Question

These are the marks of students: 66, 48, 59,89,67,79. Find the median, the mode, the lower quartile, the upper quartile, the interquartile range.

Answer 1

Data set $=66,48,59,89,67,79$

Reordered $=48,59,66,67,79,89$

$n=6$

$$median={66+67 \over 2}=66.5$$

There is no mode for this data set.

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. 

So, the bottom half is 48,59,66.

$$lower\ quartile=59.$$

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers.

So, the upper half is 67,79,89.

$$upper\ quartile=79.$$

The interquartile range (IQR) is the difference between the upper and lower quartiles.

$$IQR=79-59=20$$

The interquartile range $=20.$