Drawing Bar Charts

Bar charts are commonly used for displaying data.

	y-axis label

The bar chart uses rectangular blocks or bars.  These bars can be drawn vertically or horizontally, close together or with a gap between them.  The bar chart is used for discrete data.  A vertical Bar Chart is sometimes called a Column Chart.

Multiple Bar Charts 

This is an example of a multiple bar chart.

A multiple bar chart is a good choice because it is as easy to read as a simple bar chart and it is easy to compare the relative sizes of the bars.

Question 1

Note: These charts can be completed electronically or drawn on paper, photographed and sent to your lecturer.

Remember to add titles / labels and do not start on the y-axis.

1. This table shows the number of ice creams sold by Ernie’s 2 vans last week.

     Draw a multiple bar chart to compare the sales of the 2 vans.

• This table shows the number of students enrolled for a College.

Show these results in a multiple bar chart to compare the different types of learning for each year.

Drawing Compound Bar Charts

In compound bar charts, the different sections are ‘stacked’ one on top of the other. Compound bar charts are sometimes called component bar charts.

The rules for compound bar charts are still the same:

• You must have a Title that goes some way toward explaining your chart.
• You must draw and Label your axes.
• Your bars must be of Equal Width.
• Choose your scale so that it is easy to draw and easy to read. (i.e. Go up in 1s or 5s or 10s etc.)
• You will need to put in a key to show which part of the bar refers to which data.
• Do not start on the y-axis.

When drawing a compound bar chart, it is important to be careful with the scale. You will need to ‘pile’ all the data up on top of each other. This means that each column will be taller than if you were displaying the same data on a multiple bar chart.

Example

This table shows the sales of 3 holiday villas owned by the same company. The company is particularly interested in the total bookings for each year and how these totals are made up.

There is more than one way of displaying this data. If we were interested in comparing the sales trends of the various villas a line graph might be best. However, because we are interested in the total sales and how they are made up we will use a compound bar chart.

Choosing the scale is important because we need to display all the data as clearly as possible. We also want a scale that will be easy to use when we draw the chart. Looking at the data, the highest number is 400 but we need to look at the total for each year to know how high we need to go.

The total for 2017 is: 250 + 280 + 210 = 740

The total for 2018 is: 310 + 260 + 180 = 750

The total for 2019 is: 400 + 290 + 120 = 810

Our scale must go up to over 800.

First draw and label the axes and put in the title. Next put in the first villa. You must differentiate between the villas so add a key to show which is which.

Now complete the compound bar chart by stacking the next villa on top.

The completed bar chart shows the overall picture. From this bar chart it is easy to see that in 2019 Villa Arilla contributed more towards total bookings than previously. Villa Croix contributed less toward total bookings than before and bookings of villa Bonnella remained about the same.

It is also easy to see that total bookings are increasing year on year.

Remember, you must put a key on your compound bar chart to tell you what is what.

Advantages of Compound Bar Charts

• Can display more columns.
• Displays the totals for each.
• Shows how the total is made up from the component parts.

Disadvantages of Compound Bar Charts

• Not so easy to draw.
• Not so easy to read data for parts of bars.
• Not so familiar to people.

Question 2

Note: These charts can be completed electronically or drawn on paper, photographed and sent to your lecturer.

Remember to add titles / labels / key and do not start on the y-axis.

1. This table shows the bookings of 3 footballers from the same team over 4 seasons.

Draw a compound bar chart to illustrate the contribution made by each footballer to the team’s annual total.

• This table shows the average monthly volume of traffic using a car ferry over 5 years.

Draw a compound bar chart to illustrate the contribution made by each type of vehicle to the total volume of traffic per year.

Drawing Flow Charts

A flow chart breaks down a sequence of actions and decisions into logical, ordered steps. Each step is usually quite small. Sometimes loops are required to finish a task. The loop is repeated until some criteria is satisfied.

Points to remember:

• Flow charts begin and end with Start and Stop boxes.

                                            Notice their shape.

They must ‘flow’ from the start to the stop, following arrows. You must start at the start. You can only stop at the stop.

• Instruction boxes are rectangular. They tell you to do something.

• Decision boxes are diamond shaped. They ask questions. The questions must have Yes/No answers.

