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Mathematics notes, unit 9

Data

Textbook Mathematics Year 3 (DLP), Part 1 and Part 2, pages Part 2, 107–116

What this chapter covers

  • You can collect data, then classify and sort it in a table using tally marks or ticks (9.1.1)
  • You can read a pie chart and say which part is the most, the least and how many are in each part (9.2.1)
  • You can see that a pictograph, a bar chart and a pie chart can show the same data, and find the same information in all three (9.3.1)
  • You can solve everyday problems using data in tables, pictographs, bar charts and pie charts (9.4.1)

9.1Collecting, classifying and sorting data

Data is information we collect, such as colours, names or numbers. To classify data means to put the same things into one group. To sort data means to arrange the groups neatly in a table.

Anuar sits in front of his house. He writes down the colour of every car that passes by. These are his notes:

Anuar's list of 30 car colours: white, red, blue, white, red, red, black, white, red, blue, white, black, red, white, white, white, red, black, black, red, red, white, black, black, blue, white, white, white, white, red
Anuar's data. It is hard to see which colour is the most.

The list is long and messy. Let us classify the colours into four groups and sort them in a table.

A tally is a quick way to count. Draw one stick for each thing. The fifth stick goes across the first four, like a little gate: |||| with a line across = 5.
Making a tally table
  1. Draw a table with three columns: Colour of car, Tally and Number.
  2. Read the list one word at a time. For each word, draw one stick in the right row. Cross out the word so you do not count it twice.
  3. Count the tally marks in fives: 5, 10, then the extra sticks. Write the total in the Number column.
  4. Check: 12 + 9 + 3 + 6 = 30. Anuar wrote 30 colours, so the table is correct.
Tally table. White: two groups of five and 2 sticks, 12. Red: one group of five and 4 sticks, 9. Blue: 3 sticks, 3. Black: one group of five and 1 stick, 6.
Anuar's data, classified and sorted. White cars are the most (12). Blue cars are the least (3).

Some people use ticks (✓) instead of tally marks. White would have 12 ticks. Both ways work, but tally marks in groups of five are faster to count.

Forgetting the gate. The fifth stick must go across the four sticks. If you draw five straight sticks in a row, it is easy to miscount. And always add the numbers at the end to check that the total is the same as the number of data you collected.
Did you know? You can collect data in many ways: by watching (like Anuar), by asking your friends questions, or by giving them a short form to fill in. Try it! Ask your classmates their favourite kuih at recess.
Make a tally for this data on favourite drinks: milo, sirap, milo, teh, milo, sirap, milo, teh, milo. How many chose milo? Which drink is the least favoured?
Show answerHide answer
Milo: |||| with a line across = 5. Sirap: || = 2. Teh: || = 2. Check: 5 + 2 + 2 = 9 drinks. Milo is chosen by 5 pupils. Sirap and teh are the least, with 2 each.

9.2Reading a pie chart

A pie chart shows data in a circle. The circle is cut into parts, like slices of a pie or a kek lapis. A bigger part means a bigger number.

Here is Anuar's car data again, drawn as a pie chart.

Pie chart titled Colours of Cars. White car 12 (largest part), red car 9, black car 6, blue car 3 (smallest part).
The same car data as a pie chart.

Every pie chart has three things to look at:

PartWhat it tells usIn this pie chart
TitleWhat the data is aboutColours of Cars
KeyWhich colour stands for which groupBlue part = blue car, and so on
Numbers in the partsHow many are in each group12, 9, 6 and 3
Getting information from the pie chart
  1. How many colours were observed? Count the parts: there are 4 colours.
  2. The largest part is white, with 12. So white cars are the most.
  3. The smallest part is blue, with 3. So blue cars are the least.
  4. How many red cars? Find red in the key, then read the red part: 9.
  5. How many cars altogether? 12 + 9 + 6 + 3 = 30 cars.
Mixing up the colours. Always check the key before you read a part. In some pie charts the part for "Blue" is not coloured blue!
Look at the pie chart of pupils' birth months. (a) How many pupils were born in March? (b) Which month has the fewest pupils? How many? (c) In which month were the most pupils born?
Pie chart titled Pupils' Birth Months. March 10, April 8, June 13, August 5.
Show answerHide answer
(a) 10 pupils. (b) August, with 5 pupils (the smallest part). (c) June, with 13 pupils (the largest part).

9.3Pictographs, bar charts and pie charts

You may have seen pictographs and bar charts before. The same data can be shown in all three kinds of chart.

