Question

The lower quartile is the value of the middle of the first set, where $25\%$ of the values are _____ than $Q_1$ and $75\%$ are larger.

• A. longer
• B. larger
• C. smaller
• D. higher

Answer 1

The correct option is C smaller

The lower quartile is the value of the middle of the first set, where $25\%$ of the values are smaller than $Q_1$ and $75\%$ are larger.
Example: $2,5,5,6,8,10,11$
Here the median is the middle number $=6$
So, the first quartile is the median of the lower half of the data.
Then, the lower quartile of the first half will be $2,5,5$ which is $25\%$ of the given data
So, the remaining $75\%$ numbers can be considered as larger.