Q1: A scatterplot is a graph that shows the relationship between which of the following? (a) Two categorical variables (b) Two quantitative variables (c) One categorical and one quantitative variable (d) Three or more variables
Solution:
Ans: (b) Explanation: A scatterplot displays the relationship between two quantitative variables, with one variable plotted on the x-axis and the other on the y-axis. Each point represents a pair of values from the dataset.
Q2: In a scatterplot showing the relationship between hours studied and test scores, which variable should typically be placed on the x-axis? (a) Test scores (b) Hours studied (c) Both variables equally (d) Neither variable
Solution:
Ans: (b) Explanation: The independent variable (hours studied) is typically placed on the x-axis, while the dependent variable (test scores) is placed on the y-axis. This shows how test scores depend on the number of hours studied.
Q3: Which of the following best describes a positive association in a scatterplot? (a) As one variable increases, the other variable decreases (b) As one variable increases, the other variable increases (c) The variables show no pattern (d) The points form a horizontal line
Solution:
Ans: (b) Explanation: A positive association occurs when both variables tend to increase together. The points in the scatterplot generally move upward from left to right, indicating that higher values of one variable correspond to higher values of the other.
Q4: A scatterplot shows points that are scattered randomly with no clear pattern. What does this indicate about the relationship between the two variables? (a) Strong positive association (b) Strong negative association (c) No association (d) Perfect correlation
Solution:
Ans: (c) Explanation: When points are scattered randomly with no clear pattern, this indicates no association between the two variables. The variables are not related in a systematic way.
Q5: In a scatterplot, an outlier is a point that: (a) Lies exactly on the trend line (b) Is far away from the general pattern of the other points (c) Has the highest x-value (d) Has the lowest y-value
Solution:
Ans: (b) Explanation: An outlier is a data point that is far away from the general pattern formed by the other points in the scatterplot. Outliers do not follow the trend shown by the majority of the data.
Q6: Which scatterplot pattern would best represent the relationship between the temperature outside and heating bill costs? (a) Positive association (b) Negative association (c) No association (d) Circular pattern
Solution:
Ans: (b) Explanation: There is a negative association between outside temperature and heating bill costs. As the temperature increases, heating costs tend to decrease because less heating is needed.
Q7: A scatterplot shows a strong linear pattern with points tightly clustered around an imaginary line. What does this suggest about the relationship? (a) Weak association (b) No association (c) Strong association (d) Impossible to determine
Solution:
Ans: (c) Explanation: When points are tightly clustered around a line, this indicates a strong association between the variables. The closer the points are to forming a line, the stronger the relationship.
Q8: What is the primary purpose of creating a scatterplot? (a) To calculate the mean of a dataset (b) To visualize the relationship between two quantitative variables (c) To organize categorical data (d) To determine the mode of a distribution
Solution:
Ans: (b) Explanation: The primary purpose of a scatterplot is to visualize the relationship between two quantitative variables. It allows us to see patterns, trends, associations, and outliers in the data.
Section B: Fill in the Blanks
Q9:In a scatterplot, each __________ represents a pair of values from the dataset.
Solution:
Ans: point Explanation: Each point on a scatterplot corresponds to one observation in the dataset, showing the values of both variables for that observation.
Q10:When the points in a scatterplot generally move downward from left to right, the association is described as __________.
Solution:
Ans: negative Explanation: A negative association is characterized by a downward trend, where one variable increases as the other decreases.
Q11:The variable that may influence or predict another variable is called the __________ variable and is typically placed on the x-axis.
Solution:
Ans: independent Explanation: The independent variable (or explanatory variable) is the variable that may cause changes in another variable and is conventionally placed on the x-axis.
Q12:A scatterplot that shows points forming a curved pattern rather than a straight line indicates a __________ relationship.
Solution:
Ans: nonlinear Explanation: A nonlinear relationship exists when the pattern of points does not form a straight line but instead forms a curve or other non-straight pattern.
Q13:The strength of an association in a scatterplot can be described as strong, moderate, or __________.
Solution:
Ans: weak Explanation: The strength of an association describes how closely the points follow a pattern. When points are loosely scattered, the association is considered weak.
