Line graphs are an efficient and useful way to present data for two mutually dependent variables.

In an ideal experiment, all variables are kept the same, except one. This is the 'control', or 'independent', variable. With each value of the control variable, a quantity is measured. For example, this is the table of data for an experiment in which an object is dropped and allowed to fall under gravity:

Time t /s | Distance /m |
---|---|

0.05 | 0.0123 |

0.10 | 0.0491 |

0.15 | 0.110 |

0.20 | 0.196 |

0.25 | 0.307 |

0.30 | 0.441 |

0.35 | 0.601 |

0.40 | 0.785 |

0.45 | 0.993 |

0.50 | 1.23 |

The control variable is changed under the control of the experimenter, and the other variable (dependent or measured variable) is measured and recorded. A table is usually the most convenient way to record this raw data.

After the raw data has been collected, it is then processed. This may involve calcuations, which assume, or reveal, the relationship between the variables. For example, the data may reveal that the acceleration (dependent variable) under gravity remains constant) through time.

- Graph title
- X-axis:
- Y-axis:
- Axis labels
- Origin
- Plot the data points
- Line of best fit
- Label the curves

Put a title at the top of the graph. Always provide a graph with a meaningful title. Be as specific as possible, but do not make it too long. Avoid vague titles like 'Data' or 'Graph of Experimental Data', which will mean little to a reader. Much better are titles like 'Position of falling object against time'.

Time always goes on the x-axis. Otherwise, the control (or independent) variable goes on the x-axis.

The measured (or dependent) variable goes on the y-axis.

Both axes need to be labelled, with the units of the quantity they represent in parentheses.

The origin is the starting point of the axes. It is usually zero. However, if the graph data always falls in a range that is not close to zero, it may make more sense to choose a different value for the origin.

Use 'x' or '+' to mark accurately the data points. Do not use dots - they are inaccurate if large, and will be hard to see if small.

If a clear trend can be seen in the data (a straight line or a curve), a line of best fit is drawn through the data points. The data points should fall equally above and below the line, so the line represents the average.

If more than one curve is drawn on a single pair of axes, make sure you label them, or use colours or a system of dashes or similar, with a key somewhere on the graph explaining what the curves represent.

Bar charts (or graphs) are an alternative to line graphs for presenting data. Whereas line graphs display data as a continuous line, bar charts represent ranges of data.

This is a table showing the number of new enrolments in a gymnasium over one year:

Month | Enrolments |
---|---|

Jan | 32 |

Feb | 34 |

Mar | 48 |

April | 46 |

May | 49 |

June | 34 |

July | 12 |

Aug | 3 |

Sep | 34 |

Oct | 23 |

Nov | 38 |

Dec | 26 |

There are many computer applications available for creating graphs of different types. You should try different ones, and learn which chart type and information in the title, axes and legend best describe the graph for your reader.

A very good programme for storing, processing and presenting data in tables and graphs is Excel of the Microsoft Office Suite. This bar chart was generated from Excel.

Plots of data do not usually fall conveniently on a line. A line of best fit can be drawn which is an average. There will be an equal distribution of points times their distance from the line, below and above the line of best fit.

The mean values (62.5%, 52.5%) of the scatter plot will fall near to the line of best fit. Knowing one data point, the line of best fit helps us determine the most probable other data point.

In the example graph here, the French test result was known (52.5 %), so the Maths test result is likely to be around 70%. The spread of the data points (distance from the line of best fit) gives an indication of the uncertainty of this measurement (in this case about ± 10%).

A more accurate uncertainty can be determined by calculating the standard deviation.

Content © Andrew Bone. All rights reserved. Created : March 21, 2014

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Jakob Bernoulli was the first of long series of Bernoulli family members, all mathematicians, whose combined contributions to mathematics and physics is unequalled in history.

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