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Modes
Salary surveys often report the average (mean) or the median of salaries. However, these numbers may or may not be a good representation of all of the salaries in the sample collected. It is useful to also look at the distribution of the salaries in the sample. A normal distribution will tell you that the average or median salary reported is representative of the sample. A skewed distribution will tell you that the reported average or median salary is too high or too low, depending on whether the distribution is skewed toward the high end or the low end. A bi-modal distribution demonstrates that the reported average or median is of little value and that the sample might have two averages or two medians instead of one (in this case, the salaries may represent two different grades for that position). The top of a distribution, or the value that occurs with the greatest frequency, is called a mode.
| Mode | The value that appears with the greatest frequency in a set of observations. |
The category with the greatest concentration is usually located at or near the center of a distribution, although this is not always the case.
For more information on modes, refer to http://davidmlane.com/hyperstat/A10032.html .
Example of modes
A salary survey reports the following for the Fast-Food Worker position:
| Fast-Food Worker Salary ($) |
|---|
| 21,000 |
| 22,000 |
| 25,000 |
| 27,000 |
| 22,000 |
| 25,000 |
| 23,000 |
| 24,000 |
| 21,000 |
| 22,000 |
| 22,000 |
| 23,000 |
| 22,000 |
| 21,000 |
| 20,000 |
| 20,000 |
| 21,000 |
What is the mode salary?
Modes solution
To find the mode salary, rearrange the salaries in order:
| Frequency | Salary ($) |
|---|---|
| 2 |
20,000 20,000 |
| 4 |
21,000 21,000 21,000 21,000 |
| 5 |
22,000 22,000 22,000 22,000 22,000 |
| 2 |
23,000 23,000 |
| 1 | 24,000 |
| 2 |
25,000 25,000 |
| 1 | 27,000 |
According to the above frequency distribution, $22,000 occurs most frequently (5 times). Therefore, $22,000 is the mode salary.
Memory Jogger
A salary survey reports the following for the position of Accountant:
| Accountant Salary ($) |
|---|
| 70,000 |
| 80,000 |
| 90,000 |
| 70,000 |
| 80,000 |
| 80,000 |
| 60,000 |
| 80,000 |
What is the mode salary?