Graphs and tables

A bar chart needs both a scale on the frequency axis and a label on each axis saying what it shows. Candidates draw neat bars, leave the axes unlabelled, and lose the label mark — the most repeated graph error in the subject. Make it a routine: before drawing a bar, label the horizontal axis (the category) and the vertical axis (Frequency), then mark an even scale.

A frequency table is a table: rows of categories or values, each with a tally and a frequency column. A bar chart and a histogram are graphs; drawing one when a table was asked for scores nothing. The marks are a usable table structure, a column heading recording a quantity (amount, frequency or tally), and correct category headings.

When the points fall from the upper left to the lower right the answer is a negative correlation, but candidates frequently write "positive". Trace the points with your eye: rising to the right is positive, falling to the right is negative. Always describe the direction in words, not just that a correlation exists — and never call a rising pattern negative.

A histogram showing the shape of a distribution is answered as a "bar chart" or even "correlation", and the direction of a skew is misread — histograms are weakly understood. Decide first what the graph shows: a comparison of categories, the shape of one distribution, or a relationship between two variables. A histogram displays continuous data with the bars touching.

A scatter diagram needs the points plotted and both axes labelled with the variable each one shows. Candidates plot the points but leave the y-axis unlabelled, and the labelling mark is lost — exactly as on a bar chart. Label both axes before you plot a single point.

Bars with gaps belong on a bar chart, where the categories are separate; bars that touch belong on a histogram, where the data are continuous. Drawing gaps on a histogram, or touching bars on a bar chart, misrepresents the data. Ask whether the horizontal axis carries separate categories (gaps) or a continuous scale (bars touch).

A scatter with a clear trend is often read as proof that one variable produced the change in the other. It does not: a correlation shows only that two variables change together. A third variable may drive both, and the direction of any influence is unknown from the graph. So read it as "the two tend to change together", never "one causes the other".

Reading a mode from a frequency table, candidates quote the largest frequency instead of the value beside it. The mode is the value that occurs most often, not the count. If score 6 has a frequency of 5, the mode is 6, not 5 — the 5 is how many scored 6. The same slip hits the range, taken from the values, not the frequencies.