Mean, Median, and Mode
Median
The median is the middle value in a dataset when arranged in ascending order.
Case-1: For even number of observations
If there is an even number of observations, the median is the average of the two middle values.
Consider a race with 6 participants and their respective finish times (in seconds):
40,45,42,38,39,41
Step 1: Sort the data in ascending order:
Sorting the finish times gives us:
38,39,40,41,42,45
Step 2: Calculate the Median:
Since there are 6 observations (an even number), the median is the average of the two middle values.
Median=40+41 =81 =40.5
Case-2: For odd number of observations
When there is an odd number of observations, the median is simply the middle value in the sorted dataset.
Consider a race with participants and their respective finish times (in seconds):
40,45,42,38,39
Step 1: Sort the data in ascending order:
Sorting the finish times gives us:
38,39,40,42,45
Step 2: Calculate the Median:
Since there are 5 observations (an odd number), the median is simply the middle value.
Median=40
Note: The median is less affected by outliers because it only considers the middle value(s) of a dataset when sorted in ascending order. Outliers have no impact on the median as long as they don’t affect the position of the middle value(s).
Mode
The mode is the value that appears most frequently in a dataset.
Example:
Consider the outcomes of rolling a dice: 3, 5, 2, 6, 3, 4, 3.
So, Mode = 3 (since 3 appears most frequently).
Note: The mode is the most robust against outliers because it represents the most frequently occurring value(s) in a dataset. Outliers that occur only once or infrequently have minimal impact on the mode.
