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Module 1 (M1) - Handling data - Presenting and interpreting data

Part of MathsM1: Handling data

Data can be presented in many ways that make it quicker and easier to read.

In this section we will look at some of these ways. It is important to choose the best way to present data.

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Frequency tables

When a lot of data needs to be sorted, one of the most efficient ways is to use a table. This is a way of organising data and making it easier to read.

  • A frequency table has at least two columns.
  • The last column shows the total or frequency for each item.

A middle column showing can sometimes be useful.

Example

This is the data gathered from a survey about the colours of cars in a car park.This data can be displayed in a frequency table.

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  1. Example one. Table listing the colours of cars. A grid of raw data. The grid has seven columns and five rows. Each cell is populated with a colour. The first row is: red, grey, red, blue, black, grey, white. The second row is: blue, blue, white, grey, blue, grey, red. The third row is: red, blue, white, black, black, black, grey. The fourth row is: red, grey, red, blue, red, black, red. The fifth row is: grey, blue, blue, grey, black, white, white.

    This is the data gathered from a survey about the colours of cars in a car park. This data can be displayed in a frequency chart.

Grouping data on a frequency table

When a lot of data needs to be sorted, one of the most efficient ways is to use a frequency table.

It is important to consider the sizes of groups when sorting data into a frequency table.

Example

Megan owns a bakery. She counts the number of customers she has each day at lunchtime on 30 consecutive days. The results are shown here.

13816121216
7181116157
111213211719
111410191312
7166141218

Using this data in list form could be time consuming and with a large set of data it may lead to mistakes or miscalculations. A grouped frequency table would help to display and give an overview of the data. The smallest number is 6 and the biggest number is 21, so groups that have a width of 5 are reasonable - this will give a reasonable amount of groups to work with, and the smaller the groups, the more accurate the analysis will be.

Number of customersTallyFrequency
5-10\(\cancel{||||}~|\)6
11-15\(\cancel{||||}~\cancel{||||}~||||\)14
16-20\(\cancel{||||}~||||\)9
21-25\(|\)1

Question

The chart below shows the results of a survey where people were asked how long it takes them to walk to school.

How many people took more than 11 minutes?

An image of a table with two columns and seven rows. The first column is labelled, journey length, measured in minutes, and is populated with the groups, zero to three, four to seven, eight to eleven, twelve to fifteen, sixteen to nineteen, and more than twenty. The second column is labelled, tally. There are two tally marks in the cell to the right of zero to three; drawn as two single tally marks. There are eight tally marks in the cell to the right of four to seven; drawn as a set of five and three single tally marks. There are four tally marks in the cell to the right of eight to eleven; drawn as four single tally marks. There are twelve tally marks in the cell to the right of twelve to fifteen; drawn as two sets of five and two single tally marks. There are two tally marks in the cell to the right of sixteen to nineteen; drawn as two single tally marks. There are three tally marks in the cell to the right of more than nineteen; drawn as three single tally marks. The cells for the labels are coloured purple.

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Pictograms

Pictograms use pictures to represent data. To make sense, a pictogram must always have a key.

In a pictogram it is important to make sure that each picture is the same size, equally spaced out and lined up one beneath the other.

Reading pictograms

This pictogram below shows the number of pizzas eaten by four friends in the past month.

The key tells you that one pizza on the pictogram represents \(4\) pizzas eaten, so Alan ate \(4 + 2 = 6\) pizzas.

Pictogram showing the number of pizzas eaten by 4 friends in the past month

Pictogram representing number of pizzas eaten using images of pizzas

Question

  1. Who ate the most pizzas?

  2. How many pizzas did Bob eat?

  3. What was the total number of pizzas eaten by the four friends?

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The pictogram shows the number of hot drinks sold during the morning in a café.
An image of a completed pictogram. The pictogram has four rows. Each row is labelled with the name of a drink, tea, coffee, hot chocolate, and other. Images of takeaway cup icons have been drawn on each row to represent the frequencies. On the tea row; four. On the coffee row; three. On the hot chocolate row; one. On the other row; two and a half. Written above: A pictogram to show drinks sold. Key: An image of the takeaway cup icon equals two drinks. The cells for the labels are highlighted purple. The label, two drinks, is coloured orange.

How many coffees were sold?

How many 'other' drinks were sold?

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Bar charts

A bar chart is a diagram which uses rectangular bars, of equal width, to show frequencies. The heights of the bars show the frequency of the categories.

It is easy to pick out the most popular as it will be the tallest bar.

Bar chart to show children's favourite pets
Bar chart showing the frequency of children's favourite pets

Question:

What was the most popular pet?

Answer:

A cat was the most popular pet as cat has the tallest bar.

Question:

How many children chose rabbits?

Answer:

4 children chose rabbits

Question:

How many more children chose a dog than a fish?

Answer:

A dog was chosen by 9 children and a fish was chosen by 3 children.
6 more children chose a dog than a fish.

Question

Leon conducts a survey to find the number of people in each of the cars arriving at the school gate between 8.30am and 9.00am.
His results are shown in the bar chart below:

Bar chart showing the number of people in each car arriving at school

Bar chart of number of people in the car against frequency

  1. How many cars contained 1 person?

  2. How many cars contained more than 3 people?

  3. Why are there only a small number of cars containing 1 person?

  4. How many cars arrived at the school gate between 8.30am and 9.00am?

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Comparative bar charts

Bar charts can be used to compare data. A stacked bar chart can show the frequency of items for two more groups.

The following frequency table shows the information for the numbers of pets owned by a class.

No pets1 pet2 pets3 or more pets
Boys2423
Girls3321
Number of pets owned vs frequency bar chart

This stacked bar chart is showing information about number of pets owned as well as comparing the number of boys and girls who own the pets.

Example

How many girls had more than one pet?

Answer

2 girls had 2 pets and 1 girl had 3 pets, so 3 girls had more than one pet.

A dual bar chart can also show the frequency of items for two more groups with the bars placed side by side.

Example
An image of a dual bar chart.

Which of the following statements is true?

  • The number of students with blue eyes in year 8 is greater than the number in year 7.
  • The number of students with green eyes in year 7 is greater than the number in year 8.
  • The number of students in year 7 is less than the number in year 8.

Answer

The number of students with green eyes in year 7 is greater than the number in year 8.

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Test yourself

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