CH1
The favorite color of each student in a class.
The height of basketball players in inches.
Categorical (Colors are descriptive labels, not numerical values)
2. Quantitative (Height is measured numerically)
A teacher recorded the number of books read by 30 students over the summer. The data is as follows:
Data Set:
2, 3, 5, 2, 4, 3, 1, 2, 6, 3, 4, 2, 5, 3, 1, 2, 4, 5, 3, 6, 2, 5, 3, 4, 2, 1, 4, 3, 2, 5
On Doc
In a large regional 5K race, the average finishing time for women is 28.4 minutes, with a standard deviation of 3.2 minutes.
The average finishing time for men is 25.6 minutes, with a standard deviation of 2.9 minutes. A runner named Jamie participated in both race divisions for data collection purposes.
a) Jamie ran the women's 5K in 23.8 minutes. Compute the z-score for her time. Round to 2 decimal places.
b) Jamie ran the men’s 5K in 22.3 minutes. Compute the z-score for his time. Round to 2 decimal places.
c) In which division did Jamie perform relatively better compared to others?
a) z ≈ –1.44
b) z ≈ –1.14
c)
Since lower times are better in races, a more negative z-score means a better performance relative to others.
Women’s z-score = –1.44
Men’s z-score = –1.14
✅ Jamie performed relatively better in the women’s division.
On DOC
a) Find the linear correlation coefficient between sleep hours and stress level.
(Round to 3 decimal places)
b) Does a linear correlation exist between sleep hours and stress level? Why or why not?
a) r≈−0.996
b) ✅ Yes.
The correlation coefficient of –0.996 suggests a very strong negative linear relationship: as sleep hours increase, stress levels tend to decrease.
The brands of smartphones owned by a group of people.
The number of pets each person in a neighborhood owns.
Categorical (Brands are names, not numbers)
2. Quantitative (Number of pets is a numerical count)
Finding the Mean, Median, and Mode
A teacher recorded the scores of 15 students on a math test:
Scores:
78, 85, 90, 92, 88, 75, 90, 85, 95, 100, 85, 78, 88, 90, 85
Mean=86.93
Median= 88
Mode=85
A film critic website shows that the average rating for action movies is 6.8 out of 10, with a standard deviation of 1.1.
The average rating for comedies is 7.2 out of 10, with a standard deviation of 0.9.
A new film receives the following ratings:
a) Compute the z-score for the action movie’s rating. Round to 2 decimal places.
b) Compute the z-score for the comedy movie’s rating. Round to 2 decimal places.
c) In which genre did the film perform relatively better, compared to other films in that category?
a) z ≈ 1.45
b) z ≈ 1.22
c) Higher z-score means the rating was further above average compared to others in that category:
Action z = 1.45
Comedy z = 1.22
✅ The film performed relatively better as an action movie.
On DOC
c) Find the equation of the least-squares regression line.
(Round the slope and y-intercept to 3 decimal places)
d) According to the model, what is the predicted stress level for someone who sleeps 6.5 hours per night?
(Round to 2 decimal places)
c) Least-Squares Regression Line
Regression equation:
Stress=−1.118⋅(Sleep Hours)+14.159
✅ Slope ≈ –1.118
✅ Intercept ≈ 14.159
d) Predicted Stress Level for 6.5 Hours of Sleep
Stress=−1.118(6.5)+14.159≈6.89
The letter grades (A, B, C, D, F) received by students on a test.
The time (in minutes) it takes for students to complete a math exam.
The types of vehicles in a parking lot (car, truck, motorcycle, etc.).
Categorical (Letter grades are labels, not numerical values)
Quantitative (Time is measured numerically)
3. Categorical (Types of vehicles are descriptive labels)
A fitness center surveyed its members to learn about their exercise frequency per week. A total of 2,800 members responded to the question:
"How often do you exercise per week?"
The results are summarized below: Chart on doc!
a)Complete the table by adding a column for relative frequencies, rounded to 4 decimal places.
b) Is this categorical or quantitative data?
c) What is the mode of the data?
a) doc
b) This is categorical data.
