Give feedback
Chapter overview
Learning goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
Other graphs
Ratio
Proportion
Rates of change
Shapes
Properties of shapes
Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
Graphs are a clear and visual way to represent data. They help you to recognise trends and irregularities, and you can use statistics such as the mean, median and mode to compare the data.
A bar chart represents each item of data as a bar with its height representing the frequency of the item.
Plot a bar chart of the following data of participants running in a race and distance ran:
DISTANCE RAN$/\text{km}$ | FREQUENCY |
$8$ | $60$ |
$10$ | $80$ |
$15$ | $120$ |
$20$ | $80$ |
A pie chart is visual display where a circle is divided into sectors that each represent a proportion of the whole.
Plot a pie chart of the following data of instruments practised by students in a class.
Instrument practised | Frequency |
Piano | $6$ |
Guitar | $2$ |
Saxophone | $2$ |
Flute | $1$ |
Drums | $2$ |
Violin | $3$ |
Trumpet | $2$ |
A scatter graph is a plot of the data where the position of each piece of data is represented by its value on each axis.
Plot a scatter graph of the following data:
$\begin{array}{c|c:c:c:c:c:c:c:c} x & 1 &2 &3 &5 &7 &9 &11 & 12 \\ \hline y & 10 & 8 & 11 & 7 & 6 & 9 & 12 & 14 \end{array}$
A line graph is a scatter plot of the data with lines between each point, where each point represents the data of a unit.
Plot a line graph of the following data:
$\begin{array}{c|c:c:c:c:c:c:c:c:c} x &0 &1 & 2 & 3 & 5 & 7 & 9 & 11 & 12 \\ \hline y & 60 & 75 & 84 & 92 & 112 & 116 & 134 & 140& 144 \end {array}$
A statistic is any calculation derived from data.
Mean | The arithmetic mean of all the data. |
Median | $50\%$ of the data lies below this value, $50\%$ of the data lies above this value. |
Mode | The most common value within the data. |
Range | The difference between the greatest and smallest values of all the data. |
Lower quartile | $25\%$ of the data lies below this value. |
Upper quartile | $25\%$ of the data lies above this value. |
Interquartile range | The difference between the upper and lower quartiles. |
For the following data, work out the mean, median, mode, range and interquartile range. Plot a box-plot diagram of the data.
$23 \quad 9 \quad 26 \quad 36 \quad 26 \quad 11 \quad 21 \quad 12 \quad 35 \quad 10 \quad 14 \quad 18$
Mean: $\dfrac{23+9+26+36+26+11+21+12+35+10+14+18}{12} = \underline{20.1} \thinspace(3\thinspace\text{s.f.})$
Median: The data is ordered as follows:
$9 \quad 10 \quad 11 \quad 12 \quad 14 \quad 18 \quad 21 \quad 23 \quad 26 \quad 26 \quad 35 \quad 36$
The median is the value in the middle of this $\dfrac{18+21}{2}=\underline{19.5}$
Mode: The most common value $= \underline{26}$
Range: $36 -9 = \underline{27}$
Lower quartile: $\underline{11.5}$
Upper quartile: $\underline{26}$
Interquartile range: $26 - 11.5 = \underline{14.5}$
A box-plot diagram shows the lowest and greatest values, and the three quartile values as follows:
Graphs are a clear and visual way to represent data. They help you to recognise trends and irregularities, and you can use statistics such as the mean, median and mode to compare the data.
A bar chart represents each item of data as a bar with its height representing the frequency of the item.
Plot a bar chart of the following data of participants running in a race and distance ran:
DISTANCE RAN$/\text{km}$ | FREQUENCY |
$8$ | $60$ |
$10$ | $80$ |
$15$ | $120$ |
$20$ | $80$ |
A pie chart is visual display where a circle is divided into sectors that each represent a proportion of the whole.
Plot a pie chart of the following data of instruments practised by students in a class.
Instrument practised | Frequency |
Piano | $6$ |
Guitar | $2$ |
Saxophone | $2$ |
Flute | $1$ |
Drums | $2$ |
Violin | $3$ |
Trumpet | $2$ |
A scatter graph is a plot of the data where the position of each piece of data is represented by its value on each axis.
Plot a scatter graph of the following data:
$\begin{array}{c|c:c:c:c:c:c:c:c} x & 1 &2 &3 &5 &7 &9 &11 & 12 \\ \hline y & 10 & 8 & 11 & 7 & 6 & 9 & 12 & 14 \end{array}$
A line graph is a scatter plot of the data with lines between each point, where each point represents the data of a unit.
Plot a line graph of the following data:
$\begin{array}{c|c:c:c:c:c:c:c:c:c} x &0 &1 & 2 & 3 & 5 & 7 & 9 & 11 & 12 \\ \hline y & 60 & 75 & 84 & 92 & 112 & 116 & 134 & 140& 144 \end {array}$
A statistic is any calculation derived from data.
Mean | The arithmetic mean of all the data. |
Median | $50\%$ of the data lies below this value, $50\%$ of the data lies above this value. |
Mode | The most common value within the data. |
Range | The difference between the greatest and smallest values of all the data. |
Lower quartile | $25\%$ of the data lies below this value. |
Upper quartile | $25\%$ of the data lies above this value. |
Interquartile range | The difference between the upper and lower quartiles. |
For the following data, work out the mean, median, mode, range and interquartile range. Plot a box-plot diagram of the data.
$23 \quad 9 \quad 26 \quad 36 \quad 26 \quad 11 \quad 21 \quad 12 \quad 35 \quad 10 \quad 14 \quad 18$
Mean: $\dfrac{23+9+26+36+26+11+21+12+35+10+14+18}{12} = \underline{20.1} \thinspace(3\thinspace\text{s.f.})$
Median: The data is ordered as follows:
$9 \quad 10 \quad 11 \quad 12 \quad 14 \quad 18 \quad 21 \quad 23 \quad 26 \quad 26 \quad 35 \quad 36$
The median is the value in the middle of this $\dfrac{18+21}{2}=\underline{19.5}$
Mode: The most common value $= \underline{26}$
Range: $36 -9 = \underline{27}$
Lower quartile: $\underline{11.5}$
Upper quartile: $\underline{26}$
Interquartile range: $26 - 11.5 = \underline{14.5}$
A box-plot diagram shows the lowest and greatest values, and the three quartile values as follows:
FAQs
Question: What is the difference between a graph and a chart?
Answer: A graph is a chart used to show the mathematical relationship between varied data sets. A chart represents information that can be in the form of a diagram, table, or graph. It comprises various methods for presenting large information.
Question: How do you read data from a graph?
Answer: To interpret a graph or chart, read the title, look at the key, read the labels. Then study the graph to understand what it shows. Read the title of the graph or chart. The title tells what information is being displayed.
Question: Why are graphs and charts used to represent information?
Answer: Graphs and charts condense large amounts of information into easy-to-understand formats that clearly and effectively communicate important points.
Theory
Exercises
© 2020 – 2023 evulpo AG
Your data protection
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners who may combine it with other information that you’ve provided them or that they’ve collected from your use of their services. By clicking on either "Accept cookies" or "Necessary cookies only", you agree to this (read more in our Privacy Policy). Privacy Policy