# What change would most improve the usefulness of the graph?

A picture, so they say, will tell a thousand also words. But what around a graph or chart?

A great graph or chart deserve to show as a lot as numerous paragraphs of words. But just how perform you pick which style of graph to use?

This page sets out some of the basics behind drawing and producing good graphs and charts. By ‘good’, we intend ones that display what you desire them to present, and also don’t mislead the reader.

You watching: What change would most improve the usefulness of the graph?

## Types of Charts

Tbelow are numerous various kinds of charts and also graphs. The four many common are more than likely line graphs, bar graphs and also histograms, pie charts, and Cartesian graphs. They are mainly used for, and are best for, quite different things.

You would certainly use:

Bar graphs to show numbers that are independent of each various other. Example data can include things like the number of world that desired each of Chinese takeamethods, Indian takeamethods and fish and also chips.

Pie charts to display you how a whole is separated right into different parts. You might, for example, want to display how a budgain had been spent on various items in a details year.

Line graphs present you just how numbers have actually changed over time. They are supplied once you have information that are associated, and also to show fads, for instance, average night-time temperature in each month of the year.

### Axes

Graphs have 2 axes, the lines that run across the bottom and also up the side. The line alengthy the bottom is dubbed the horizontal or x-axis, and the line up the side is called the vertical or y-axis.

The x-axis may contain categories or numbers. You check out it from the bottom left of the graph. The y-axis generally includes numbers, aacquire beginning from the bottom left of the graph.

The numbers on the y-axis primarily, yet not constantly, start at 0 in the bottom left of the graph, and also move upwards. Usually the axes of a graph are labelresulted in indicate the type of data they display.

Beware of graphs wright here the y-axis does not begin at 0, as they may be trying to fool you around the information displayed (and also tbelow is even more about this on our page, Everyday Mathematics).

## Bar Graphs and also Histograms

Bar graphs primarily have categories on the x-axis, and also numbers on the y-axis (however these are interchangeable). This implies that you can compare numbers between various categories. The categories must be independent, that is alters in among them carry out not influence the others.

Here is a review of "some data" in a file table:

 Some Data Category 1 4.1 Category 2 2.5 Category 3 3.5 Classification 4 4.7

And the very same data presented in a bar chart:

You can view instantly that this graph gives you a clear picture of which category is biggest and which is smallest. It offers a clear comparison in between categories.

You deserve to additionally usage the graph to review off information around just how many kind of are in each category without having to refer ago to the data table, which may or might not be provided through eexceptionally graph you see.

In basic, you deserve to attract bar graphs with the bars either horizontal or vertical, because it doesn’t make any distinction. The bars carry out not touch.

A histogram is a specific type of bar chart, wright here the categories are arrays of numbers. Histograms therefore show linked consistent information.

Histogram - Worked Example

You have actually been offered a list of eras in years, and you must display them in a graph.

The eras are: 5, 12, 23, 22, 28, 17, 11, 21, 25, 23, 7, 16, 13, 39, 35, 42, 24, 31, 35, 36, 35, 34, 37, 44, 51, 53, 46, 45, and also 57.

You can pick to group them right into ten-year age categories, 0–10, 11–20, 21–30 and also so on:

 Age Number of people 0-10 2 11-20 5 21-30 7 31-40 8 41-50 4 51-60 3

To show this information in a histogram, your x-axis would be numbered in 10s from 0 to your highest possible age, your y-axis from 0 to 8 (the highest possible number of human being in any kind of group), and tbelow would certainly be no gaps between the bars, bereason there are no gaps between the age arrays.

### Pictograms

A pictogram is a distinct form of bar graph. Instead of making use of an axis through numbers, it supplies photos to represent a specific variety of items. For instance, you can usage a pictogram for the data above about periods, with an image of a perkid to display the variety of civilization in each category:

## Pie Charts

A pie chart looks like a circle (or a pie) cut up into segments. Pie charts are used to present exactly how the entirety breaks down into components.

For example, this information reflects the sales numbers for a year, broken down by quarters:

 Quarterly Sales Figures 1st Qtr second Qtr 3rd Qtr fourth Qtr 8.2 3.2 1.4 1.2

From the pie chart you can check out automatically that sales in Quarter 1 were much bigger than all the others: more than 50% of full annual sales.

Quarter 2 was following, with about 25% of sales.

Without knowing anypoint even more around this business, you can be concerned about the way that sales showed up to have dropped over the year.

