Question

Quick question a lot of points help please

Answer 1

First, sort the data from least to greatest:

{3, 5, 6, 7, 7, 7, 8, 8}

The quartiles of this set are 3 values that separate the list into 4 groups,

• the lowest 25% of the set

• the lower-middle 25% of the set

• the upper-middle 25% of the set

• the highest 25% of the set

Since there are 8 data points, each set consists of 2 data points:

• {3, 5}

• {6, 7}

• {7, 7}

• {8, 8}

The quartiles are then the average of the adjacent endpoints of these sets. That is,

• the first quartile is (5 + 6)/2 = 5.5

• the second quartile (a.k.a. median) is (7 + 7)/2 = 7

• the third quartile is (7 + 8)/2 = 7.5

The IQR is the difference between the third and first quartiles, so

IQR = 7.5 - 5.5 = 2