whiskers

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

• You may be given a box plot

  • from which you can read off the five values

  • calculate other statistics like the range and interquartile range (IQR)

How do I compare box plots?

• 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 boys (12) is greater than the median for girls (8)

    • the second comment should explain it in the context of the question
      e.g. the boys were, on average, 4 seconds slower than the girls

  • 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 boys (6) is lower than the IQR for girls (9)

    • the second comment should explain it in the context of the question
      e.g. the boys times were less spread out than the girls, the boys were more consistent