Interpretation：練習問題

A researcher finds that as the number of hours spent studying increases, the test scores of students also tend to increase. Which of the following best describes this correlation?

Two classes, A and B, took the same math test. Class A had a mean score of \( 75 \) and a range of \( 10 \). Class B had a mean score of \( 75 \) and a range of \( 25 \). Which of the following statements is correct?

Two box plots are used to compare the marks of Group A and Group B in a test.
Group A: Median = 70, Interquartile Range (IQR) = 15
Group B: Median = 70, Interquartile Range (IQR) = 10
Which of the following statements correctly compares the distributions?<\/p>

A scatter graph shows the relationship between the age of a car and its value. The points on the graph generally follow a downward trend from left to right. Which term best describes this correlation?

A scatter graph shows the relationship between the age of a car, \( a \) years, and its value, \( v \) dollars. The line of best fit is given by the equation \( v = 25000 - 1800a \). What is the interpreted meaning of the value 25000 in this context?<\/p>

A scatter graph comparing the number of hours spent exercising to resting heart rate shows a strong negative correlation. If a person increases their exercise hours, what would typically happen to their resting heart rate?

The box plots for the marks of two classes in a science test are compared. Class X has a median mark of \(55\) and an interquartile range of \(12\). Class Y has a median mark of \(55\) and an interquartile range of \(22\). Compare the distributions of the marks for the two classes.

A histogram represents the heights of trees. The class \(2 < h \le 5\) has a frequency density of \(12\). If the total number of trees in the survey is \(200\), what percentage of the trees fall into this specific class?

The table below shows the summary statistics for the scores of two groups of students in a science test.

Group A: Median = 45, Lower Quartile = 38, Upper Quartile = 48
Group B: Median = 42, Lower Quartile = 30, Upper Quartile = 48

(a) Calculate the Inter-Quartile Range (IQR) for both groups.
(b) Compare the performance and consistency of the two groups based on these statistics.

The scores for two groups of students in a physics test are recorded below.
Group A: \( 2, 5, 8, 12, 13, 15, 15, 18, 20, 22 \)
Group B: \( 10, 11, 12, 12, 13, 14, 14, 15, 16, 18 \)
(a) Calculate the mean and range for Group A.
(b) Calculate the mean and range for Group B.
(c) Compare the performance and consistency of the two groups using your answers to parts (a) and (b).