Construct and interpret frequency tables and diagrams, bar charts and…

The idea

The display has to match the data. Counts of people in named categories, or the mean score of each condition, go in a bar chart, whose bars are drawn with gaps between them because the categories do not run into one another and could be reordered without changing the meaning. Continuous data grouped into equal class intervals, such as reaction times sorted into bands, go in a histogram, whose bars touch because the underlying scale is unbroken and the intervals follow a fixed order. Before either comes the tally: sort the raw scores into categories or intervals, total each row, and check the grand total against the number of participants to construct a frequency table. Every display needs a title, both axes labelled with what they show and their units, and a frequency scale beginning at zero, because a truncated scale makes a small difference look dramatic.

What earns the marks

• Bar chart conventions: discrete or nominal categories along the horizontal axis, frequency or mean score up the vertical axis, bars of equal width with clear gaps between them.
• Histogram conventions: continuous data along the horizontal axis in equal intervals in their natural order, frequency up the vertical axis, bars touching with no gaps, and intervals that do not overlap.
• Frequency table conventions: a column of categories or class intervals, a tally column and a frequency column, with the frequencies summing to the number of scores collected.
• Interpretation requires stating the shape of the distribution, identifying which category or interval holds the highest frequency, and relating that to the hypothesis rather than just reading the numbers aloud.

Common mistakes and how to put them right

• Drawing a histogram with gaps or a bar chart with the bars touching, which tells the examiner the data are continuous when they are categories, or the reverse.

• Leaving the axes unlabelled or omitting the unit, so the sketch cannot be read at all.

  Put it right: Labels are essential for clarity.

• Using a scattergram for the two conditions of an experiment, when a scattergram shows a relationship between two co-variables measured on the same people and not a difference between groups.

• Starting the frequency axis part way up the scale so that two nearly equal bars look very different.

Exam tips

• A sketching question requires selecting the right type of display, labelling axes with units, and accurate plotting, so ensure all three are completed even when time is short.
• Where a finished graph is printed and you are asked what it shows, give the pattern and the comparison in the terms of the study, not a description of the drawing.
• If asked to choose an appropriate display, name it and justify it by naming the level of measurement, for example that data counted into named categories are nominal and so go in a bar chart.