Textbook Question
Finding the Mean of a Frequency Distribution In Exercises 49–52, approximate the mean of the frequency distribution.
Social Media The average daily amounts of time (in minutes) spent on Snapchat
267
views
Ch. 2 - Descriptive Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 2, Problem 2.5.38
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?
Verified step by step guidance1
Step 1: Organize the data set in ascending order. This is necessary to determine percentiles, as percentiles are based on the position of values in an ordered data set.
Step 2: Identify the formula for finding the position of the 50th percentile (median). The formula is: P = (n + 1) * (percentile / 100), where n is the total number of data points.
Step 3: Calculate the position of the 50th percentile using the formula. Substitute the total number of data points (n) and the desired percentile (50) into the formula.
Step 4: Locate the value at the calculated position in the ordered data set. If the position is a whole number, the value at that position is the 50th percentile. If the position is not a whole number, interpolate between the two closest values.
Step 5: Interpret the 50th percentile. The 50th percentile represents the median wait time, meaning that 50% of the wait times are less than or equal to this value, and 50% are greater than or equal to this value.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2mWas this helpful?
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 50th percentile, also known as the median, is the value that separates the higher half from the lower half of the data set. Understanding percentiles helps in interpreting the distribution of data and identifying relative standings within a dataset.
Median
The median is a specific type of percentile that represents the middle value of a dataset when it is ordered from least to greatest. If there is an even number of observations, the median is calculated as the average of the two middle numbers. It is a robust measure of central tendency, less affected by outliers than the mean, making it useful for skewed distributions.
Recommended video:
Guided course
03:26
Calculating the Median
Interpreting Percentiles
Interpreting percentiles involves understanding what the percentile value signifies in the context of the data. For instance, if a wait time is at the 50th percentile, it means that 50% of the wait times are less than or equal to this value. This interpretation provides insights into the typical experience of individuals in the dataset, allowing for better decision-making and understanding of service efficiency.
Recommended video:
04:48Population Standard Deviation Unknown
Related Practice
Textbook Question
use the given information about the data set and the number of classes to find the class width, the lower class limits, and the upper class limits.
min=17, range=118, 8 classes
189
views
Textbook Question
Project Find a real-life data set and use the techniques of Chapter 2, including graphs and numerical quantities, to discuss the center, variation, and shape of the data set. Describe any patterns.
117
views
Textbook Question
What is the difference between a frequency polygon and an ogive?
418
views
Textbook Question
Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2020 is approximately bell-shaped. The mean age is 27.9 years, with a standard deviation of 3.4 years. In Exercises 43–48, use the corresponding z-score to determine whether the age is unusual. Explain your reasoning. (Source: Le Tour de France)
100
views
Textbook Question
Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.
Grades A student receives the grades shown below, with an A worth 4 points, a B worth 3 points, a C worth 2 points, and a D worth 1 point. What is the student’s grade point average?
238
views