Sometimes it is convenient to use another measure of central tendency called Mode. The mode is very useful in trade and industry.
Mode is that value of the variable in the data which occurs most frequently, that is, an observation with the maximum frequency is called the Mode.
For example, if the following represent shoe sizes.
5, 6, 7, 8, 6, 7, 7, 7, 6, 8, 9
The shoe size with the maximum frequency of 4 is 7.
The mode is 7.
The clothing and shoe industries have made use of this idea. They manufacture those collar/shoe sizes which have the maximum demand and reduce the production of other sizes of these products.
Example : 17
Find the mode of the following data:
15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15
Solution:
We make a frequency table.
| xi |
14 |
15 |
16 |
17 |
18 |
19 |
20 |
fi |
4 |
5 |
1 |
1 |
1 |
2 |
1 |
Here 15 has a maximum frequency of 5
Mode = 15
In this case the mode is unique and the data is said to be uni-modal.
Example : 18
Find the mode for the data
4, 5, 5, 7, 6, 6, 3, 2, 7, 6, 7
Solution
In the data
3 observations are 6
3 observations are 7
The modes are 6 and 7.
Since the data has 2 modes it is said to be bi-modal.
The mean, median and mode are related by the formula
Mode = 3Median – 2Mean
Try these problems
Find the mode of the following observations state if the data is uni-modal or bimodal.
- 17, 6, 19, 14, 8, 6, 12, 15, 6, 16
- 27, 14, 42, 27, 25, 31, 28, 31, 43
Answers
- Rewriting 17, 6, 19, 14, 8, 6, 12, 15, 6, 16 with frequencies
xi |
6 |
8 |
12 |
14 |
15 |
16 |
17 |
18 |
fi |
3 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
Mode = 6 since the maximum frequency is 3. The data is uni-modal.
- Rewriting 27, 14, 42, 27, 25, 31, 28, 31, 43 with frequencies.
xi |
14 |
25 |
27 |
28 |
31 |
42 |
43 |
fi |
1 |
1 |
2 |
1 |
2 |
1 |
1 |
Modes = 27, 31 as they both have the maximum frequency of 2. Data is bi-modal.