Question

Describe in your own words the two terms: Lower Quartile and Upper Quartile and give an example for each of your chosen term.

Answer 1

A quartile is a statistical term describing a division of observations into four defined intervals based upon the values of the data and how they compare to the entire set of observations.

A quartile divides data into three points – a lower quartile, median, and upper quartile – to form four groups of the data set. The lower quartile or first quartile is denoted as Q1 and is the middle number that falls between the smallest value of the data set and the median. The second quartile, Q2, is also the median. The upper or third quartile, denoted as Q3, is the central point that lies between the median and the highest number of the distribution.

Each quartile contains 25% of the total observations. Generally, the data is arranged from smallest to largest:

1. First quartile: the lowest 25% of numbers
2. Second quartile: between 25.1% and 50% (up to the median)
3. Third quartile: 51% to 75% (above the median)
4. Fourth quartile: the highest 25% of numbers

Example

The distribution of math scores in a class of 19 students in ascending order is:

59, 60, 65, 65, 68, 69, 70, 72, 75, 75, 76, 77, 81, 82, 84, 87, 90, 95, 98

First find median (middle value), Q2, which is:75.

Q1 is the central point between the smallest score and the median. In this case, Q1 falls between the first and fifth score: 68.

Q3 is the middle value between Q2 and the highest score: 84.

Interpretation

A score of 68 (Q1) represents the first quartile and is the 25^th percentile. 68 is the median of the lower half of the score set in the available data i.e. the median of the scores from 59 to 75.

Q1 tells us that 25% of the scores are less than 68 and 75% of the class scores are greater. Q2 (the median) is the 50^th percentile and shows that 50% of the scores are less than 75, and 50% of the scores are above 75. Finally, Q3, the 75^th percentile, reveals that 25% of the scores are greater and 75% are less than 84.