Given the data set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, find the third quartile (Q3).
Answer
Step 3: Find the median of the upper half of the data set, which is {6, 7, 8, 9, 10}. Since the number of data points is 5, an odd number, the median is the 3rd data point, which is 8. This is the third quartile (Q3).
Step 1 ：Step 1: Order the data set from least to greatest: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Step 2 ：Step 2: Find the median of the whole data set. Since the number of data points is 10, an even number, the median is the average of the 5th and 6th data points, which is \(\frac{5+6}{2} = 5.5\).
Step 3 ：Step 3: Find the median of the upper half of the data set, which is {6, 7, 8, 9, 10}. Since the number of data points is 5, an odd number, the median is the 3rd data point, which is 8. This is the third quartile (Q3).
