What is the 75th percentile of the data set {10, 20, 30, 40, 50}?

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Q: What is the 75th percentile of the data set {10, 20, 30, 40, 50}?

Solution: The 75th percentile (Q3) is the value below which 75% of the data falls, which is 40.

Steps: 8

Step 1: Understand what the 75th percentile means. It is the value below which 75% of the data points fall.
Step 2: Arrange the data set in order. The data set {10, 20, 30, 40, 50} is already in order.
Step 3: Count the number of data points. There are 5 data points in this set.
Step 4: Calculate the position of the 75th percentile using the formula: P = (n + 1) * (percentile / 100), where n is the number of data points. Here, P = (5 + 1) * (75 / 100) = 6 * 0.75 = 4.5.
Step 5: Since 4.5 is not a whole number, we round it up to the next whole number, which is 5. This means we look at the 5th data point.
Step 6: Identify the 5th data point in the ordered data set. The 5th data point is 50.
Step 7: Since we need the value below which 75% of the data falls, we look at the 4th data point, which is 40.
Step 8: Conclude that the 75th percentile of the data set {10, 20, 30, 40, 50} is 40.