Box and Whisker Plots

Understanding Box and Whisker Plots

  • Box and whisker plots, also known as box plots, are graphical representations used to describe the spread and central tendency of a dataset.
  • They can display a large amount of data, and allow for easy comparison between datasets.
  • A box plot displays the minimum value, maximum value, and the quartiles of data.
  • Quartiles are values that divide the data into four equal parts.

Constructing Box and Whisker Plots

  • First, arrange your data in ascending order – from smallest to largest.
  • Identify the minimum and maximum value in your dataset.
  • Calculate the median, which is the middle number in an odd sized dataset or the average of the two middle numbers in an even sized data set.
  • Determine the lower quartile (Q1), which is the median of the lower half of data, leaving out the overall median if necessary.
  • Similarly, calculate the upper quartile (Q3), the median of the upper half of data, again leaving out the overall median if necessary.
  • Now, draw a number line and mark the minimum, Q1, median, Q3, and maximum values on it.
  • Draw a box from the first quartile to the third quartile with a line in the box representing the median, and draw the whiskers from each quartile to the corresponding minimum or maximum value.
  • Each whisker represents the variability outside the upper and lower quartiles, hence they provide a glimpse into the tails of the distribution.

Interpreting Box and Whisker Plots

  • The box in the box plot determines the interquartile range (IQR), which illustrates the middle 50% of the scores.
  • The range (difference between maximum and minimum) and the IQR give an idea about the spread of values.
  • A longer box or whisker indicates greater spread or variability in the dataset.
  • The line in the middle of the box is the median, indicating the centre of the data.
  • Comparing box plots helps identify differences between groups. Look for differences in medians, the spread of data (as indicated by the size of the box and whiskers), and any signs of skewness.
  • Outliers, if any, are usually plotted as individual points outside the whiskers.

Box and whisker plots are a popular way to display data in many fields. They offer a quick visual summary of the data, facilitating comparison across datasets and providing insights into the dataset’s symmetry and skewness.