Question

If there are 21 values in a data set in order from smallest to largest, what is the third quartile of the data set?

Answer 1

I do not know the values of the numbers so I cannot give u a direct answer.
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21

Q1 (quartile 1) = take the 5th and 6th number and divide it by 2
Q2 (quartile 2, median) = the 11th number
Q3 (quartile 3) = take the 16th and 17th number and divide it by 2

Answer 2

The third quartile of the data is calculated as:

(Value in the 16th position + Value in the 17th position)/2

Explanation:

Taking into account that the values are order from smallest to largest, the position of quartile number i of the date set is calculated using the following equation:

Position Qi = i * (n+1)/4

Where i can be 1, 2, 3 and n is the size of the data. So, if we replace n by 21 and i by 3, we get:

Position Q3 = 3 * (21+1)/4 = 16.5

So, the third quartile of the data is between the values that are in position 16th and 17th and it is calculated as:

(Value in the 16th position + Value in the 17th position)/2