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When is the mode not a good measure of central tendency?
WHEN IS THE MODE NOT A GOOD MEASURE OF CENTRAL TENDENCY?
There are a number of reasons when the mode would not be the best measure of central tendency. Some are illustrated below.
Example
If there is more than one mode these modes will not be meaningful if a single measure of central tendency is required.
Employment details of 'The Widget Company' |
| |
Observation | Position in company | Salary ($) | |
| |
1 | CEO | 100 000 | |
2 | Manager | 100 000 | |
3 | Manager | 59 000 | |
4 | Factory Worker | 52 000 | |
5 | Factory Worker | 51 000 | |
6 | Factory Worker | 50 000 | |
7 | Factory Worker | 49 000 | |
8 | Trainee | 40 000 | |
9 | Trainee | 40 000 | |
| |
In the above table there are two modes, 100,000 and 40,000, therefore it is impossible to determine one measure of central tendency using mode in this case.
Example
If there is no mode in a
data set (as all
data items are different) then a different measure of central tendency is required.
Employment details of 'The Widget Company' |
| |
Observation | Position in company | Salary ($) | |
| |
1 | CEO | 100 000 | |
2 | Manager | 98 000 | |
3 | Manager | 59 000 | |
4 | Factory Worker | 52 000 | |
5 | Factory Worker | 51 000 | |
6 | Factory Worker | 50 000 | |
7 | Factory Worker | 49 000 | |
8 | Trainee | 45 000 | |
9 | Trainee | 40 000 | |
| |
In the above table there is no mode as all salaries are different.
Example
The mode may not fall near the centre of the
data.
Employment details of 'The Widget Company' |
| |
Observation | Position in company | Salary ($) | |
| |
1 | CEO | 100 000 | |
2 | Manager | 98 000 | |
3 | Manager | 59 000 | |
4 | Factory Worker | 52 000 | |
5 | Factory Worker | 51 000 | |
6 | Factory Worker | 50 000 | |
7 | Factory Worker | 49 000 | |
8 | Trainee | 40 000 | |
9 | Trainee | 40 000 | |
| |
In the above table the mode is now $40,000, which is not a good measure of central tendency.