The hardest part of drawing flow charts is breaking the sequence of events into little steps. Sequence is important in many our daily tasks; we do this naturally and without thinking about it.

Example

In this flow chart a decisionhas to be made. The flowchart shows the sequence of sums when calculating a bill when the ticket cost is £7.95. Discount would be 5% if required.

Flow Chart Showing Bill Calculation

Here are a few symbols you might use as a shorthand way of writing:

Question 3

1. A flowchart is needed to calculate the wages in an office. The basic wage is £5.80 per hour for a 40-hour week. Any hours over 40 are paid at £7.20 per hour.

Complete the following flow chart by inserting each letter into the appropriate section of the chart or write down the order they should go into the chart – do not redraw the flow chart.

A = 40

B = Stop

C = £5.80

D = Start

E = £7.20

F = Yes

G = No

Wages Calculation

•  
• The Theatre Royal offers cut price tickets to large groups of people. The prices are:

• Groups up to 20 in size, tickets are £5.50 each
• Groups over 20 in size, the first 20 tickets at £5.50 each and the rest at £5.00 each.

Complete the following flow chart by inserting each letter into the appropriate section of the chart or write down the order they should go into the chart – do not redraw the flow chart.

A = 20

B = Start

C = 20

D = Stop

E = £5.50

Theatre Royal Ticket Discount

Drawing Stem and Leaf Charts

One way of ordering your data is to construct a stem and leaf diagram. You cannot make a stem and leaf diagram if the data is qualitative (words) or all the numbers are in single figures (1,2,3…).

Example

Jess is checking out her mobile phone bill and is looking at the number of text messages sent during the month of June.

Now look for the lowest and highest values (5 and 35). Set up a stem using the first digit, when you have single digits write them as 05

Notice that the stem is arranged in order, lowest first. The second digits become the leaves and are written to the right of the line.  You must be methodical when entering the leaves on the chart. One way of doing this is to take one column at a time.

Here is the first column.

Transfer the numbers to the chart.

Now complete the chart recording the rest of the second digits as the “leaves”.

Number of Texts sent in June.

Now order the leaves. The leaves increase outward from the stem.

Add a key at the bottom.

Number of Texts sent in June.

n = 30            1   2    represents 12 texts.

Notice that:

           The leaves are in straight columns it makes the chart easier to read.

Question 4

Note: These charts can be completed electronically or drawn on paper, photographed and sent to your lecturer.

1. The number of customers at a restaurant in July is shown in the table below. Construct a stem and leaf chart with the results.

• “Smokefree” has just run an advertising campaign and wants to look at how successful it was. Their helpline received the following number of phone calls per day. Construct a stem and leaf chart with the results. Use the first digit for the stem and the next 2 digits for the leaves.

If they received more than 280 phone calls on most of the days, then their campaign was a success. Was it successful?

          
When two sets of data have to be compared stem and leaf charts are very useful when drawn back-to-back.

Example

Natasha needs to compare the number of Americano and Cappuccino coffees sold over the last 20 days. The numbers sold are recorded in the table below.

The lowest number sold is 180 and the largest is 480.

The stem will therefore be 1 to 4.

Number of Coffees Sold

Notice that this time the stem has been drawn in the middle of the page. The leaves are recorded in the same way as before. The results from the Americanos are recorded to the left of the stem and the results of the Cappuccinos to the right.

Number of Coffees Sold

Now order the leaves and put in a key.

Number of Coffees Sold

Question 5

Note: These charts can be completed electronically or drawn on paper, photographed and sent to your lecturer.

The number of goals scored by teams from 2 different leagues, over 31 weeks is shown in the tables below. Construct a back-to-back stem and leaf chart with the results.

1. Drawing Mileage Maps

When drawing mileage maps there are some points to remember:

• You must have a title.
• Points (towns) must be labelled.
• Distances must be put in.
• Units (miles, km etc) must be specified either on the map or beside it.

Example

This simple table shows the distances between 3 towns, measured in miles. This map will be for Amir, who must travel between the three towns as part of his job as a software developer with Computer Solutions.

This will be a very simple map with only 4 towns so we will have a diamond. Each town will have 2lines leaving it.

