Classifying and Interpreting Data
Types of data, tally tables, two-way tables and fair conclusions
Types of data.
- Categorical data are words or labels: favourite sport, colour of a car, type of animal.
- Numerical data are numbers. They can be:
- Discrete — counted, so only certain values are possible: number of goats, number of goals, shoe size.
- Continuous — measured, so any value in a range is possible: height, mass, time, temperature.
Tally and frequency tables. To sort a list of data, make a tally mark for each value. Group tallies in fives (four lines and one line across) so they are easy to count. The frequency is how many times each value appears. The frequencies must add up to the total number of data values.
Two-way tables sort data by two things at once, for example boys/girls and how they travel to school. Each row and each column has a total. If you know all but one number in a row or column, you can find the missing one by subtracting from the total.
Interpreting tables. Read the headings and units first. Then answer exactly what is asked: “how many”, “which is the most”, “what is the difference”.
Comparing and drawing conclusions. To compare two groups, use a measure such as the mean (average) or the range (spread), and say what it means: “Class B did better on average”, “Class A’s marks were more spread out”. A conclusion can only be as good as the data. Be careful when the sample is small, or when it comes from only one place or one group of people — it may not represent everyone.
Is each type of data categorical, discrete or continuous? (a) the time taken to run 100 m; (b) the number of pupils in a class; (c) a student’s favourite subject; (d) the height of a tree.
(a) Time is measured → continuous. (b) Pupils are counted → discrete.
(c) A subject is a word → categorical. (d) Height is measured → continuous.
The numbers of goals scored in 20 football matches in a Gaborone school league are:
1, 0, 2, 3, 1, 1, 0, 2, 4, 1, 2, 0, 1, 3, 2, 1, 0, 1, 2, 1
Make a frequency table. How many matches had more than 2 goals?
| Goals | Tally | Frequency |
|---|---|---|
| 0 | |||| | 4 |
| 1 | 8 | |
| 2 | 5 | |
| 3 | || | 2 |
| 4 | | | 1 |
Check: 4 + 8 + 5 + 2 + 1 = 20 ✔. More than 2 goals means 3 or 4 goals: 2 + 1 = 3 matches.
Complete the two-way table showing how 60 students travel to school.
| Walk | Combi | Car | Total | |
|---|---|---|---|---|
| Boys | 12 | 10 | … | 28 |
| Girls | … | 15 | 4 | … |
| Total | 25 | … | … | 60 |
Boys by car: 28 − 12 − 10 = 6. Girls total: 60 − 28 = 32. Girls who walk: 25 − 12 = 13.
Combi total: 10 + 15 = 25. Car total: 6 + 4 = 10.
Check: girls 13 + 15 + 4 = 32 ✔ and totals 25 + 25 + 10 = 60 ✔.
The table shows the approximate road distances, in km, between four places in Botswana.
| Gaborone | |||
| 270 | Palapye | ||
| 435 | 165 | Francistown | |
| 925 | 655 | 490 | Maun |
(a) How far is it from Gaborone to Francistown? (b) Which two places in the table are closest together?
(a) Go down the Gaborone column to the Francistown row: 435 km.
(b) The smallest number in the table is 165, so Palapye and Francistown are closest.
In a distance table, find the column of one place and the row of the other — the number where they meet is the distance.
Q1. Write down whether each type of data is categorical, discrete or continuous.
(a) The mass of a bag of oranges. (b) The number of chickens on a farm. (c) The type of phone a student owns.
👀 Show answer
(b) discrete ✓ B1
(c) categorical ✓ B1
Q2. The numbers of children in 16 families in a village near Mahalapye are:
2, 3, 1, 2, 4, 2, 0, 3, 2, 1, 2, 3, 1, 2, 0, 5
(a) Make a frequency table for the data. (b) How many families have more than 2 children?
👀 Show answer
(B1 for 4 or 5 correct frequencies)
(b) 3 + 1 + 1 = 5 families ✓ B1
Q3. Form 3 students each chose one club. Complete the two-way table.
| Art | Music | Drama | Total | |
|---|---|---|---|---|
| Boys | 8 | … | 5 | 20 |
| Girls | … | 11 | 7 | … |
| Total | 17 | … | … | … |
👀 Show answer
Music total 7 + 11 = 18 Drama total 5 + 7 = 12 ✓ B1
Girls total 9 + 11 + 7 = 27 Grand total 47 ✓ B1
Q4. Use the distance table in Example 4.
(a) How far is it from Palapye to Maun? (b) Neo drives from Gaborone to Palapye and then on to Francistown. How far does he drive altogether?
👀 Show answer
(b) 270 + 165 = 435 km ✓ B1
Q5. The table shows the rainfall, in mm, in Maun and Gaborone for three months of one year.
| January | February | March | |
|---|---|---|---|
| Maun | 110 | 85 | 70 |
| Gaborone | 95 | 80 | 75 |
(a) In which month and in which place was the rainfall lowest? (b) How much more rain fell in Maun than in Gaborone in January?
👀 Show answer
(b) 110 − 95 = 15 mm ✓ B1
Q6. Two classes took the same test. Class 3A: mean 58 marks, range 40 marks. Class 3B: mean 64 marks, range 22 marks. Make two comparisons between the classes.
👀 Show answer
Class 3B’s marks were more consistent / less spread out (smaller range) ✓ B1
Q7. Lesedi asked 10 members of her netball club for their favourite sport. 8 of them said netball. She says, “Netball is the most popular sport in Botswana.” Give two reasons why her conclusion may not be reliable.
👀 Show answer
she only asked netball club members — they are likely to choose netball (biased sample) ✓ B1
Q8. In a class of 30 students, 18 are girls. 12 of the girls and 5 of the boys walk to school. (a) How many boys are in the class? (b) How many boys do not walk to school?
👀 Show answer
(b) 12 − 5 = 7 boys ✓ B1
- Calling counted data continuous: shoe size and number of people are discrete, even though they are numbers.
- Missing values when tallying: cross off each value as you tally it, then check the frequencies add up to the total.
- “More than 2” including 2: more than 2 means 3 and above.
- Not checking a two-way table: rows and columns must both add up to the grand total.
- Comparing with numbers only: say which group is better on average and which is more consistent.
- Trusting a small or one-sided sample: say why the data may not represent everyone.
- Paper 1 and Paper 3 often include “complete the frequency table” and “complete the two-way table” — usually 2–3 marks.
- Reading tables (timetables, distance charts, price lists) appears in many questions, not only in the statistics ones.
- Command words: complete, write down, how many, compare, give a reason.
- “Give a reason” questions about conclusions reward simple, clear points: sample too small, sample not representative.
(then move on to the next unit in the Statistics strand)