Problem

A teacher has recorded the test scores of five students in her class as follows: 72, 88, 90, 94, 96. What is the upper or third quartile of these scores?

Answer

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Answer

Step 3: Calculate the value of the upper quartile using interpolation. The formula is Q3=x4+0.5(x5−x4), where x4 and x5 are the 4th and 5th data points respectively. Substituting the values gives Q3=94+0.5(96−94)=95

Steps

Step 1 ：Step 1: First, sort the data in ascending order. The sorted data is: 72,88,90,94,96

Step 2 ：Step 2: Calculate the position of the upper quartile using the formula Q3=34(n+1), where n is the number of data points. Substituting n=5 into the formula gives Q3=34(5+1)=4.5. This tells us that the upper quartile is between the 4th and 5th data points.

Step 3 ：Step 3: Calculate the value of the upper quartile using interpolation. The formula is Q3=x4+0.5(x5−x4), where x4 and x5 are the 4th and 5th data points respectively. Substituting the values gives Q3=94+0.5(96−94)=95

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