Question

the data set below represents the ages of 30 executives. which ages are above the 75th percentile? determine the values in the data set above the 75th percentile. if a data value above the 75th percentile appears more than once in the data set, make sure to include that value in your answer the appropriate number of times. the ages above the 75th percentile are □. (use a comma to separate answers as needed.) 44, 56, 54; 58, 49, 41; 65, 66, 48; 48, 56, 46; 57, 50, 29; 42, 61, 36; 56, 48, 38; 52, 40, 43; 61, 51, 41; 54, 42, 45

Explanation:

Step1: Order the data set

First, we need to order the data set of 30 ages from smallest to largest. Let's list out all the ages: 29, 36, 38, 40, 41, 41, 42, 42, 43, 44, 45, 46, 48, 48, 48, 49, 50, 51, 52, 54, 54, 56, 56, 56, 57, 58, 61, 61, 65, 66.

Step2: Find the position of the 75th percentile

The formula to find the position \( i \) of the \( p \)-th percentile is \( i=\frac{p}{100}(n + 1) \), where \( n \) is the number of data points. Here, \( p = 75 \) and \( n=30 \). So, \( i=\frac{75}{100}(30 + 1)=\frac{3}{4}\times31 = 23.25 \).

Step3: Determine the 75th percentile value

Since \( i = 23.25 \), the 75th percentile is the value at the 23rd position plus 0.25 times the difference between the value at the 24th position and the value at the 23rd position. Looking at the ordered data:

• The 23rd value: 56
• The 24th value: 56
• The 75th percentile \(=56+0.25\times(56 - 56)=56\)

Step4: Identify values above the 75th percentile

Now we find all values in the data set that are greater than 56. Looking at the ordered data, the values greater than 56 are: 57, 58, 61, 61, 65, 66.

Answer:

57, 58, 61, 61, 65, 66