Question

Could someone please help me with this problem?

The semester point totals of 16 students are listed below. Find the interquartile range (IQR).
787 639 820 677
475 601 531 650
583 684 875 507
599 460 543 490

Answer 1

IQR (interquartile range) is the difference in data values between the first and third quartiles.

First order the number in increasing order. The first (smallest) number will be X1, the last (largest) number will be X16. Then calculate the first and third quartiles according to the formula below and take the difference between them.

There could be different definitions of quartiles when the number of observations is even. Here's is one that is used in business statistics:
Q₁ = X_{[(n/4)+(1/2)]}
Q₃ = X_{[(3n/4)+(1/2)]}

For example, with 8 ordered observations,
1 1 2 3 5 8 13 21 34
First quartile:
the (8/4+1/2)th = 2.5th observation is the average of 1 and 2=1.5
Third quartile:
the (3*8/4+1/2)th = 6.5th observation is the average of 8 and 13 = 10.5
The interquartile range (IQR) the thus 10.5-1.5=9

Post your answer for a check if you wish.