Charts and Graphs
Section: Statistics | Syllabus: Cambridge Lower Secondary Checkpoint Mathematics (0862)
Bar Charts: Dual and Compound
- Dual bar chart: bars for two categories sit side by side at each label, for direct comparison.
- Compound (stacked) bar chart: bars are stacked on top of each other to show how a total is made up of parts.
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Question: A compound bar chart shows total sales of 120 units in March, with Product A making up 80 units. How many units were Product B?
- Step 1: 120 − 80
- Answer: 40 units
Pie Charts
A pie chart shows proportions as sectors of a circle. Each sector's angle = (frequency ÷ total) × 360°.
Pie chart angles always add up to 360°
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Question: A survey of 60 people asks favourite fruit: Apple 24, Banana 15, Orange 21. Find each sector's angle.
- Step 1: Apple: (24/60) × 360 = 144°
- Step 2: Banana: (15/60) × 360 = 90°
- Step 3: Orange: (21/60) × 360 = 126°
- Check: 144 + 90 + 126 = 360° ✓
- Answer: Apple 144°, Banana 90°, Orange 126°
Line Graphs and Time Series Graphs
A line graph connects data points with straight lines. A time series graph specifically plots time on the horizontal axis, useful for spotting trends.
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Question: A time series graph shows a shop's monthly sales rising steadily from January to June, then dropping sharply in July. What might this indicate?
- The steady rise could reflect growing seasonal demand.
- The sharp July drop could indicate a seasonal effect, reduced demand, or a supply issue.
Frequency Polygons
A frequency polygon plots the midpoint of each class interval against its frequency, then joins the points with straight lines - useful for comparing the shape of two distributions.
Plot each midpoint against its frequency, then join the points with straight lines only - no bars
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Question: A grouped frequency table has classes 0-10 (frequency 4), 10-20 (frequency 9), 20-30 (frequency 12), 30-40 (frequency 5). Describe how to plot the frequency polygon.
- Step 1: Find each midpoint: 5, 15, 25, 35
- Step 2: Plot (5,4), (15,9), (25,12), (35,5)
- Answer: Join the four points with straight lines
Scatter Graphs: Correlation
A scatter graph plots pairs of values to show whether a relationship (correlation) exists between two variables.
- Positive correlation: points trend upward - as one variable increases, so does the other.
- Negative correlation: points trend downward - as one variable increases, the other decreases.
- No correlation: no clear pattern.
- Strong correlation: the points lie close to a clear line or pattern.
- Weak correlation: a trend is visible, but the points are more spread out from it.
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Question: A scatter graph plots hours of study against exam score, with points trending upward from bottom-left to top-right. What type of correlation is this?
- Answer: Positive correlation - more study hours are associated with higher exam scores
Scatter Graphs: Line of Best Fit
When a scatter graph shows correlation, a line of best fit can be drawn through the points, following their overall trend with roughly equal numbers of points above and below it. It can be used to estimate a value for one variable given the other - but only safely WITHIN the range of the plotted data.
Reading up from x = 5 to the line of best fit, then across, gives an estimated score of about 60
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Question: Using the line of best fit shown, estimate the exam score of a student who studied for 5 hours.
- Step 1: Find 5 hours on the horizontal axis, and draw a line up to the line of best fit
- Step 2: From that point, read across to the score axis
- Answer: approximately 60 marks
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Question: Explain why it would NOT be sensible to use this line of best fit to estimate the score of a student who studied for 20 hours.
- Answer: 20 hours is far outside the range of the data actually collected (1 to 8 hours). Extrapolating this far beyond the plotted range is unreliable, since the relationship might not continue in the same way - for example, a score can't exceed 100, so the trend must eventually level off.
Stem-and-Leaf Diagrams
A stem-and-leaf diagram splits each value into a stem (all digits except the last) and a leaf (the last digit), keeping the actual values visible while showing their distribution shape.
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Question: The ages of 8 people are: 23, 25, 31, 34, 34, 42, 45, 47. Construct a stem-and-leaf diagram.
- Stem 2: leaves 3, 5 (23, 25)
- Stem 3: leaves 1, 4, 4 (31, 34, 34)
- Stem 4: leaves 2, 5, 7 (42, 45, 47)
- Answer: Key: 2 | 3 means 23
Back-to-Back Stem-and-Leaf Diagrams
A back-to-back stem-and-leaf diagram compares two data sets using ONE shared column of stems in the middle: leaves for the first data set are written on the LEFT (ascending outward, smallest closest to the stem), and leaves for the second data set are written on the RIGHT (ascending outward, smallest closest to the stem).
Chess Club ages sit on the left of the shared stem; Art Club ages sit on the right
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Question: Chess Club ages: 22, 25, 25, 31, 34, 38, 41. Art Club ages: 19, 23, 28, 28, 30, 33, 45. Construct a back-to-back stem-and-leaf diagram, then find the median age of each club.
- Step 1: Sort each group and split into stem (tens) and leaf (units) - shown in the diagram above
- Step 2 (Chess median): 7 values ordered 22, 25, 25, 31, 34, 38, 41 - the 4th value is the median
- Step 3 (Art median): 7 values ordered 19, 23, 28, 28, 30, 33, 45 - the 4th value is the median
- Answer: Chess Club median = 31, Art Club median = 28
Choosing the Right Representation
Cambridge exams often ask you to choose AND explain which representation suits given data - not just name one. Match the representation to what you need to show:
Interactive revision notes, videos and practice questions load below.