Distances between four towns

All distances in miles

Example

There are to be 5 childcare training workshops this summer in Aberdeen, Edinburgh, Glasgow, Inverness and Perth. The head of the training centre has asked for a map showing the relationship between all the cities. This is a more complex situation with five cities; distances are again measured in miles.

To display this data on a map we will obviously need 5 cities. We will need 10 lines to connect the cities (one line for each distance). You will notice that each town has 4 lines leaving it.

Now check:

• Have you named every city?
• Have you one line for every distance?
• Have you written a title?
• Have you put in a key for the units?

Question 6

Note: These charts can be completed electronically or drawn on paper, photographed and sent to your lecturer.

Mileage Chart

Using this chart, draw mileage maps for other conferences to show the links between each of the following groups of towns.

1. Cardiff, Edinburgh, Perth and Southampton

• Edinburgh, Dover, Glasgow, Perth, and York

Drawing Complex Tables

Example – 2 chefs work for the same chain but in different locations.  The head chef of the chain collected information from them about the type of main course they were providing. The results were:

Chef Tony prepared 180 meals            50 of them were fish and the rest were meat.

Of the meat dishes 40 were red meat and the rest were white.

Chef Monica prepared 200 meals            70 of them were fish and the rest were meat.

Of the meat dishes 30 were red meat and the rest were white.

This is quite a lot of information and we must be careful how we handle it. You need 2 rows for the chefs, two columns for the ‘fish’ and ‘meat’ and you need to split the ‘meat’ column into 2 for the ‘red’ and the ‘white’.

First put in the numbers that you can read straight from the page.

Now you have to some sums to find the numbers of white meats. First add up the totals. For Chef Tony: 180 – 90 = 90 for white meat.

The final table should look like this.

Note: Remember that each table must include:

• Title
• Total column
• Total row

Question 7

Note: These charts can be completed electronically or drawn on paper, photographed and sent to your lecturer.

1. A catering supplier is carrying out a stock take. There are vegan products and meat products in stock. Put the following information into the table below, paying particular attention to the totals.

There were 486 vegan products and 532 meat products of which:

• 148 vegan burgers and 219 meat burgers
• 112 vegan sausages and 88 meat sausages
• 96 vegan pizzas and 25 meat pizzas
• 33 vegan sausage rolls and 80 meat sausage rolls
• 13 vegan kebabs and 24 meat kebabs
• 84 vegan curries and 96 meat curries

Title:

• 400 students were interviewed about their exercise preferences. They had to say whether they exercised or not. If they exercised, they were asked if they preferred classes or to exercise alone. Put the following information into the table below, paying particular attention to the totals.

• 45 under 30s and 25 in the 30 + group did not exercise
• 115 under 30s and 52 in the 30+ age group preferred classes.
• 98 under 30s and 65 in the 30+ age group preferred to exercise alone.

Title:

Tutor Marked Assignment 2 – Using Graphical Information

Question A

300 students were surveyed to establish which core skills subject was their favourite. The students made a choice from ICT or Numeracy. If the students chose Numeracy they were further asked if they preferred using numbers (UN) or using graphical information (UGI). Of the 300 students taking part in the survey, 180 were female and 120 male. Display the following information in a suitable graphical form:

• 62 female students selected ICT as their favourite core skills subject
• Of those females who chose Numeracy, 78 preferred using numbers (UN)
• 74 male students selected ICT
• Of those males who chose Numeracy, 12 preferred using graphical information (UGI)

Question B

Over a period of time the amount of sales from each department within 3 large hotels is given below:

Illustrate this information graphically to show the contribution made by each department to the total sales in each hotel.

Question C

Mileage Chart

Using this chart, display the information to show the links between each of the following towns in a suitable graphical form:

• Bristol, Glasgow, Manchester, Norwich, and London

Answers

Question 1

Question 2

Answers have been removed – please check with your lecturer

Question 3

a)        D, C, F, G A, E then B

Wages Calculation

b)        B, E, C, A then D

Theatre Royal Ticket Discount

Question 4

Number of Customers in July

n = 31 1 | 7 = 17customers

           Number of Phone Calls Received

n = 30            1 | 80 = 180 calls

There were more than 280 calls on 22 days – so it was a success.

Question 5

Question 6

Answers have been removed – please check with your lecturer

Question 7

Answers have been removed – please check with your lecturer

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