What is data?
Data is a collection of facts, numbers or observations gathered to answer a question. The marks of your class in a test, the number of cars passing your school each hour, and your friends' favourite fruits are all data.
Raw data in a long list is hard to understand. Data handling means organising it so that patterns jump out.
Organising with tally marks
Suppose 20 students named their favourite sport. Instead of counting the list again and again, go through it once and make a tally mark (ǀ) for each answer. Every fifth mark is drawn across the previous four, so the marks fall into easy-to-count bundles of five.
Sport | Tally marks | Number of students |
|---|---|---|
Cricket | 卌 卌 ǀǀ | 12 |
Football | 卌 | 5 |
Badminton | ǀǀǀ | 3 |
The number of times something occurs is its frequency, and a table like this is a frequency table. The frequencies should add up to the total: 12 + 5 + 3 = 20.
Pictographs
A pictograph shows data with pictures or symbols. Each symbol stands for a fixed number of items, which is stated in a key.
Example. Key: one 🍎 symbol = 10 apples sold.
Day | Apples sold |
|---|---|
Monday | 🍎🍎🍎 |
Tuesday | 🍎🍎🍎🍎🍎 |
Wednesday | 🍎🍎 and half a 🍎 |
Monday: 3 × 10 = 30 apples. Tuesday: 5 × 10 = 50 apples. Wednesday: 2½ × 10 = 25 apples.
Pictographs are attractive and easy to read, but drawing many symbols is slow and part-symbols are hard to draw exactly.
Bar graphs
A bar graph shows data with bars of equal width. The length (or height) of each bar stands for its value. Gaps between the bars should be equal.
Steps to draw a bar graph:
Draw two axes: a horizontal one for the categories (days, sports, subjects) and a vertical one for the values.
Choose a scale that fits your largest value, for example 1 unit = 10 students. Write it on the graph.
Draw one bar for each category, to the correct height.
Label both axes and give the graph a title.
Example. If the scale is 1 cm = 5 students, a category with 35 students gets a bar 35 ÷ 5 = 7 cm tall.
Reading a bar graph
When you read a bar graph, you can answer questions such as:
Which category is largest or smallest? Look for the tallest and shortest bars.
How much more is one than another? Subtract their values.
What is the total? Add all the values.
Always check the scale first. A bar reaching the 6th mark on a scale of 1 unit = 50 stands for 300, not 6.
Common mistakes
Ignoring the key or scale. Count symbols or units, then multiply by what each one is worth.
Unequal bar widths or gaps. They make some categories look more important than they are.
Missing labels. A graph without a title and axis labels can't be understood by a reader.
Summary
Tally marks and frequency tables organise raw data quickly.
A pictograph uses symbols; the key tells you what each symbol is worth.
A bar graph uses bars of equal width whose heights show the values, drawn to a stated scale.