Learning to Calculate Interquartile Range

Interquartile range definition: In statistics, for any given set of data, the difference between the smallest and the largest observation is called the range.
However if we consider only the middle half of the observations and then find the difference between the smallest and largest observations of these middle half of the observations then that number would be our inter quartile range.
We can also define interquartile range as the difference between the first quartile and the third quartile. The first quartile represents the first one fourth of the observations. The third quartile is the first three fourths of the observations.
In other words, if first quartile is Q1, then one fourths of the data lies below Q1.
If third quartile is Q3, then three fourths of the observations lie below Q3. Then, the inter quartile range = Qr = Q3 - Q1.
Interquartile range example: Example: Find the inter quartile range of the following set of numbers that represent the scores of 11 students in a surprise test out of total of 30 marks.
19, 1, 2, 5, 9, 15, 12, 7, 18, 27, 6.

Solution: Step 1: First arrange the numbers in order from the smallest to the largest: 1,2,5,6,7,9,12,15,18,19,27 Step 2: Next find the median (the middle observation) and mark it. 1,2,5,6,7,9,12,15,18,19,27.

So for our problem, median is 9.

Step 3: Enclose the numbers smaller and larger than the median in brackets.
That makes it simpler to calculate the quartiles.
We can also calculate Interquartile Range. (1,2,5,6,7),9,(12,15,18,19,27) Step 4: Now find Q1.
Q1 or the first quartile can be said to be the middle value of the left bracket numbers.
So here it is 5.

(1,2,5,6,7) Step 5: Next find the Q3. The Q3 or the third quartile is the same as the middle number of the second or the right bracket.

Which is 18 for our example.
( 12,15,18,19,27) Step 6: The difference between the values of Q1 and Q3 that we found in the steps 4 and 5 above is our inter quartile range. So Qr = Q3 - Q1 = 18 - 5 = 13!!! Uses of interquartile range: As compared to the range, the inter quartile range is a more useful measure of central tendency.

That is because, it represents the spread of the middle 50% of the values.
If the data has outliers, the range can be a very large but yet not represent the data properly.
But inter quartile range is not affected by outliers.