Tally charts and frequency tables
🎯 In this topic you will
- Conduct investigations to answer both statistical and non-statistical questions.
- Record, organise, and represent data using tally charts and frequency tables.
- Describe data clearly and discuss conclusions based on evidence.
🧠 Key Words
- frequency table
- survey
Show Definitions
- frequency table: A table that shows how often each value or category appears in a set of data.
- survey: A method of collecting data by asking questions to a group of people.
Using a Tally Chart
A tally chart uses marks to record data. The marks are grouped in fives, which makes counting quicker and easier. Each group of five is shown as four vertical lines with a diagonal line across them.
Frequency Tables
A frequency table uses numbers to show how many times something occurs. It is usually created after collecting data with a tally chart.
The table below shows the number of Stage 3 learners who chose water or milkshake as their favourite drink.
Seven children chose water as their favourite drink, and nine children chose milkshake.
❓ EXERCISES
1. You will need a coin. Flip the coin $20$ times. Use tally marks to show the results of heads or tails.
Write two things that you have found out using the data in the tally chart.
You can count each result and you can compare the results.
Do you think that the same thing will happen if you repeat the activity? Explain what you think.
👀 Show answer
2. Stage $3$ learners did a survey to see which sports were liked. Santilla wrote her data as a tally chart. Rose wrote her data in a frequency table.
a. Which sport is liked the most?
b. Which two sports have results that are almost the same?
c. How many people took part in the survey?
d. Write two things that the data do not tell you.
👀 Show answer
b. Cricket ($8$) and basketball ($9$).
c. $8+14+9+12+6 = 49$.
d. Example: who the learners are, and whether they like more than one sport.
3. The children in a class did a survey of the number of brothers and sisters each of them have. The results are in this frequency table. Add the tally marks to show the same results.
👀 Show answer
4. Make a tally chart with a frequency table to show the information below.
👀 Show answer
5. Choose a page in your reading book. Choose two lines of text. Count how many times each letter appears. Record the results in a tally chart and frequency table. Add more rows if you need to.
👀 Show answer
🧠 Think like a Mathematician
A cereal company is offering six free gifts. One gift appears in every cereal packet. How many packets do you think you would need to buy so that you have all of the gifts?
Using a six-sided dice, you can create a tally chart to represent each gift. This could lead to an estimate of the number of packets.
Method:
- Throw the dice and record the result each time.
- Use tally marks to represent each gift.
- Continue throwing until every gift has appeared at least once.
- Count how many throws were needed.
Record your results:
| Gift | Tally |
|---|---|
| $1$ | |
| $2$ | |
| $3$ | |
| $4$ | |
| $5$ | |
| $6$ |
How will you know when to stop throwing?
👀 Show answer
- Stopping rule: You stop when all six gifts ($1$ to $6$) have appeared at least once.
- Estimate: Because results are random, the total number of throws will vary. A typical result is often around $12$–$20$ throws, but sometimes more are needed.
- Reason: This is a chance experiment, so some gifts may repeat many times before the last missing gift appears.