Question

1. some adults were surveyed to find out if they would prefer to buy a sports utility vehicle (suv) or a sports car. the results of the survey are summarized in the table to the right. of the number of adults that preferred sports cars, approximately what percent were males? (1) 15.8 (2) 45.2 (3) 64.4 (4) 82.6 2. a line of best fit has been drawn on the scatter plot below. the relationship between these variables can be described as having: (1) a negative correlation (2) no correlation (3) a positive correlation (4) zero correlation 3. a class of 20 students was surveyed to determine the number of pets each student owned. the data are represented in the dot plot to the right. which statement about the data is correct? (1) the mean and the median are the same. (2) the median and the mode are the same. (3) the mean and the mode are the same. (4) the mean, median, and mode are all the same.

Explanation:

Problem 1

Step1: Identify the number of males and total adults who prefer sports cars

From the table, the number of males who prefer sports cars is \(38\), and the total number of adults who prefer sports cars is \(84\).

Step2: Calculate the percentage

The formula for percentage is \(\frac{\text{Part}}{\text{Whole}}\times100\). So, \(\frac{38}{84}\times 100=\frac{3800}{84}\approx45.2\)

In a scatter - plot, if the line of best fit has a positive slope (as \(y\) increases when \(x\) increases), it indicates a positive correlation. Here, the line of best fit has a positive slope.

Step1: Calculate the mean

The data from the dot - plot: \(0:1\) student, \(1:4\) students, \(2:6\) students, \(3:4\) students, \(4:4\) students, \(5:1\) student.
The sum of the data is \(0\times1 + 1\times4+2\times6 + 3\times4+4\times4+5\times1=0 + 4+12 + 12+16+5=49\).
The mean is \(\frac{49}{20}=2.45\)

Step2: Calculate the median

Since \(n = 20\) (even), the median is the average of the \(10^{th}\) and \(11^{th}\) values.
Counting the dots: \(0\) (1), \(1\) (2 - 5), \(2\) (6 - 11). The \(10^{th}\) and \(11^{th}\) values are both \(2\), so the median is \(2\)

Step3: Calculate the mode

The mode is the value that appears most frequently. The number \(2\) has the most dots (6 dots), so the mode is \(2\)

Answer:

(2) \(45.2\)

Problem 2