Finding a Percentile In Exercises 33–36, use the data set, which represents the ages of 30 executives.
43 57 65 47 57 41 56 53 61 54
56 50 66 56 50 61 47 40 50 43
54 41 48 45 28 35 38 43 42 44


Which ages are above the 75th percentile?

Verified step by step guidance

1. Step 1: Organize the data set in ascending order. This will allow us to determine the position of the 75th percentile more easily. The ordered data set is: 28, 35, 38, 40, 41, 41, 42, 43, 43, 43, 44, 45, 47, 47, 48, 50, 50, 50, 53, 54, 54, 56, 56, 56, 57, 57, 61, 61, 65, 66.
2. Step 2: Determine the position of the 75th percentile using the formula for the percentile position: P = (k/100) * (n + 1), where k is the percentile (75 in this case) and n is the number of data points (30 here). Substitute the values into the formula: P = (75/100) * (30 + 1).
3. Step 3: Calculate the position (P) from the formula. If P is an integer, the value at that position in the ordered data set is the 75th percentile. If P is not an integer, interpolate between the two closest positions in the ordered data set to find the 75th percentile.
4. Step 4: Identify the ages that are above the 75th percentile. Once the 75th percentile value is determined, any age in the data set greater than this value is considered above the 75th percentile.
5. Step 5: List all the ages from the ordered data set that are greater than the 75th percentile value. These are the ages that are above the 75th percentile.

Key Concepts

Percentiles

A percentile is a measure used in statistics to indicate the value below which a given percentage of observations fall. For example, the 75th percentile is the value below which 75% of the data points lie. Understanding percentiles helps in interpreting data distributions and identifying thresholds for categorizing data points.

Data Set

A data set is a collection of related data points, often organized in a structured format. In this case, the data set consists of the ages of 30 executives. Analyzing a data set involves sorting, calculating measures of central tendency, and determining percentiles to draw insights from the data.

Calculating Percentiles

To calculate a percentile, the data set must first be ordered from least to greatest. The formula for finding the rank of a percentile is P = (n + 1) * (percentile/100), where P is the position in the ordered list and n is the total number of observations. This process allows us to identify which values correspond to specific percentiles, such as the 75th percentile.