Drawing Conclusions from Data

Introduction

Numbers tell stories — but only if you know how to read them. In the FSCE 11+ exam, you may be given tables, charts, or sets of data and asked to draw conclusions from them. This isn't just a maths skill — it's a critical thinking skill. You need to look at the data carefully and work out what it tells you AND what it doesn't tell you.

In this lesson, you'll learn how to interpret data in tables and charts, how to make correct inferences, and how to avoid common data interpretation mistakes.

What Does "Drawing Conclusions from Data" Mean?

Drawing conclusions from data means looking at the numbers and working out what they show. But critically, it also means recognising what the data does NOT show.

graph TD
    A["Look at the data carefully"] --> B["What does the data SHOW?"]
    A --> C["What does the data NOT show?"]
    B --> D["Supported conclusions"]
    C --> E["Things you CANNOT conclude"]
    D --> F["Check: Is your conclusion justified by the numbers?"]
    E --> F
    F -->|Yes| G["Valid conclusion"]
    F -->|No| H["Over-interpretation — be careful!"]
    style G fill:#e8f5e9
    style H fill:#fce4ec

How to Read Data Tables

When you see a data table, follow these steps:

1. Read the title — What is the table about?
2. Read the column and row headings — What do the numbers represent?
3. Look for patterns — Are numbers going up, down, or staying the same?
4. Look for outliers — Is anything surprisingly high or low?
5. Check the units — Are the numbers percentages, amounts, totals, or averages?

Worked Examples

Worked Example 1: Reading a Data Table

Table: Number of books read by students in Year 6 during one term

Student	Fiction	Non-fiction	Total
Amira	8	3	11
Ben	2	7	9
Charlotte	6	6	12
David	1	1	2
Eva	10	2	12

What the data shows:

• Charlotte and Eva read the most books overall (12 each).
• Eva read the most fiction (10), while Ben read the most non-fiction (7).
• David read the fewest books in total (2).
• Most students read more fiction than non-fiction (Amira, Eva), but Ben is the exception — he read more non-fiction.

What the data does NOT show:

• Whether the students enjoyed the books (data only tells us quantity, not quality).
• How long the books were (reading 10 short picture books is different from 10 long novels).
• Whether David read fewer books because he chose not to, or because the books he read were very long.
• Whether these students are typical of the whole year group.

Worked Example 2: Spotting Trends

Table: Average temperature in London (°C) by month

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Temp (°C)	5	5	8	11	14	17	19	19	16	12	8	5

Conclusions that CAN be drawn:

• Temperatures rise from January to July and then fall from August to December.
• July and August are the warmest months (19°C).
• January, February, and December are the coldest months (5°C).
• There is a clear seasonal pattern.

Conclusions that CANNOT be drawn:

• That every day in July will be 19°C (this is an average — some days will be hotter, some cooler).
• That London is always warmer than other cities (we have no data about other cities).
• That temperatures will be the same next year (weather can vary year to year).

Worked Example 3: Comparing Data Sets

Table: Favourite sport by gender (survey of 200 Year 6 students)

Sport	Boys	Girls	Total
Football	45	20	65
Swimming	15	30	45
Tennis	10	15	25
Gymnastics	5	25	30
Athletics	20	15	35
Total	95	105	200

Valid conclusions:

• Football is the most popular sport overall (65 votes).
• Football is the most popular sport among boys (45 out of 95).
• Swimming is the most popular sport among girls (30 out of 105).
• Gymnastics is much more popular with girls (25) than boys (5).

Invalid conclusions:

• "Boys don't like gymnastics" — 5 boys chose it, so some do; just fewer than girls.
• "All girls prefer swimming to football" — 20 girls chose football, so some girls do prefer it.
• "Boys are more sporty than girls" — this data shows preferences, not ability or participation levels.

Worked Example 4: Before and After

Table: School absence rates (%)

Year	2020	2021	2022	2023
School A	5.2	4.8	4.1	3.5
School B	3.0	3.1	3.2	6.5

Question: "What conclusions can you draw from this data?"

Before (a student who over-interprets): "School A is getting better and School B is getting worse. School A must have a better headteacher."

This answer makes assumptions about WHY the numbers changed.

After (a student who interprets carefully): "School A's absence rate has decreased steadily from 5.2% in 2020 to 3.5% in 2023, which is a positive trend. School B had a stable absence rate around 3% from 2020 to 2022, but it more than doubled to 6.5% in 2023, which is a sharp increase. However, the data doesn't tell us WHY these changes happened. The increase at School B in 2023 could be due to an illness outbreak, changes in the school's policy, or other factors we can't determine from this data alone."

Worked Example 5: Percentages Can Be Misleading

Statement: "Crime in Littletown increased by 100% last year!"

This sounds terrifying. But what if the actual numbers were:

• Last year: 2 crimes
• This year: 4 crimes

A 100% increase sounds dramatic, but going from 2 to 4 crimes in a whole town is not particularly alarming. Percentages without context can be misleading.

Similarly: "Our product is 50% more effective!" — 50% more effective than what? Than doing nothing? Than a competitor? Without knowing the baseline, the percentage is meaningless.

Worked Example 6: Reading Charts Described in Text

Chart description: "A bar chart shows the amount of rainfall (in mm) for a town over six months. January: 80mm, February: 65mm, March: 50mm, April: 45mm, May: 40mm, June: 30mm."

Analysis:

• Rainfall decreases each month from January (80mm) to June (30mm).
• The biggest drop is between January and February (15mm decrease).
• The decrease slows down: the drops are 15, 15, 5, 5, 10mm.
• Total rainfall over six months: 310mm.