Homework SourseShow that if a distribution is symmetric about m then m is t
Show that if a distribution is symmetric about m, then m is the median.
Show that if a distribution is symmetric about m, then m is the median.
Show that if a distribution is symmetric about m, then m is the median.
Solution
When the distribution is symmetric to some value in this case m,
m is the mean and median at the same time
For an odd number of values
As an example, we will calculate the sample median for the following set of observations: 1, 5, 2, 8, 7.
Start by sorting the values: 1, 2, 5, 7, 8.
In this case, the median is 5 since it is the middle observation in the ordered list.
For an even number of values
As an example, we will calculate the sample median for the following set of observations: 1, 6, 2, 8, 7, 2.
Start by sorting the values: 1, 2, 2, 6, 7, 8.
In this case, the arithmetic mean of the two middlemost terms is (2 + 6)/2 = 4. Therefore, the median is 4 since it is the arithmetic mean of the middle observations in the ordered list.