Q14:A scatterplot showing the relationship between shoe size and height would most likely show a __________ association.
Solution:
Ans: positive Explanation: There is generally a positive association between shoe size and height because taller people tend to have larger feet, though this is not a perfect relationship.
Section C: Word Problems
Q15:A researcher collected data on the number of hours 10 students spent on social media per day and their GPAs. The data is shown below: Hours on social media: 1, 2, 2, 3, 3, 4, 4, 5, 5, 6 GPA: 3.8, 3.6, 3.5, 3.4, 3.2, 3.0, 2.9, 2.7, 2.5, 2.3 If you were to create a scatterplot with this data, what type of association would you expect to see? Explain your reasoning.
Solution:
Ans: Final Answer: Negative association. As hours spent on social media increase from 1 to 6, the GPA values decrease from 3.8 to 2.3. This indicates that students who spend more time on social media tend to have lower GPAs, which is characteristic of a negative association.
Q16:A scatterplot is created showing the relationship between the age of a car (in years) and its resale value (in thousands of dollars). The points show a downward trend from left to right. One point shows a 10-year-old car with a resale value of $25,000, while most 10-year-old cars in the dataset have values around $8,000. Identify this unusual point and explain why it might exist.
Solution:
Ans: Final Answer: The point representing the 10-year-old car valued at $25,000 is an outlier. This outlier might exist because the car could be a classic or luxury vehicle, has been exceptionally well-maintained, has low mileage, or is a rare model that retains value better than typical cars of the same age.
Q17:The table below shows the average temperature (°F) and the number of ice cream cones sold at a shop for 6 different days: Temperature: 65, 70, 75, 80, 85, 90 Ice cream cones sold: 45, 52, 61, 68, 77, 85 Describe the association between temperature and ice cream sales. What would you predict about ice cream sales on a day when the temperature is 95°F?
Solution:
Ans: Final Answer: There is a strong positive association between temperature and ice cream sales. As temperature increases, the number of ice cream cones sold also increases. Based on this trend, I would predict that ice cream sales on a 95°F day would be higher than 85 cones, likely around 90-95 cones, continuing the upward pattern.
Q18:A student creates a scatterplot comparing the number of pages in books and the time it took to read them. The scatterplot shows points that are widely scattered with no clear upward or downward trend. What can the student conclude about the relationship between the number of pages and reading time? Provide a possible explanation for this pattern.
Solution:
Ans: Final Answer: The student can conclude that there is little to no association between the number of pages and reading time. A possible explanation is that reading time depends on many other factors besides page count, such as reading speed, difficulty of the material, font size, amount of free time available, and reader interest level, which can vary greatly between different books and readers.
Q19:A fitness instructor tracks the relationship between the number of hours clients exercise per week and their resting heart rate (beats per minute). For 8 clients, the data shows that as weekly exercise hours increase from 2 to 10 hours, resting heart rates decrease from 78 to 58 beats per minute in a fairly consistent pattern. Describe both the direction and strength of this association, and identify which variable should be on the x-axis.
Solution:
Ans: Final Answer: The association has a negative direction (as exercise hours increase, resting heart rate decreases) and appears to be strong based on the consistent pattern described. The number of hours of exercise per week should be on the x-axis because it is the independent variable that may influence the dependent variable (resting heart rate), which should be on the y-axis.
Q20:A scatterplot displays the relationship between the number of years of education and annual salary for 50 adults. Most points show an upward trend, but there are two points that stand apart: one person with 18 years of education earning only $25,000 annually, and another with 12 years of education earning $150,000 annually. Identify these points and suggest one possible real-world explanation for each outlier.
Solution:
Ans: Final Answer: Both points are outliers. The person with 18 years of education earning only $25,000 might be working in a field they are passionate about but that pays poorly (such as nonprofit work), recently graduated and in an entry-level position, or working part-time. The person with 12 years of education earning $150,000 might be a successful entrepreneur, skilled tradesperson, professional athlete, or someone working in a high-demand technical field where experience and skills matter more than formal education.
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