Unit 11 Section 2 : Collecting Data

In this section, we will see how data is collected and organised, using a tally chart, and displayed using
  • pictograms
  • bar charts
  • pie charts

NOTE
A hypothesis is an idea that you want to investigate to see if it is true or false. For example, you might think that most people in your school get there by bus. You could investigate this using a survey. A tally chart can be used to record your data.

Example

The pupils in a class were asked how they got to school. The results are shown below.
The frequency is how often a particular response occurred.
We can see that the frequency of Walk is 9, so there must have been 9 pupils who said that they walked to school.

NOTE
We can also see that the most common way of getting to school is by bus, because it has the highest frequency. The category or value with the highest frequency is known as the modal class or mode.

We can illustrate the data in the table above using:
  • a pictogram
  • a bar chart
  • a pie chart

(1) Pictogram

Note how a half-person picture is used to represent one person.

(2) Bar Chart

Note how the height of the bar represents the frequency; each section represents one person.

(3) Pie Chart
A pie chart uses a circle divided into several pieces of pie or sectors to represent each of the frequencies.
The first step is to work out what angle in the circle will represent one person.
There are 360 in a full circle and 30 pupils in this survey, so:

To find the angle for 'Walk', we simply multiply the angle per pupil (12) by the number of pupils who said 'Walk':

The completed calculations for this are shown in the table below.

It is important to always check that the angles add up to 360. If they don't add up to 360, then you have made a mistake.
The completed pie chart looks like this:


You should always label each sector of the pie chart with a name and an angle.

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

When plotting a bar chart, simply click a point on the grid and a bar will appear leading up to that point.
Click on a different point in the same column and the bar will change height.

Question 1
The children in a class were asked to state their favourite crisps. The results are given in the chart below.

(a) Complete the frequency column in the table
Flavour Tally Frequency
Ready Salted
Salt and Vinegar
Cheese and Onion
Prawn Cocktail
Smokey Bacon
 
TOTAL

(b) Represent the data on a bar chart using the axes below.

(c) Complete the angle column in this pie-chart table (you will probably find it helpful to fill in the frequency column).
Flavour Frequency Angle
Ready Salted 5
5
360
= 5 12 = 60
30
Salt and Vinegar
Cheese and Onion
Prawn Cocktail
Smokey Bacon
 
TOTAL

(d) Draw the pie chart for this information on a sheet of paper.
When you have finished, click on the button below to see what the pie chart should look like.


(e) What flavour of crisps is the mode?

Question 2
The pictogram below illustrates the ages of some children who belong to a junior tennis club.

(a) What is the modal age?

(b) How many pupils are aged 8?

(c) How many pupils are 9 or younger?

Question 3
The bar chart below gives information about the pets owned by the children who live in a particular road.

(a) How many girls do not have a pet?

(b) How many children own hamsters?

(c) Are the hamsters more popular with girls or boys?

(d) How many girls have rabbits?

(e) What is the most popular pet with the boys?

(f) What is the least popular pet with the girls?

Question 4
Malcolm thinks that the dice in his Monopoly set is unfair because he never gets a 6 when he wants one.
He decides to test the dice and rolls it 60 times. The picture below shows his results.

Enter the data in the bar chart on the right. You could either make up a tally table to find the frequencies or you could attempt to add the data into the chart directly.


You have now completed Unit 11 Section 2
Your overall score for this section is
Correct Answers
You answered questions correctly out of the questions in this section.
Incorrect Answers
There were questions where you used the Tell Me button.
There were questions with wrong answers.
There were questions you didn't attempt.
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Produced by A.J.Reynolds January 2001