Question

Find the median of 21, 21, 22, 23, 23, 24, 24, 24, 24, 25 and 25.

Answer 1

Median is a statistical value in statistics and probability theory. Mean is the middle value when a set of data values are arranged in the order from lowest to highest. If the number of observations in a given set of data are odd, then the mean is the middle value of the observations. But if the number of observations are even in the data set, then the median is the average of the two observations in the middle.

Complete step-by-step solution:
Here the number of observations in the given data are 11.
$\Rightarrow$1st observation is 21
$\Rightarrow$2nd observation is 21
$\Rightarrow$3rd observation is 22
$\Rightarrow$4th observation is 23
$\Rightarrow$5th observation is 23
$\Rightarrow$6th observation is 24
$\Rightarrow$7th observation is 24
$\Rightarrow$8th observation is 24
$\Rightarrow$9th observation is 24
$\Rightarrow$10th observation is 25
$\Rightarrow$11th observation is 25
We have to find out the middle most observations in the given set of data.
In the given set of data the middle observation is the 6th observation.
The set of data: 21, 21, 22, 23, 23, 24, 24, 24, 24, 25, 25. Total of 11 observations.
From the set of data the 6th observation is 24.

The median is 24.

Note: While finding the median of any given data is always the total number of observations correctly, else everything could go wrong. As already discussed, if the total number of observations are odd, then the mean is the middle value of the observation else the mean of the two middle values in the data.