Maths

Tallying, collecting and grouping data

In some investigations you may collect an awful lot of information. How can you use this raw data and make it meaningful? This section will help you to collect, organise and interpret the data efficiently.

# Explaining your results

Imagine that you are asked to carry out a survey to find the number of pets owned by pupils in your school. You decide to ask 50 people, and record your results as follows:

0  2  1  2  0  4  1  0  2  2  1  6  1  1  2  8  0  12

2  1  2  0  3  2  0  1  3  0  1  4  0  3  0  2  3  6

3  3  0  1  2  0  1  1  3  0  2  0  3  2

You now have the information you need, but is this the most efficient way to collect and display the data?

# Tallying

Tallying is a method of counting using groups of five.

= 1

= 2

= 3

= 4

= 5

= 6

= 7

= 8

= 9

= 10

Because we have used groups of five, it is easy to find the total.

Question

Which numbers do the following tally marks represent?

a.)

b.)

=13

=24

Using the tally system to record results is much faster than writing out words or figures all the time. For example, if you had to investigate the most popular type of vehicle that passed the school gates, it would be easier to draw tally marks in one of three columns than write: car, car, lorry, bike, car, car, and so on.

By using a tally chart, the data is already collected into groups, and will not require further grouping at a later date.

# Collecting data

The easiest way to collect data is to use a tally chart.

When collecting data for the number of pets survey, it would have been useful to draw a table similar to this one.

As each person answers the question, we put a tally next to the appropriate number of pets. The frequency column is completed once all of the data has been collected. The table below shows the results of a new pets survey.

## Number of pets survey

Number of petsTallyFrequency
03
18
212
31
42

These frequencies can be displayed in a bar chart, as shown.

Frequency means the 'number of times it occurs'.

In this example, three people had no pets, so the frequency of 0 pets was three.

Remember that the total frequency should be the same as the number of people in your survey. Always check that this is correct.

In this example, we know that 26 people were questioned in the survey. Check this by adding up the frequency totals: 3 + 8 + 12 + 1 + 2 = 26

Here is the same information but this time we have two tables, one for the number of pets owned by boys and one for the number of pets owned by girls.

## Number of pets owned by boys

Number of petsTallyFrequency
02
13
25
31
41

## Number of pets owned by girls

Number of petsTallyFrequency
01
15
27
30
41

These frequencies can be displayed in a dual bar chart.

We can find more information from looking at this graph.

Question

How many pets were owned by the same number of boys as for girls?

Four pets.

We can see that the height of the bar is the same for both boys and girls for four pets.

Question

How many more girls than boys were there in the survey?

Two more girls.

Adding the bars for girls and for boys we find:

• the total for girls is: 1 + 5 + 7 + 0 + 1 = 14
• the total boys is: 2 + 3 + 5 + 1 + 1= 12

# Grouping data

When a large amount of data has to be collected, use a grouped frequency distribution.

The following tally chart represents the ages of 200 people entering a park on a Saturday afternoon.

The ages have been grouped into the classes 0-9, 10-19, 20-29, and so on.

AgeTallyFrequency
0-98
10-1912
20-2924
30-3943
40-4941
50-5927
60-6923
70-7918
80-893
90-991

These frequencies can also be shown in a histogram.

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