Question

Find the median of: 80, 48, 66, 61, 75, 52, 45, 70

Answer 1

Hint: To find the median of the given data set we will first arrange the given data in increasing order and then count the total number of terms in it and :
If the number of terms is odd then the median is given by: ${{\left( \dfrac{n+1}{2} \right)}^{th}}$ term.
And, if the number of terms is even then median is given by: $\dfrac{{{\left( \dfrac{n}{2} \right)}^{th}}term+{{\left( \dfrac{n}{2}+1 \right)}^{th}}term}{2}$

Complete step-by-step answer:
Let us first define the median: Median of a given set is the value which lies exactly in the middle of the given set when we arrange the given set in increasing order.
So, to find the median of the 80, 48, 66, 61, 75, 52, 45, 70 we will first arrange the given data set in ascending (i.e. increasing order).
After arranging the data set in ascending order, the data set will be: 45, 48, 52, 61, 66, 70, 75, 80.
Now, we will count the total number of terms in the given data set:
So, the number of terms in the given data is: 8.
Since, the total number of terms in the given data is even and we know that when number terms in given data is even then median is given by $\dfrac{{{\left( \dfrac{n}{2} \right)}^{th}}term+{{\left( \dfrac{n}{2}+1 \right)}^{th}}term}{2}$, where n is the number of the terms.
So, median of given data is: $\dfrac{{{\left( \dfrac{8}{2} \right)}^{th}}term+{{\left( \dfrac{8}{2}+1 \right)}^{th}}term}{2}$
$=\dfrac{{{4}^{th}}term+{{5}^{th}}term}{2}$
Now, from the data which is arranged in ascending order we can see that the ${{4}^{th}}$ term is 61 and the ${{5}^{th}}$ term is 66.
$\therefore $ Median = $\dfrac{61+66}{2}$ = 63.5
Hence, 63.5 is our required answer.

Note: Students are required to take care that they should not start calculating the median without arranging the given data set in ascending order, and if they do so they will not get the correct answer and their marks will also be deducted if they do this mistake in examination. And, students are also required to note that if the number of terms in the given data set is odd then median is equal to ${{\left( \dfrac{n+1}{2} \right)}^{th}}$term.