Home » Further Maths Unit 3 & 4 » A1 - Data Analysis » 1.4 Displaying Numerical Data

1.4 Displaying Numerical Data

Dot Plot

  • Dot plots consist of a number line with each individual datapoint listed as a dot above it’s value. If multiple data points have the same value, they are placed in a column.

Example

Picture 2

Stem Plot

  • Stem plots are useful for displaying small to medium sized datasets.
  • The leading term for each value is referred to as a stem and is placed on the left side of a vertical line.
  • The following terms in each value are referred to as the leaf and are placed to the right of the line.
  • Multiple data points can share a common stem, but each leaf must represent only one datapoint.

Note: you may also see stem plots referred to as stem and leaf plots.

Note: When drawing a stem plot, always include a key of the form: \text { Key: } 1\ \mid\ 2=12

Example

Dataset: 7 11 23 25 31

Stem Plot:

Picture 1

Histogram

  • Histograms are used to display frequency for data ranges (i.e. how many data points have values between points). Multiple data ranges are shown in a single histogram.
  • Histograms appear similar in appearance to bar charts: the x-axis shows the values at either end of each range. In between each successive value along the x-axis, a bar representing the corresponding range is drawn up to the frequency of that range on the y-axis.

Note: unlike bar charts, you should not leave gaps between the bars on a histogram.

Example

Dataset: 1 3 4 11 13 15 17

Histogram with a range interval of 5:

Picture 6

log base 10 scale

  • The log function is the inverse of an exponential, for example:

10^{2} =100

Is equivalent to saying:

\log _{10}(100) =2

Note: the 10 in this case is called the base. Log functions can be made with almost any number as the base, however in Further Maths, assume you are using a base of 10 unless otherwise specified.

  • When displaying data with multiple orders of magnitude (i.e. when some data points are many times larger than others), using a linear scale makes our graphs difficult to read. Using a log scale, where the x or y value is the log of the datapoint’s original value, allows for a neater display.

Example

The following two plots show the same data with different scales.

Picture 7
Picture 8

We can see on the left plot, using a linear scale, it is difficult to see the difference in x-values for the first 3 points, while it is easy to see on the right plot, using a logarithmic scale.