Although the responses represent frequencies of a numerical activity, the categories themselves are qualitative groupings (e.g., "Never", "Three to four times", etc.), not precise numerical values.
c)Five to six times
Bob has just completed his second semester in college. He earned a grade of B in his 4 units anthropology course, a grade of C in his 4 unit Psychology course, a grade of A in his 5 unit chemistry course and a grade of A in his 4 unit math course. Assuming that A equals 4 points, B equal 3 points, C equals 2 points. Determine Bob’s GPA for the semester
3.29 GPA
ON DOC
e) If a person has a stress level of 5.8, how many hours of sleep does the model predict they get?
(Round to 2 decimal places)
e) Predicted Sleep Hours for Stress Level of 5.8
Sleep=(5.8−14.159)/1.118≈7.48
The annual salary of employees in a company.
The zip codes of different cities in a state.
The shoe sizes of customers in a shoe store.
Quantitative (Salary is measured in numerical values)
Categorical (Zip codes are numerical but do not represent a measurable quantity)
3. Quantitative (Shoe sizes follow a numerical scale)
A local library conducted a survey to understand how often members borrow books each month. A total of 2,500 library members responded to the question:
"How many books do you typically borrow in a month?"
a)Complete the table by adding a column for relative frequencies, rounded to 4 decimal places.
b) Is this categorical or quantitative data?
c) What is the mode of the data?
a) docs
b) This data is categorical.
Even though the categories imply quantities (e.g., “3–4 books”), the responses are grouped into ranges and not treated as exact numerical values.
c) 3–4 books
Jessica has just completed her third semester in college. She earned the following grades: A grade of A in her 3-unit Biology course,A grade of B in her 4-unit English course, A grade of C in her 5-unit History course, A grade of B in her 3-unit Art course. Assume the following grade point scale:A = 4 points, B = 3 points, C = 2 points
What is Jessica's GPA for the semester?
(Round your final answer to 2 decimal places, if needed.)
GPA= 2.87
ON DOC 2)
a) Find the linear correlation coefficient between screen time and sleep duration.
(Round to 3 decimal places)
b) Does a linear correlation exist between screen time and sleep duration? Why or why not?
c) Find the equation of the least-squares regression line.
(Round the slope and y-intercept to 3 decimal places)
a) r≈−0.998
b) ✅ Yes.
The correlation coefficient of –0.998 indicates a very strong negative linear relationship: as screen time increases, sleep duration tends to decrease.
c) Regression equation:
Sleep=−0.637⋅(Screen Time)+10.054
✅ Slope ≈ –0.637
✅ Intercept ≈ 10.054
The type of phone a person uses (e.g., iPhone, Samsung, Google Pixel)
The number of hours a student studies per week
A person’s blood type (A, B, AB, O)
The temperature in degrees Fahrenheit recorded each day for a week
The brand of cereal preferred by a consumer
1) Answer: 🟩 Categorical
2)Answer: 🟦 Quantitative
3) Answer: 🟩 Categorical
4)Answer: 🟦 Quantitative
5)Answer: 🟩 Categorical
Construct a frequency distribution with a class width of 5 for the following set of data (ages in years):
23, 27, 25, 31,
29, 34, 36, 40,
22, 28, 33, 35,
30, 39, 26, 24
Answer on doc
What is Marcus’s average commission per item sold for the week?
(Round your final answer to 2 decimal places.)
DOC for table
53.20= avg
On Doc
d) According to the model, what is the predicted sleep duration for a teen with 5.5 hours of screen time per day?
(Round to 2 decimal places)
e) If a teen sleeps 6.8 hours per night, how many hours of screen time does the model predict?
(Round to 2 decimal places)
d) Predicted Sleep for 5.5 Hours of Screen Time
Sleep=−0.637(5.5)+10.054≈6.55 hours
e) Predicted Screen Time for 6.8 Hours of Sleep
Screen Time=6.8−10.054/0.637≈5.11 hours