ChartHow it shows a numberThe most is…
PictographPictures. The key tells you what one picture stands for.the row with the most pictures
Bar chartBars. Read the number on the axis at the top of the bar.the highest (or longest) bar
Pie chartParts of a circle, with the number written inside.the largest part

Cikgu Aminah asked four pupils how many books they read last month. She showed the answers in three charts.

Number of Books Read in three charts. Pictograph with one book picture for 1 book: Ali 5, Sara 8, Yi Min 5, Mohan 7. Bar chart with the same numbers; Sara's bar is the highest at 8. Pie chart with parts 5, 8, 5 and 7; Sara's part, 8, is the largest.
Three charts, one set of data.
Who reads the most books?
  1. Pictograph: Sara has the most pictures. 8 pictures × 1 book = 8 books.
  2. Bar chart: Sara's bar is the highest. It reaches 8.
  3. Pie chart: the largest part is 8. The key shows it is Sara.
  4. All three charts agree: Sara reads the most books.

The charts also show that Ali and Yi Min read the same number of books, which is 5. In the pictograph they have the same number of pictures. In the bar chart their bars are the same height. In the pie chart their parts are the same size.

Did you know? A pie chart is good for seeing which part is biggest at a glance. A bar chart is good for comparing numbers that are close. A pictograph is fun and easy to count.
The Young Entrepreneurs Club sold some fruits. Look at the three charts. (a) What is the title? (b) What does one blue circle stand for? (c) Which fruit was sold the most? (d) Which fruit was sold the least, and how many?
Fruits Sold in three charts: pictograph with one circle for 1 fruit, a horizontal bar chart and a pie chart. Apple 7, Orange 3, Kiwi 2, Mangosteen 4, Mango 4.
Show answerHide answer
(a) Fruits Sold. (b) 1 fruit. (c) Apple: the most circles, the longest bar and the largest part (7). (d) Kiwi, with 2 fruits.

9.4Solving problems with data

To solve a data problem: read the question, find the numbers in the table or chart, then calculate if you need to.

Problem 1: Sukdev asks 12 friends their favourite colour. Which colour is the least favoured?
Twelve paint splats with names. Sali purple, Nisa red, Hani green, Wafi purple, Bella yellow, Chen red, Geta yellow, Jia Li purple, Omar red, Nada purple, Kabin red, Andy purple.
  1. Classify and sort the data in a tally table.
  2. Count: purple 5, red 4, green 1, yellow 2. Check: 5 + 4 + 1 + 2 = 12 friends.
  3. The smallest number is 1. The least favoured colour is green.
Tally table. Purple 5, red 4, green 1, yellow 2.
Problem 2: The pie chart shows the favourite subjects of 100 pupils.
Pie chart titled Favourite Subjects. Mathematics 25, Science 15, English 10, Bahasa Melayu 50.
  1. How many pupils like Mathematics? The key shows Mathematics is blue. The blue part says 25.
  2. Which subject is the most favoured? The green part is the largest (50). The key shows green is Bahasa Melayu.
  3. How many more pupils like Bahasa Melayu than English? 50 − 10 = 40 pupils.
  4. Check the total: 25 + 15 + 10 + 50 = 100 pupils. Correct!

Sometimes one picture in a pictograph stands for more than one thing. Always read the key first!

Problem 3: How many kuih were sold altogether?
Pictograph titled Kuih Sold at the Canteen. One picture represents 2 pieces of kuih. Karipap 5 pictures, onde-onde 3 pictures, kuih lapis 4 pictures, seri muka 2 pictures.
  1. The key: 1 picture = 2 pieces of kuih.
  2. Karipap: 5 × 2 = 10. Onde-onde: 3 × 2 = 6. Kuih lapis: 4 × 2 = 8. Seri muka: 2 × 2 = 4.
  3. Altogether: 10 + 6 + 8 + 4 = 28 pieces of kuih.
Counting pictures instead of things. There are 5 karipap pictures, but each picture stands for 2 karipap. So 10 karipap were sold, not 5.
Use the kuih pictograph. How many more karipap than seri muka were sold?
Show answerHide answer
Karipap 5 × 2 = 10. Seri muka 2 × 2 = 4. 10 − 4 = 6 more karipap.

Summary

RememberKey fact
DataInformation we collect by watching, asking or using a form
Classify and sortPut the same things in one group, then arrange them in a table
TallyOne stick for each thing. The 5th stick goes across: a group of 5. Count in fives.
CheckThe numbers in the table add up to the number of data collected
Pie chartData in a circle. Largest part = the most. Smallest part = the least. Read the key.
Three chartsMost pictures = highest bar = largest part. They can show the same data.
Pictograph keyIf 1 picture = 2, multiply the number of pictures by 2