Dot Diagrams

A dot diagram is drawn by placing dots that represent the values of a set of data above a horizontal number line. The number of dots above each value indicates how many times the value occurred.

Stem and Leaf Diagrams

In a stem and leaf diagram, each value is split into two parts, the stem and the leaf, by a vertical line. The following video teaches you how to plot stem and leaf diagrams:

Definitions

The mode, median and mean are measures of central tendency. A measure of central tendency is a single value that describes where the data are centred, i.e. its average value.

Mode
1. The mode of a set of data is the value that occurs most frequently.
2. In some distributions, no value appears more than once so there is no mode. In other distributions, there may be more than one mode.
Note: The class interval with the highest frequency is called the modal class.

For example, in the following set of data, the mode is 7.
1, 1, 2, 6, 7, 7, 7, 8, 9

Median
1. The value exactly in the middle of a set of ordered numbers (ascending or descending) is the median.
2. To find the median of a set of n data:
- arrange the numbers in ascending order
- if n is odd, the median is the middle value. If n is even, the median is the mean of the two middle values. 
3. To find the middle position of a set of n data, use (n+1)/2.

For example, in the following set of data, the median is 5.5
1, 4, 5, 6, 8, 9

Mean
The mean of a set of data is obtained by dividing the sum of all the data by the total number of data.
The principle is the same when calculating mean for grouped data.

For example, in the following set of data, the mean is 5.
8, 3, 1, 2, 6, 7, 5, 5, 4, 9

Comparison

The table below gives the comparison of the strengths and weaknesses for the mean, median and mode.

Mean for Grouped Data

View the following formula and question, and attempt it before viewing the answer later.

Answer

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