Translate information between graphical, numerical and algebraic forms (to…

The idea

Candidates must translate information between graphical, numerical and algebraic forms. This includes using a set of numerical data (a set of scores) from a record sheet to construct a bar graph. Scores can be grouped into categories and counted in a frequency table, drawn as a bar graph, expressed algebraically using symbols such as $<$ and $>$, or substituted into formulas such as Spearman's rho. For a bar graph, categories sit on the horizontal axis, frequency on the vertical axis, bars are of equal width and stand apart for discrete data, axes carry labels, and the vertical scale starts at zero. Translating back involves reading a chart to find a numerical total, calculating a percentage, or expressing a relationship algebraically.

What earns the marks

• Summarising numerical forms: counting the observations in each category and checking that the category frequencies sum to the total number of observations ($N$).
• Translating into algebraic forms: substituting numerical data into algebraic formulas (like Spearman's rho) or using inequality symbols to express findings (e.g., Condition A $>$ Condition B).
• Justifying the bar graph over a histogram: data fall into separate, discrete categories rather than a continuous scale, so bars must not touch.
• Translating graphical forms back into numerical/algebraic forms: stating the frequency a bar represents or calculating the difference between bars.

Common mistakes and how to put them right

• Drawing bars touching, which turns the display into a histogram, losing presentation marks for discrete categorical data.

  Put it right: Leave equal gaps between bars for discrete data.

• Starting the vertical axis part way up the scale, inflating the visual difference between conditions.

  Put it right: Start the vertical frequency axis at zero.

• Failing to translate numerical data into algebraic forms when required, such as forgetting to use standard symbols ($<$, $>$) or formula notation.

  Put it right: Use standard mathematical symbols rather than just words when asked for algebraic forms.

Exam tips

• When using a set of numerical data (a set of scores) from a record sheet to construct a bar graph, use a ruler, label both axes with the variable and unit, and leave equal gaps.
• If asked to translate a relationship algebraically, use standard mathematical symbols rather than just words.
• Where a record sheet gives frequencies, you may need to translate this numerical data into an algebraic formula for a statistical test, such as calculating $r_s$ for Spearman's rho.