Question

Find the median of the following set of values.
1) $83,66,86,30,82$
2) $45,49,46,44,38,37,55,51$
3) $70,71,70,68,67,69,70$
4) $51,55,46,47,53,55,51,46$.

Answer 1

The median is also the number that is halfway into the set. To find the median, the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers. And if there are odd number of terms then middle number is the median.

(1) $83,66,86,30,82$

Arranging in ascending order.

$30,66,82,83,86$

Number of terms is odd, then median is the middle number i.e., $82$

(2) $45,49,46,44,38,37,55,51$

Arranging in ascending order

$37,38,44,45,46,49,51,55$

The number of terms is even then median is average of two middle numbers

$\therefore$ Median $=\frac{45+46}{2}=45.5$

(3) $70,71,70,68,67,69,70$

Arranging in ascending order

$67,68,69,70,70,70,71$

Then terms are odd then median is middle number i.e., $70$

(4) $51,55,46,47,53,55,51,46$

Arranging in ascending order

$46,46,47,51,51,53,55,55$

The number of terms is even then median is average of two middle numbers

$\therefore$ Median$=\frac{51+51}{2}=51$