Table of contents
- 1. Intro to Stats and Collecting Data55m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically1h 45m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables2h 33m
- 6. Normal Distribution and Continuous Random Variables1h 38m
- 7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
3. Describing Data Numerically
Mean
Problem 2.T.1
Textbook Question
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.

1
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.

This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mPlay a video:
Was this helpful?
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.
Recommended video:
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.
Recommended video:
Guided course
Parameters vs. Statistics
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.
Recommended video:
Guided course
Visualizing Qualitative vs. Quantitative Data
Watch next
Master Calculating the Mean with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice