Interpreting statistical data
Section: Statistics | Syllabus: Cambridge IGCSE Mathematics (0580)
Reading Bar Charts and Pictograms
- A bar chart displays categorical data as bars of equal width with gaps between them; the height of each bar shows its frequency, read against the scale on the vertical axis
- A pictogram displays data using repeated symbols; a key shows how many items a full symbol represents, and a partial symbol represents a fraction of that amount
- If one bar or symbol total is missing but the overall total is known, subtract the known values from the total to find it
Worked Example: Reading and Completing a Bar Chart
- Question: 32 people were asked how they usually travel to work: bus, car, or bike. The bar chart shows car =14 and bike =6; the bus bar has not yet been drawn. (a) Find the height of the bus bar. (b) How many more people travel by car than by bus?
- Step 1 (a): Car and bike together =14+6=20
- Step 2 (a): Bus =32-20=12
- Step 3 (b): Car minus bus =14-12=2
- Answer: the bus bar has height 12; 2 more people travel by car than by bus
Common Mistakes
MistakeMisreading a bar's height against the wrong gridline, especially when the scale goes up in steps other than 1
Fixcheck the value of each gridline first (e.g. steps of 5 or steps of 2) before reading any bar's height from the chart
MistakeCounting a partial symbol on a pictogram as a whole symbol, or ignoring it completely
Fixa partial symbol represents that fraction of the key's value - e.g. half a symbol worth 4 people represents 2 people, not 0 or 4
Drawing Inferences from Data
- Interpreting data means going beyond reading single values - explaining what the data shows, spotting patterns, and comparing categories or data sets
- Any conclusion should refer to specific figures from the data to support it (e.g. "18 out of 30" rather than just "a lot")
- A conclusion should only claim what the data actually supports - avoid over-generalising from a small or limited sample
Worked Example: Comparing Two Data Sets
- Question: The table shows the number of days in a 30-day month on which each of two shops, P and Q, sold more than 50 items.
On how many more days did Shop P sell more than 50 items compared with Shop Q?Shop Days selling more than 50 items Days not P 18 12 Q 11 19 - Step 1: Shop P sold more than 50 items on 18 days; Shop Q sold more than 50 items on 11 days
- Step 2: 18-11=7
- Answer: Shop P sold more than 50 items on 7 more days than Shop Q
Common Mistakes
MistakeDrawing a sweeping general conclusion (e.g. "Shop P is always better") from a single month's data
Fixa conclusion should stay within what the given data actually covers - one month's figures only support a conclusion about that month
MistakeComparing the wrong pair of figures between two categories or data sets
Fixidentify exactly which two figures the question is asking to compare before subtracting or commenting on them
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