1. Meaning of Mode
The mode is the value that appears most frequently in a data set. It represents the item that occurs again and again more than others.
The mode is useful when we want to know the most common or popular value in the data.
For example, if the numbers are 4, 6, 4, 3, 4, then the mode is 4 because it appears the most times.
2. Finding Mode in Raw Data
To find the mode from raw (ungrouped) data, simply look for the value that repeats the most.
Steps:
- List all values.
- Count how many times each value appears.
- The value with the highest count is the mode.
2.1. Example
Find the mode of the data: 2, 7, 2, 5, 7, 2, 9.
Counting occurrences:
- 2 → 3 times
- 7 → 2 times
- 5 → 1 time
- 9 → 1 time
The value that appears the most is 2.
So, mode = 2.
3. Mode in Frequency Tables
When data is large or repeated frequently, frequency tables help identify the mode easily. The mode is simply the value with the highest frequency.
3.1. Example
| Value (x) | Frequency (f) |
|---|---|
| 3 | 2 |
| 4 | 5 |
| 6 | 1 |
The highest frequency is 5, which corresponds to the value 4.
So, mode = 4.
4. Special Cases of Mode
Sometimes the data may have no repeated value, or more than one value may repeat the same number of times.
4.1. No Mode
If all values occur only once, there is no mode. For example: 3, 5, 8, 10 — none repeat, so there is no mode.
4.2. More Than One Mode
If two or more values have the same highest frequency, the data is called multimodal. For example, in the data 4, 6, 4, 6, 9 — both 4 and 6 appear twice, so there are two modes.