Question

Find the median of : $233, 173, 189, 208, 194, 204, 194, 185, 200$ and $220$.

Answer 1

Hint: Here first we will arrange the number in ascending order and then find the median on the given formula.

Formula Used:
Median$ = \dfrac{1}{2}\left[ {valueof{{\left( {\dfrac{n}{2}} \right)}^{th}}term + valueof{{\left( {\dfrac{n}{2} + 1} \right)}^{th}}term} \right]$

Complete step by step answer:
Firstly arrange the numbers in ascending order$173,185,189,194,194,200,204,208,220,223$
Median $ = \dfrac{1}{2}\left[ {valueof{{\left( {\dfrac{n}{2}} \right)}^{th}}term + valueof{{\left( {\dfrac{n}{2} + 1} \right)}^{th}}term} \right]$
$ = \dfrac{1}{2}\left[ {valueof{{\left( {\dfrac{{10}}{2}} \right)}^{th}}term + valueof{{\left( {\dfrac{{10}}{2} + 1} \right)}^{th}}term} \right]$
$ = \dfrac{1}{2}\left[ {200 + 194} \right]$
$\dfrac{1}{2}\left[ {394} \right] = 197$

Thus median is $197$.

Note:
The median is the middle score of a distribution. The "middle" of a sorted list of numbers.
To find the Median, place the numbers in value order and find the middle number. Median is the middle number in a sorted list of numbers. To determine the median value in a sequence of numbers, the numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest. The median can be used to determine an approximate average, or mean, but is not to be confused with the actual mean. To calculate the median the Steps are:
 $1$ Arrange your numbers in numerical order.
 $2$ Count how many numbers you have.
 $3$ If you have an odd number, divide by two and round up to get the position of the median number.
 $4$ If you have an even number, divide by two. Go to the number in that position and average it with the number in the next higher position to get the median.
KEY TAKEAWAYS
The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average.
The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values.
If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above.
If there is an even amount of numbers in the list, the middle pair must be determined, added together, and divided by two to find the median value.