Calculation of Mode from a frequency distribution for ungrouped data

Mode

The mode is the data point which occurs most frequently. It is possible to have more than one mode, if there are two modes the data is said to be bimodal. It is also possible for a set of data to not have any mode, this situation occurs if the number of modes gets to be “too large”. It it not really possible to define \too large” but one should exercise good judgement. A reasonable, though very generous, rule of thumb is that if the number of data points accounted for in the list of modes is half or more of the data points, then there is no mode.

Note: if the data is given as a list of data points, it is often easiest to find the mode by creaating a frequency distribution. This is certainly the most organized method for finding it. In our examples we will use frequency distributions.

Example 1. A data set with a single mode.
Consider the data from example 8:

Number of television sets Frequency
0 2
1 13
2 18
3 0
4 10
5 2

You can see from the table that the data point which occurs most frequently is 2 as it has a frequency of 18. So the mode is 2 television sets.

Example 2. A data set with two modes.
Consider the data:

Number of hours of television Frequency
0 1
0.5 4
1 8
1.5 9
2 13
2.3 10
3 11
3.5 13
4 5
4.5 3

You can see from the table that the data points 2 and 3.5 both occur with the highest frequency of 13. So the modes are 2 and 3.5 hours.

Example 12. A data set with no mode.
Consider the data:

Total

Age Frequency
18 12
19 5
20 3
21 9
22 1
23 8
24 12
25 12
26 5
27 3
71

You can see from the table that the data points 18, 24 and 25 all occur with the highest
frequency of 12. Since this would account for 36 of the 71 data points, this would qualify as “too large” a number of data points taken accounted for. In this case, we would say there is no mode.

MODE
The Mode is defined as the observation in the sample which occurs most frequently.
Or
The Mode is defined the most common value of a series.

• If each observation occurs the same number of times, then there is no mode.

• If two or more observations occur the same number of times, then there is more than one mode and the sample is said to be multimodal. If there is only one mode, the sample is said to be unimodal.

Example 3:
Size of
item 2 3 4 5 6 7 8 9 10 11 12 13
Frequency 3 8 10 12 16 14 10 8 17 5 4 1
Size 10 is the mode because it occurs maximum number of times i.e. 17 times.

Let’s read post The Mode Common Formula for Continuous or Discrete Distribution (Grouped Data).

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