Reading Statistical Tables

Tables Are the Language of Data

In IGCSE Maths, data is frequently presented in tabular form. Being able to read, interpret, and extract information from statistical tables is essential — not just for statistics questions, but also for probability calculations, graph-drawing questions, and real-world problems.

Many students lose marks not because they cannot do the calculations, but because they misread the table. A careful, systematic approach to reading tables prevents these avoidable errors.

Type 1: Simple Frequency Tables

A simple frequency table lists individual values (or categories) and how many times each occurs.

Example:

Score	Frequency
1	4
2	7
3	12
4	8
5	5

Reading the table: 4 people scored 1, 7 people scored 2, and so on.

Total frequency: Add all frequencies: 4 + 7 + 12 + 8 + 5 = 36

Finding the mean: Mean = sum of (score × frequency) / total frequency

= (1×4 + 2×7 + 3×12 + 4×8 + 5×5) / 36

= (4 + 14 + 36 + 32 + 25) / 36

= 111 / 36

= 3.083 (to 3 decimal places)

Finding the median: The median is the middle value when all data is in order. With 36 values, the median is the average of the 18th and 19th values.

Count through the cumulative frequencies: 4, 11, 23, 31, 36. The 18th and 19th values both fall in the “score = 3” group (since positions 12-23 all have score 3). Median = 3.

Finding the mode: The mode is the score with the highest frequency. Score 3 has frequency 12 (the highest), so mode = 3.

Type 2: Grouped Frequency Tables

Grouped frequency tables are used when data covers a wide range or is continuous.

Example:

Height (h cm)	Frequency
140 ≤ h < 150	5
150 ≤ h < 160	12
160 ≤ h < 170	18
170 ≤ h < 180	10
180 ≤ h < 190	3

Important features to notice:

• The class intervals use inequalities (≤ and <), not just number ranges
• The intervals do not overlap — 150 is in the 150-160 group, not the 140-150 group
• The class width is 10 for each group (this matters for histograms)

Finding the mean of grouped data: Use the midpoint of each class.

Midpoints: 145, 155, 165, 175, 185

Mean = (145×5 + 155×12 + 165×18 + 175×10 + 185×3) / (5+12+18+10+3)

= (725 + 1860 + 2970 + 1750 + 555) / 48

= 7860 / 48

= 163.75 cm

Note: This is an estimate of the mean because we do not know the exact values within each group.

Finding the modal class: The class with the highest frequency. Here, 160 ≤ h < 170 (frequency 18).

The median class: Total frequency is 48. The median is between the 24th and 25th values. Cumulative frequencies: 5, 17, 35. The 24th and 25th values are in the 160 ≤ h < 170 group.

Type 3: Two-Way Tables

Two-way tables show data categorised by two variables simultaneously.

Example:

	Bus	Car	Walk	Total
Boys	15	8	12	35
Girls	18	5	7	30
Total	33	13	19	65

Reading the table: 15 boys travel by bus. 5 girls travel by car. 65 students in total.

Completing two-way tables: Exam questions often give a partially completed table and ask you to fill in the gaps. Use the fact that each row and column must sum to its total.

If you know that 35 boys and 15 travel by bus and 8 by car, then boys who walk = 35 − 15 − 8 = 12.

Type 4: Cumulative Frequency Tables

These show the running total of frequencies up to each class boundary. They are essential for drawing cumulative frequency curves.

Example (from the height data above):

Height (h cm)	Cumulative Frequency
h < 150	5
h < 160	17
h < 170	35
h < 180	45
h < 190	48

Important: Cumulative frequency is plotted against the upper class boundary, not the midpoint. This is a common source of error when drawing cumulative frequency curves.

Extracting Information for Calculations

When working with tables, you often need to calculate specific values. Here is a checklist of common calculations and how to extract the information:

Mean from a frequency table:

• Multiply each value (or midpoint) by its frequency
• Sum these products
• Divide by the total frequency

Range from a frequency table:

• Range = highest value − lowest value (for ungrouped data)
• For grouped data, you can only estimate the range using class boundaries

Interquartile range from cumulative frequency:

• Q1 is at the ¼ × total frequency position
• Q3 is at the ¾ × total frequency position
• IQR = Q3 − Q1

Probability from a frequency table:

• P(event) = frequency of event / total frequency

Common Table-Reading Mistakes

Mistake 1: Misreading class boundaries “140 < h ≤ 150” is different from “140 ≤ h < 150.” The first includes 150 but not 140; the second includes 140 but not 150. Read the inequalities carefully.

Mistake 2: Using the wrong midpoint For the class 140 ≤ h < 150, the midpoint is (140 + 150)/2 = 145, not 140 or 150.

Mistake 3: Forgetting to use all rows/columns in a two-way table When finding totals, make sure you include every category.

Mistake 4: Confusing frequency with cumulative frequency Frequency is the count for one class. Cumulative frequency is the running total up to and including that class.

Mistake 5: Reading from the wrong row or column In large tables, use a ruler or your finger to track across the row or down the column to avoid reading from the wrong line.

Tips for Exam Success

• Add a totals row or column if one is not provided — this helps with checking
• Calculate cumulative frequencies alongside the frequency table, even if not asked — you may need them later
• Use a ruler to read across rows in printed tables
• Double-check your midpoints for grouped data — a wrong midpoint affects the mean calculation
• Show your working — write out the fx column (value × frequency) to earn method marks

Summary

Statistical tables are a fundamental way to present data in IGCSE Maths. Whether you are reading simple frequency tables, grouped data tables, two-way tables, or cumulative frequency tables, the key is careful, systematic reading. Check class boundaries, verify your totals, and use the correct formulae for the type of table you are working with. These skills are essential for statistics questions and also support probability and graph work.

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