Question

How do you find the first and third quartiles, Q1 and Q3 , of the following set of numbers 10,4,9,14,6,11,6,1,7,6?

Answer 1

Hint: To find the first and third quartiles of the set of numbers first set given numbers in ascending order and then find the median of that set of numbers . To find the first quartile find the middle number of lower numbers from left before the median and to find the third quartile find the middle number of higher numbers from the right after the median.

Complete step-by-step answer:
The objective of the problem is to find the first and third quartiles of the given set of numbers.
Given set of numbers are 10,4,9,14,6,11,6,1,7,6
Now , arrange the given numbers in ascending order.
1,4,6,6,6,7,9,10,11,14
Now we have to find the median of the ascending ordered numbers. The median is nothing but the middle number. If there is more than one middle take the average of two numbers.
In the given set of number we have two numbers 6 and 7
The average of numbers is $\dfrac{{6 + 7}}{2} = 6.5$
To find the first quartile let us trace out the middle number from the left .
The first quartile is 6.
Now to find the third quartile let us trace out the middle number from the right.
Therefore , the third quartile is 10.
Thus , the first quartile Q1 is 6 and the third quartile Q3 is 10.

Note: The second quartile is the median of a given set of numbers. The middle number from the given set of numbers is the median if there is more than one number add the numbers and the result we get after adding the numbers is divided by two. The resultant number is the median of that set of numbers.