See more: If The Time Required For A Student To Swim 500, Circles, Energy, And Momentum

Pie charts, unprefer bar graphs, display dependent data.

The complete sales in the year need to have to have occurred in one quarter or an additional. If you’ve acquired the numbers wrong, and Q1 must be smaller, among the other quarters will certainly have sales added to compensate, assuming that you haven’t made a mistake with the total.

Pie charts show percentages of a whole - your complete is therefore 100% and also the segments of the pie chart are proportionally sized to represent the percentage of the total. For more on percentperiods view our page: Summary to Percentages.

Usually it is not proper to usage pie charts for more than 5 or 6 various categories. Lots of segments are challenging to visualise and also such information may be much better shown on a different form of chart or graph.

## Line Graphs

Line graphs are typically supplied to present dependent data, and also particularly trends over time.

Line graphs depict a allude value for each category, which are joined in a line. We can usage the data from the pie chart as a line graph as well.

You have the right to watch also even more obviously that sales have fallen swiftly over the year, although the slow-down is levelling out at the finish of the year. Line graphs are specifically valuable for identifying the point in time at which a particular level of sales, revenue (or whatever the y value represents) was got to.

In the instance above, suppose we desire to recognize during which quarter sales initially fell listed below 5. We can attract a line throughout from 5 on the y-axis (red line on the example), and view that it was throughout quarter 2.

## Cartesian Graphs

Cartesian graphs are what mathematicians really mean once they talk about graphs. They compare two sets of numbers, among which is plotted on the x-axis and one on the y-axis. The numbers deserve to be created as Cartesian coordinates, which look like (x,y), where x is the number read from the x-axis, and also y the number from the y-axis.

Warning!

Cartesian graphs execute not constantly start at 0; rather often (0,0) is the mid-point of the graph.

Cartesian Graph - Worked Example

John is 2 years older than Mary, and their eras included together equal 12. What age are they both now?

We can fix this by drawing two lines, one of John’s age compared with Mary’s, and also one of the periods that add together to provide 12.

Line 1: John’s (actual) age once Mary is various ages between 1 and also 9

 Mary"s Age 1 2 3 4 5 6 7 8 9 John"s Age (=Mary + 2) 3 4 5 6 7 8 9 10 11

Line 2: John’s (hypothetical) age as soon as Mary is various eras in between 1 and 9 if their ages include up to 12

 Mary"s Age 1 2 3 4 5 6 7 8 9 John"s Era (=12 - Mary"s Age) 11 10 9 8 7 6 5 4 3

Plotting the two lines on graph, through Mary’s age as the x-axis, you can check out that tright here is a point at which the lines cross. This is the just point at which a) John is two years older than Mary and b) their eras add up to 12. This must be their current ages, which are therefore 5 for Mary and 7 for John.

For more about the offers of Cartesian graphs to settle difficulties in maths, take a look at our peras on Algebra and Simultaneous and Quadratic Equations.

### Drawing Graphs utilizing Computer Packages

You have the right to usage various computer software application packperiods, consisting of Word and Excel, to draw graphs.

Some packperiods are incredibly capable when provided successfully. However, be conscious that some applications are quite restricted in the kind of charts that they have the right to attract, and you might not uncover the results entirely what you expected! You really require a simple knowledge of graphs and also charts so that you have the right to compare what the computer has actually developed to what you desire to present.

Computer applications additionally make it basic to develop overly-complicated graphs. A 3D exploding pie chart may look "cool" yet does it assist you or others to visualise the data? It is often best to store graphs and charts simple with neat, clear formatting.

More Reading from Skills You Need

Documents Handling and also Algebra Part of The Skills You Need Guide to Numeracy

This eBook covers the basics of data managing, information visualisation, basic statistical evaluation and also algebra. The book includes plenty of functioned examples to enhance expertise and real-world examples to display you how these principles are helpful.

Whether you desire to brush up on your basics, or aid your kids with their discovering, this is the book for you.

### A Graph is Worth…

However before you select to current your data, when you have actually mastered the skills of developing clear graphs and also charts, you will virtually certainly discover that the old saying is right: a picture really deserve to tell a thousand words.

See more: _____ Are Normally Expressed In The Form Of Rules., Chapter 2 Review Flashcards

Whether your well-drawn graph is worth a thousand also numbers or a dozen, it will definitely be an reliable means of presenting your data and also demonstrating the relationships or differences in between them.