Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 25m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

3. Describing Data Numerically

Describing Data Numerically Using a Graphing Calculator

Statistics

3. Describing Data Numerically

Describing Data Numerically Using a Graphing Calculator

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2:54 minutes

Problem 2.5.35

Textbook Question

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

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.

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).

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.

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.

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.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Textbook Question

Using and Interpreting Concepts

Using and Interpreting Concepts Finding Quartiles, Interquartile Range, and Outliers In Exercises 11 and 12,

56 63 51 60 57 60 60 54 63 59 80 63 60 62 65

Textbook Question

Graphical Analysis In Exercises 13 and 14, use the box-and-whisker plot to identify the five-number summary.

Textbook Question

Drawing a Box-and-Whisker Plot In Exercises 15–18,

(a) find the five-number summary

4 7 7 5 2 9 7 6 8 5 8 4 1 5 2 8 7 6 6 9

Textbook Question

Drawing a Box-and-Whisker Plot In Exercises 15–18,

(a) find the five-number summary

2 7 1 3 1 2 8 9 9 2 5 4 7 3 7 5 4

2 3 5 9 5 6 3 9 3 4 9 8 8 2 3 9 5

Textbook Question

Finding and Interpreting Percentiles In Exercises 37– 40, use the data set, which represents wait times (in minutes) for various services at a state’s Department of Motor Vehicles locations.

6 10 1 22 23 10 6 7 2 1 6 6 2 4 14 15 16 4

19 3 19 26 5 3 4 7 6 10 9 10 20 18 3 20 10 13

14 11 14 17 4 27 4 8 4 3 26 18 21 1 3 3 5 5

Which wait time represents the 50th percentile? How would you interpret this?

Textbook Question

In Exercises 37– 40, use the data set, which represents the model 2020 vehicles with the highest fuel economies (in miles per gallon) in the most popular classes. (Source: U.S. Environmental Protection Agency)

36 30 30 45 31 113 113 33 33 33 52 141 56 117 58

118 50 26 23 23 27 48 22 22 22 121 41 105 35 35

Find the five-number summary of the data set.

Textbook Question

36 30 30 45 31 113 113 33 33 33 52 141 56 117 58

118 50 26 23 23 27 48 22 22 22 121 41 105 35 35

About how many vehicles fall on or below the third quartile?

Textbook Question

A student’s test grade of 75 represents the 65th percentile of the grades. What percent of students scored higher than 75?

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