Representation of data covers histograms, cumulative frequency graphs, box plots, stem-and-leaf diagrams, and the mean, median, quartiles and standard deviation, including from grouped data. The reports show that students know the formulae. The marks go missing in the details of the diagrams and in what goes into the grouped calculations. This guide collects what Cambridge examiners say students get wrong, based on recent reports.
Summarised in our own words from a reading of the examiner reports.
Mistakes that cost marks
- Class midpoints. Using the class width or the upper boundary as the midpoint. In one report the midpoints of the first and last class were found incorrectly, with 7.25 and 64.5 the most common errors. Another report mentions 4.5 used as the midpoint of the first class, and one mentions the cumulative frequency being used instead of the frequency.
- Class boundaries. Assuming that the upper boundary of a class is the value stated in the table, which leads to wrong frequency densities and wrong placement of bars on a histogram.
- Variance and standard deviation. Squaring the frequency instead of the midpoint, not dividing by the total frequency (in one report, 32460 not divided by 60), and leaving out the square root at the end, so giving the variance instead of the standard deviation. Others used cumulative frequencies, upper bounds or class widths in the formula.
- Combining sets of data. Finding the mean of each set separately and adding them, or adding all the values given and dividing by 45.
- Percentiles and quartiles. Confusing the 60th percentile with a cumulative frequency of 60 and drawing a line from 60. In another report the problem was misreading the success criteria and finding the 38th percentile rather than the 62nd. Others assumed that the positional value of the lower quartile was a time.
- Interquartile range. Stating only the upper and lower quartiles without subtracting, or subtraction errors such as 82 − 65 = 17.
- Median of grouped data. Stating the middle class from the table without any justification.
- Histograms. A blunt or thick pencil hid the height of the bar. Reports also say a ruler should be used, because statistical diagrams must be accurate.
- Cumulative frequency graphs. Not starting the curve at the right point, such as (0, 0) in one question, labelling the horizontal axis only "time" without the units, choosing a small scale that made plotting hard, and allowing the graph to rise above the total before the last point.
- Stem-and-leaf diagrams. Not ordering the leaves, using a split stem that did not suit the data range, using a single digit for the stem (such as 8 instead of 18), leaving out the key, or leaving out the units from the key. Leaves not aligned vertically was also frequent, along with commas between values, and a missing heading.
- Box plots. Not labelling the scale, and drawing a single unlabelled box plot.
- Labels. The most common error in several reports was to label the axes incompletely: "time" or "minutes" but not both, or no reference to the variable in the data table.
What examiners advise
- Draw diagrams in pencil with a ruler, with a sharp pencil so lines are clear. If you make an error, erase it carefully so that the alignment of a stem-and-leaf diagram is kept.
- Label axes with the variable and its units.
- Include the key, with units, in a stem-and-leaf diagram.
- List the frequencies and midpoints before substituting into the mean or variance formula, and show the calculation in full.
- Identify each answer clearly when a question asks for more than one item.
Habits that help
- Write the class boundaries under each class in the table before you do anything else.
- When finding a percentile, write down the cumulative frequency value you need (for example 0.62 of the total) and then read across.
- After finding a standard deviation, check that it is a sensible size for the data and that you took the square root.
Questions students ask
How do I find the midpoint of a class for grouped data?
Use the middle of the class boundaries, not the class width or the upper boundary. Reports record the midpoints of the first and last class found incorrectly. List the frequencies and midpoints before you substitute into the mean or variance formula.
Why are my histogram frequency densities wrong?
Often because the upper boundary was assumed to be the value in the table. Check the class boundaries before working out frequency densities and placing the bars. Draw bars in pencil with a ruler.
What mistakes happen with variance and standard deviation from grouped data?
Squaring the frequency instead of the midpoint, not dividing by the total frequency, and leaving out the square root at the end. Show the calculation in full.
How do I read a percentile from a cumulative frequency graph?
Work out the cumulative frequency value you need, such as 0.62 of the total, then read across. Students confused the 60th percentile with a cumulative frequency of 60. The curve should also start at the right point.
What must a stem-and-leaf diagram include?
Ordered leaves, a sensible stem, a key with units, and consistent alignment. Reports record leaves not ordered, a single digit used for the stem when two were needed, and the key left out.
Practice this topic
Ready to try some? Work through past paper questions on this topic one at a time. Attempt each question fully first, and open the mark scheme only afterwards.