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Ch. 2 - Descriptive Statistics
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 2 - Descriptive StatisticsProblem 2.3.50
Chapter 2, Problem 2.3.50

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

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Step 1: Identify the midpoints of each class interval. The midpoint is calculated as the average of the lower and upper boundaries of each interval. For example, for the interval 0–19, the midpoint is (0 + 19) / 2 = 9.5.
Step 2: Multiply each midpoint by its corresponding frequency to find the 'frequency × midpoint' product for each class interval. For example, for the interval 0–19, the product is 9.5 × 8 = 76.
Step 3: Sum all the 'frequency × midpoint' products obtained in Step 2. This gives the total of all weighted midpoints.
Step 4: Calculate the total frequency by summing all the frequencies provided in the table. For example, the total frequency is 8 + 8 + 15 + 10 + 7 = 48.
Step 5: Divide the sum of 'frequency × midpoint' products (from Step 3) by the total frequency (from Step 4) to approximate the mean of the frequency distribution. The formula is Mean = (Σ(frequency × midpoint)) / (Σ(frequency)).

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Key Concepts

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

Mean of a Frequency Distribution

The mean of a frequency distribution is calculated by multiplying each class midpoint by its corresponding frequency, summing these products, and then dividing by the total number of observations. This provides a weighted average that reflects the distribution of data across different intervals.
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Intro to Frequency Distributions

Class Midpoint

The class midpoint is the value that lies in the middle of a class interval. It is calculated by averaging the lower and upper boundaries of the interval. For example, for the interval 0-19, the midpoint is (0 + 19) / 2 = 9.5, which is used in calculating the mean.
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Frequency Polygons Example 1

Frequency

Frequency refers to the number of occurrences of a particular value or range of values in a dataset. In the context of a frequency distribution, it indicates how many data points fall within each specified interval, which is essential for calculating measures like the mean.
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Related Practice
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?

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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)


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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?


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Textbook Question

Finding the Mean of a Frequency Distribution In Exercises 49–52, approximate the mean of the frequency distribution.


Populations The populations (in thousands) of the counties in Montana in 2019 (Source: U.S. Census Bureau)

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Textbook Question

Constructing a Frequency Distribution and a Frequency Polygon In Exercises 35 and 36, construct a frequency distribution and a frequency polygon for the data set using the indicated number of classes. Describe any patterns.

Declaration of Independence

Number of classes: 5

Data set: Number of children of those who signed the Declaration of Independence (Source: The U.S. National Archives & Records Administration) 5 2 12 18 7 4 10 8 16 3 3 7 3 1 2 7 13 0 8 3 7 5 2 6 0 6 7 9 0 11 9 10 7 8 13 5 8 3 5 0 3 13 3 15 5 6 3 2 5 2 0 3 7 12 4 1

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Textbook Question

Comparing Variation in Different Data Sets In Exercises 45–50, find the coefficient of variation for each of the two data sets. Then compare the results.

Annual Salaries Sample annual salaries (in thousands of dollars) for entry level architects in Denver, CO, and Los Angeles, CA, are listed.

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