Given the data set {3, 7, 8, 5, 12, 14, 21, 13, 18}, find the upper or third quartile (Q3).
Answer
Step 4: Since 7.5 is not a whole number, we find the average of the 7th and 8th data points to get the value of Q3. So, \(Q3 = \frac{14 + 18}{2} = 16\).
Step 1 ：Step 1: Sort the data set in ascending order: \(3, 5, 7, 8, 12, 13, 14, 18, 21\).
Step 2 ：Step 2: Determine the position of the upper quartile using the formula \(Q3 = \frac{3(N+1)}{4}\), where N is the number of data points. Substituting N = 9 into the formula, we get \(Q3 = \frac{3(9+1)}{4} = 7.5\). This means that the upper quartile is halfway between the 7th and 8th data point.
Step 3 ：Step 3: Identify the 7th and 8th data point, which are 14 and 18, respectively.
Step 4 ：Step 4: Since 7.5 is not a whole number, we find the average of the 7th and 8th data points to get the value of Q3. So, \(Q3 = \frac{14 + 18}{2} = 16\).
