Data Handling and Statistics

Data handling is about collecting, organising, and interpreting information. In the CEM 11+ exam, you need to read charts and graphs accurately, calculate averages, and understand basic probability. CEM questions can present data in unfamiliar formats, so being confident with the underlying concepts is more important than memorising one type of chart.

---

Types of Charts and Graphs

Bar Charts

Bar charts use bars of different heights to represent data. The height of each bar shows the frequency (how many).

How to read a bar chart:

1. Read the title and axis labels carefully.
2. Use the scale on the y-axis to read the value for each bar.
3. Compare bars to answer questions.

Line Graphs

Line graphs show how data changes over time. Points are plotted and connected with straight lines.

Key skills:

• Read values at specific points
• Identify trends (increasing, decreasing, staying the same)
• Find the difference between two points

Pie Charts

A pie chart uses a circle divided into sectors (slices) to show proportions. The whole circle represents 360°.

Worked Example: A pie chart shows "Walk to school" as a 120° sector. If 60 students were surveyed, how many walk?

• 120° out of 360° = 120/360 = 1/3
• 1/3 of 60 = 20 students

Pictograms

A pictogram uses symbols to represent data. Each symbol represents a fixed number of items.

CEM Tip: Always check the key! A half-symbol means half the value. CEM papers sometimes use unusual keys to test whether you read carefully.

---

Averages

There are three types of average and the range:

Measure	How to Find It	What It Tells You
Mean	Add all values, divide by how many	The typical value (uses all data)
Median	Put in order, find the middle value	The middle value
Mode	The value that appears most often	The most popular value
Range	Largest value minus smallest value	How spread out the data is

Worked Example: Find the Mean

Data: 4, 7, 8, 3, 8

• Sum = 4 + 7 + 8 + 3 + 8 = 30
• Number of values = 5
• Mean = 30 ÷ 5 = 6

Worked Example: Find the Median

Data: 12, 5, 8, 3, 15

1. Put in order: 3, 5, 8, 12, 15
2. Middle value = 8

For an even number of values: Find the mean of the two middle values.

Data: 4, 7, 9, 12

• Two middle values: 7 and 9
• Median = (7 + 9) ÷ 2 = 8

Worked Example: Find the Mode and Range

Data: 3, 5, 7, 5, 9, 5, 3