Question

Find the median of the data: $22,28,34,49,44,57,18,10,33,41,66,59$

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:
First the given set of data has to be arranged in the order from the lowest to the highest.
The set of observations are arranged in the increasing order :
$\Rightarrow 10,18,22,28,33,34,41,44,49,57,59,66$
The total number of observations is 12.
As the number of observations is an even number, therefore the median of the observations would be the average of the two observations which are the middle most of the given set of observations.
$\Rightarrow$The $1^{st}$ observation is 10.
$\Rightarrow$The $2^{nd}$ observation is 18.
$\Rightarrow$The $3^{rd}$ observation is 22.
$\Rightarrow$The $4^{th}$ observation is 28.
$\Rightarrow$The $5^{th}$ observation is 33.
$\Rightarrow$The $6^{th}$ observation is 34.
$\Rightarrow$The $7^{th}$ observation is 41.
$\Rightarrow$The $8^{th}$ observation is 44.
$\Rightarrow$The $9^{th}$ observation is 49.
$\Rightarrow$The $10^{th}$ observation is 57.
$\Rightarrow$The $11^{th}$ observation is 59.
$\Rightarrow$The $12^{th}$ observation is 66.
The two middle most observations of 12 observations are $6^{th}$ observation and $7^{th}$ observation.
Hence the median would be the average of $6^{th}$ observation and the $7^{th}$ observation.
The $6^{th}$ observation is 34 and the $7^{th}$ observation is 41.
$\Rightarrow$The median is $\dfrac{{34 + 41}}{2} = \dfrac{{75}}{2}$
$\Rightarrow \dfrac{{75}}{2} = 37.5$
$\therefore$The median is 37.5

The median of the data is 37.5

Note: While calculating the median of the given data, first it has to be arranged in the increasing order that is arranging the data from the lowest to highest only then we can find the correct value of the median. Also the median of the even no. of observations is the average of the two middle observations whereas for the odd no. of observations it is just the middle value.