What you'll learn
Statistical diagrams turn raw data into pictures that reveal patterns at a glance, and they are an important part of the Statistics section of the CSEC Mathematics syllabus. You will learn to draw and interpret the main diagrams CSEC expects — bar charts, pie charts, pictograms, line graphs and frequency polygons — and to choose the right one for a given set of data. You will also learn to read information from these diagrams to answer questions, and to calculate the angles and frequencies they are built from. These skills appear in Paper 1 and Paper 2 and connect to measures of average, frequency tables and data handling, which are common sources of marks in the exam.
Key terms and definitions
Data — the values or information collected, often organised in a frequency table.
Frequency — how many times a value or category occurs.
Bar chart — a diagram using bars of equal width whose heights show frequency.
Pie chart — a circle divided into sectors, each representing a category's share of the total.
Pictogram — a diagram using symbols, each standing for a fixed number of items.
Line graph — points joined by straight lines, used to show change over time.
Frequency polygon — a line graph of frequencies plotted at class midpoints, used for grouped data.
Core concepts
Bar charts
A bar chart displays categories along the horizontal axis and frequency on the vertical axis, with bars of equal width separated by gaps. The height of each bar shows the frequency of that category. Bar charts are ideal for comparing discrete categories such as favourite subjects or types of fruit sold. Always label both axes and use a consistent scale, and read frequencies straight from the bar heights.
Pie charts
A pie chart shows how a whole is divided among categories, using sectors of a circle. Because a full circle is 360°, the angle for each category is:
angle = (category frequency ÷ total frequency) × 360°.
To read a pie chart, reverse the process: a sector's fraction of 360° equals its fraction of the total. Pie charts are best for showing proportions of a whole, not exact counts, unless the total is given.
Pictograms
A pictogram represents data with symbols, where one symbol stands for a fixed quantity (a key, e.g. one ☺ = 5 students). Part-symbols show fractions of that quantity. Always read the key first; the frequency is the number of symbols multiplied by the value each represents.
Line graphs
A line graph plots points (usually against time) and joins them with straight lines, making trends easy to see — rising, falling or fluctuating. They suit continuous data measured over time, such as temperature through a day or monthly rainfall. Read values by going up from the time axis to the line and across to the vertical axis.
Frequency polygons
A frequency polygon is drawn by plotting each class frequency against the midpoint of its class interval, then joining the points with straight lines. It is used for grouped continuous data and is helpful for comparing two distributions on the same axes. The midpoint is found by averaging the class boundaries.
Choosing the right diagram
Match the diagram to the data: bar charts and pictograms for discrete categories; pie charts for parts of a whole; line graphs for change over time; frequency polygons for grouped continuous data. Choosing well is itself sometimes examined.
Worked examples
Example 1: Pie chart angles (Paper 2 style)
In a survey of 60 students, 25 chose football, 20 cricket, and 15 netball. Find the angle for each sector of a pie chart.
Each angle = (frequency ÷ 60) × 360°. Football: (25 ÷ 60) × 360° = 150°. Cricket: (20 ÷ 60) × 360° = 120°. Netball: (15 ÷ 60) × 360° = 90°. Check: 150 + 120 + 90 = 360°. ✓
Example 2: Reading a pictogram (Paper 1 style)
On a pictogram, one ◼ represents 8 mangoes. A stall shows 4½ symbols for Tuesday. How many mangoes were sold?
Mangoes = 4.5 × 8 = 36 mangoes.
Example 3: Frequency polygon midpoints (Paper 2 style)
A class records masses in the interval 50–60 kg with frequency 7. State the coordinate to plot for the frequency polygon.
The midpoint of 50–60 is (50 + 60) ÷ 2 = 55. So the point to plot is (55, 7).
Common mistakes and how to avoid them
Pie-chart angles not summing to 360°. After finding each angle, add them; a total other than 360° signals an arithmetic error.
Ignoring the pictogram key. Always multiply the number of symbols by the value of one symbol; a part-symbol represents a fraction of it.
Plotting frequency polygons at class boundaries instead of midpoints. Use the midpoint of each interval for the horizontal coordinate.
Unequal bar widths or missing gaps. Bar charts must have equal-width bars with gaps; otherwise they can mislead.
Forgetting axis labels and scales. Unlabelled axes or inconsistent scales lose marks and make a diagram unreadable.
Exam technique for Statistical Diagrams
Use the pie-chart formula carefully. Angle = (frequency ÷ total) × 360°, and check the angles total 360°.
Read the key and scale first. For pictograms and bar charts, the key or axis scale determines every value you read off.
Label everything. Title, axis labels and a key (where needed) are expected and often carry marks.
Match the diagram to the data type. Discrete categories, parts of a whole, change over time, or grouped data each call for a particular diagram.
Use class midpoints for frequency polygons, and join points with straight lines.
Quick revision summary
Statistical diagrams present data visually. Bar charts use equal-width bars with gaps to compare discrete categories, with frequency on the vertical axis. Pie charts divide a circle into sectors, each angle = (frequency ÷ total) × 360°, and are best for showing proportions of a whole. Pictograms use symbols with a key (one symbol = a fixed number); read the key and count symbols, including part-symbols. Line graphs join plotted points to show trends over time, while frequency polygons plot grouped-data frequencies at class midpoints and join them with straight lines. Choose the diagram that fits the data: categories → bar chart or pictogram; parts of a whole → pie chart; change over time → line graph; grouped continuous data → frequency polygon. Always label axes, include a key where needed, check that pie-chart angles sum to 360°, and use class midpoints (not boundaries) for frequency polygons.