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
Step 3: Calculate the value of the upper quartile using interpolation. The formula is \(Q_3 = x_{4} + 0.5(x_{5}-x_{4})\), where \(x_{4}\) and \(x_{5}\) are the 4th and 5th data points respectively. Substituting the values gives \(Q_3 = 94 + 0.5(96-94) = 95\)
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 \(Q_3 = \frac{3}{4}(n+1)\), where \(n\) is the number of data points. Substituting \(n = 5\) into the formula gives \(Q_3 = \frac{3}{4}(5+1) = 4.5\). 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 \(Q_3 = x_{4} + 0.5(x_{5}-x_{4})\), where \(x_{4}\) and \(x_{5}\) are the 4th and 5th data points respectively. Substituting the values gives \(Q_3 = 94 + 0.5(96-94) = 95\)
