Textbook Question
Use frequency distribution formulas to estimate the sample mean and the sample standard deviation of the data set in Exercise 2.
Ch. 2 - Descriptive Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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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.T.1
According to data from the city of Toronto, Ontario, Canada, there were nearly 112,000 parking infractions in the city for December 2020, with fines totaling over 5,500,000 Canadian dollars. The fines (in Canadian dollars) for a random sample of 105 parking infractions in Toronto, Ontario, Canada, for December 2020 are listed below. (Source: City of Toronto)
In Exercises 1–5, use technology. If possible, print your results.
Find the sample mean of the data.
Verified step by step guidance1
Step 1: Understand the problem. The goal is to calculate the sample mean of the fines listed in the dataset. The sample mean is the average of all the values in the dataset.
Step 2: Organize the data. The fines are listed in the images provided. Combine all the values into a single list for calculation purposes.
Step 3: Use the formula for the sample mean: \( \text{Sample Mean} = \frac{\sum x_i}{n} \), where \( x_i \) represents each individual fine and \( n \) is the total number of fines in the sample.
Step 4: Add all the fines together to calculate \( \sum x_i \). This involves summing up all the values provided in the dataset.
Step 5: Divide the total sum of fines (\( \sum x_i \)) by the total number of fines (\( n = 105 \)) to compute the sample mean.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sample Mean
The sample mean is the average of a set of values obtained from a sample of a population. It is calculated by summing all the values in the sample and dividing by the number of observations. The sample mean provides a measure of central tendency, helping to summarize the data and understand its overall behavior.
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Sampling Distribution of Sample Proportion
Descriptive Statistics
Descriptive statistics are methods for summarizing and organizing data to provide a clear overview of its main features. This includes measures such as mean, median, mode, and standard deviation, which help to describe the data's distribution and variability. Descriptive statistics are essential for interpreting data before conducting further analysis.
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Data Visualization
Data visualization involves representing data graphically to identify patterns, trends, and insights more easily. Techniques such as charts, graphs, and tables help convey complex information in a more digestible format. In the context of the parking fines data, visualizing the distribution of fines can enhance understanding and facilitate comparisons.
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Related Practice
Textbook Question
The overall averages of 12 students in a statistics class prior to taking the final exam are listed.
67 72 88 73 99 85 81 87 63 94 68 87
d. Display the data in a stem-and-leaf plot. Use one line per stem.
Textbook Question
For the four test scores 96, 85, 91, and 86, the first 3 test scores are 20% of the final grade, and the last test score is 40% of the final grade. Find the weighted mean of the test scores.
Textbook Question
The overall averages of 12 students in a statistics class prior to taking the final exam are listed.
67 72 88 73 99 85 81 87 63 94 68 87
a. Find the mean, median, and mode of the data set. Which best represents the center of the data?
Textbook Question
The data set represents the number of movies that a sample of 20 people watched in a year.
121 148 94 142 170 88 221 106 18 67
149 28 60 101 134 168 92 154 53 66
c. Display the data using a relative frequency histogram.
Textbook Question
In Exercises 1 and 2, use the data set, which represents the overall average class sizes for 20 national universities. (Adapted from Public University Honors)
37 34 42 44 39 40 41 51 49 31
52 26 31 40 30 27 36 43 48 35
Construct a relative frequency histogram using the frequency distribution in Exercise 1. Then determine which class has the greatest relative frequency and which has the least relative frequency.
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