Data Handling
5.0 Data Handling and Probability · 5.1 Data Handling
Syllabus tag: Kenya CBC | Grade 7 Mathematics | Strand 5.0 Data Handling and Probability | Sub-Strand 5.1 Data Handling (10 lessons)
Lesson objectives
By the end of this topic, you will be able to:
- State the meaning of data, and collect it from different situations
- Draw a frequency distribution table, and determine a suitable scale for a graph
- Draw and interpret pictographs, bar graphs, pie charts and line graphs
- Interpret travel graphs from real-life situations
Data Handling
Data is information collected to answer a question. This topic collects it, organises it, and draws it so the pattern shows.
a) Collecting data
Decide the question first. "Which fruit do learners prefer?" is answerable. "Are fruits good?" is not.
Collect by observing, by counting, by measuring, or by asking. Asking gives a questionnaire; counting as things happen gives a tally.
Record as you go. Memory is unreliable, and a tally chart is faster than writing words.
b) Frequency distribution table
A frequency distribution table lists each item with how many times it occurred.
| Fruit | Tally | Frequency |
|---|---|---|
| Mango | IIII IIII II | 12 |
| Banana | IIII III | 8 |
| Orange | IIII I | 6 |
| Pawpaw | IIII | 4 |
Group tallies in fives, with the fifth stroke crossing the other four. It makes counting quick and accurate.
Add the frequency column and check it matches the number of people asked.
c) Choosing a scale
Before drawing, look at the largest frequency and the space available.
Choose a scale that fits and is easy to read. Counting in 1s, 2s, 5s or 10s is sensible; counting in 3s or 7s is not.
Start the frequency axis at zero. Starting higher makes small differences look large and misleads the reader.
d) Bar graphs
A bar graph compares separate categories. Bar height shows the frequency.
Leave gaps between the bars, because the categories are separate things.
Label both axes and give the graph a title. Without labels nobody else can read it.
e) Pictographs
A pictograph uses a picture to stand for a number of items.
The key says what one picture is worth, such as one drawing standing for 4 learners.
Part-pictures show part-values. Half a picture means half of whatever the key says.
Pictographs are easy to read but poor for awkward numbers. Drawing three-sevenths of a picture is not practical.
f) Pie charts
A pie chart shows how a whole is shared out. The whole circle is 360°.
Each slice takes its share of the 360°.
Divide 360 by the total to find what one item is worth, then multiply by each frequency.
Check that all your angles add to 360°. If they do not, something is wrong before you draw anything.
A pie chart shows proportions well but compares exact values poorly. Use a bar graph when the actual numbers matter.
g) Travel graphs
A travel graph plots distance against time.
A steep line means fast. A gentle line means slow. A flat line means stopped, since time passes but distance does not change.
Speed on any section is the distance covered divided by the time taken for that section.
h) Where this is used
A school records attendance. A shopkeeper tracks which goods sell. A health worker charts cases by week. A newspaper turns a survey into a picture.
Words to know
- Data — information collected that can be organised and analysed.
- Frequency — how many times a value or category occurs in a data set.
- Scale (on a graph) — the value each unit of an axis represents.
- Travel graph — a line graph plotting distance against time for a journey.
:::checkpoint Check yourself
- Why should the frequency axis start at zero?
- In a pie chart of 40 people, how many degrees does one person represent?
- What does a flat section of a travel graph mean?
- When is a bar graph better than a pie chart? :::
Bridge to practice
Try the exercises below — on frequency tables, pictographs, bar graphs, pie charts and travel graphs.