Question

Find the median of: - 10, 32, 17, 19, 21, 22, 9, 35?

Answer 1

Hint: To calculate the median of the given data first arrange all the numbers in either ascending order or descending order. Now, count the number of observations and say it as n. For n = even number apply the formula Median = \[\dfrac{{{\left( \dfrac{n}{2} \right)}^{th}}term+{{\left( \dfrac{n}{2}+1 \right)}^{th}}term}{2}\] to calculate the median while for n = odd number apply the formula Median = \[{{\left( \dfrac{n}{2}+1 \right)}^{th}}\] term to get the answer.

Complete step-by-step solution:
Here we have been provided with the numbers: - 10, 32, 17, 19, 21, 22, 9, 35 and we are asked to calculate the median of these numbers.
Now, to calculate the median first we have to arrange the given numbers in ascending order or descending order of their numerical value. So, let us arrange them in ascending order here. On arrangement we get 9, 10, 17, 19, 21, 22, 32, 35. On counting the numbers of observations we get n = 8 which is an even number. Therefore applying the formula for median of n = 8 observations we get,
$\Rightarrow $ Median = \[\dfrac{{{\left( \dfrac{n}{2} \right)}^{th}}term+{{\left( \dfrac{n}{2}+1 \right)}^{th}}term}{2}\]
$\Rightarrow $ Median = \[\dfrac{{{\left( \dfrac{8}{2} \right)}^{th}}term+{{\left( \dfrac{8}{2}+1 \right)}^{th}}term}{2}\]
$\Rightarrow $ Median = \[\dfrac{{{\left( 4 \right)}^{th}}term+{{\left( 5 \right)}^{th}}term}{2}\]
In the above arrangement we see that ${{4}^{th}}$ and ${{5}^{th}}$ terms are 19 and 21 respectively, so on substituting these numbers in the above relation we get,
$\Rightarrow $ Median = \[\dfrac{19+21}{2}\]
$\Rightarrow $ Median = \[\dfrac{40}{2}\]
$\therefore $ Median = 20
Therefore, the median of the given data is 20.

Note: Note that here we have even number of terms whose median we were asked to find and that is why the formula \[\dfrac{{{\left( \dfrac{n}{2} \right)}^{th}}term+{{\left( \dfrac{n}{2}+1 \right)}^{th}}term}{2}\] for the median is applied. In case the number of observations is odd then the formulas of the median becomes \[{{\left( \dfrac{n}{2}+1 \right)}^{th}}term\]. So you need to count the number of terms properly before applying the formula. Also, here we have arranged the terms in ascending order. You may also arrange them in descending order, in that case also you will get the same answer.