To find the mean , median , and mode of a data set, follow these steps:
Mean (Average)
- Add up all the numbers in the data set.
- Divide the total sum by the number of values in the data set.
Formula:
Mean=Sum of all valuesNumber of values\text{Mean}=\frac{\text{Sum of all values}}{\text{Number of values}}Mean=Number of valuesSum of all values
Example: For data set {1, 2, 3, 4, 5},
Mean = (1 + 2 + 3 + 4 + 5) ÷ 5 = 15 ÷ 5 = 3
Median (Middle Value)
- Arrange the data values in order from smallest to largest.
- If the number of values is odd, the median is the middle number.
- If the number of values is even, the median is the average of the two middle numbers.
Example: For data set {1, 3, 5}, median is 3 (middle value).
For data set {1, 3, 5, 7}, median = (3 + 5) ÷ 2 = 4
Mode (Most Frequent Value)
- Identify the value(s) that occur most frequently in the data set.
- There can be more than one mode if multiple values have the same highest frequency.
- If all values occur equally, there is no mode.
Example: For data set {1, 2, 2, 3, 4}, mode is 2 because it appears most often
. These measures summarize the data by showing typical or common values:
- Mean gives the average.
- Median shows the middle point.
- Mode highlights the most frequent value
