- Which of the following box plots correctly represents the data set shown below?
- Box plot 1
- Box plot 2
- Box plot 3
- Box plot 4
The minimum and maximum values are 7 and 50, respectively. The median is 23, while the first and third quartiles are 15 and 38. The box plot for Choice A correctly represents these five values.
- Given the parallel box plots shown below, which of the following statements is true?
- The box plot for data set A has a larger interquartile range and a larger median.
- The box plot for data set B has a larger interquartile range and a larger median.
- The box plot for data set A has a larger interquartile range and a smaller median.
- The box plot for data set B has a larger interquartile range and a smaller median.
The box plot for data set B shows a larger range between the first and third quartiles. In addition, its median is approximately 25, which is higher than the median of data set A.
- Given the double bar graph shown below, which of the following statements is true?
- Group A is negatively skewed, while Group B is approximately normal.
- Group A is positively skewed, while Group B is approximately normal.
- Group A is approximately normal, while Group B is negatively skewed.
- Group A is approximately normal, while Group B is positively skewed.
Data is said to be positively skewed when there are a higher number of lower values, indicating data that is skewed right. An approximately normal distribution shows an increase in frequency, followed by a decrease in frequency, of approximately the same rate.
- Which of the following data sets is represented by the histogram shown below?
- 6, 7, 7, 8, 12, 13, 18, 22, 26, 27, 28, 31, 36, 36, 36, 36, 37, 38, 38, 38, 39, 41, 41, 41, 42, 42, 43, 43, 48, 49
- 2, 3, 4, 4, 8, 9, 10, 10, 11, 15, 19, 21, 21, 21, 21, 22, 24, 24, 25, 29, 31, 33, 40, 43, 45, 46, 48, 48, 49, 50
- 1, 2, 8, 8, 9, 9, 12, 13, 15, 15, 16, 17, 18, 19, 19, 21, 29, 31, 31, 35, 36, 38, 41, 42, 42, 45, 46, 47, 47, 49
- 1, 4, 4, 5, 10, 10, 10, 12, 12, 16, 20, 22, 23, 23, 25, 27, 31, 31, 37, 39, 40, 41, 41, 43, 45, 46, 48, 49, 49, 50
The data set shown in Choice A correctly represents a frequency of 4 for the interval 1 – 10, a frequency of 3 for 11 – 20, a frequency of 4 for 21 – 30, a frequency of 10 for 31 – 40, and a frequency of 9 for 41 – 50.
- The statistics scores for Sections 101 and 102 are shown below. Which of the following statements accurately compare the center and variability of the sets of scores?
- The statistics scores for Section 101 show a greater center and variability.
- The statistics scores for Section 101 show a greater center but smaller variability.
- The statistics scores for Section 101 show a smaller center but greater variability.
- The statistics scores for Section 101 show a smaller center and variability.
The scores for Section 101 have a mean of approximately 81.1, with a standard deviation of approximately 13.2. The scores for Section 102 have a mean of approximately 78.5, with a standard deviation of approximately 12.0. Thus, the center and variability of scores for Section 101 are greater.
- Given the histograms shown below, which of the following statements is true?
- Group A is negatively skewed and has a mean that is less than the mean of Group B.
- Group A is positively skewed and has a mean that is more than the mean of Group B.
- Group B is negatively skewed and has a mean that is more than the mean of Group A.
- Group B is positively skewed and has a mean that is less than the mean of Group A.
Group B is negatively skewed since there are more high scores. With more high scores, the mean for Group B will be higher.
- Given a normal distribution, which of the following best represents the area under the curve to the right of a \(z\)-score of 1.38?
- 0.03
- 0.08
- 0.12
- 0.15
Using a standard \(z\)-table, the area from the mean to \(z\) is shown to be 0.4162.
This area should be subtracted from 0.5 in order to show the area to the right of a \(z\)-score of 1.38. Thus, the area to the right of the \(z\)-score is 0.0838, or approximately 0.08.
- Given \(\mu = 18\) and \(\sigma = 2\), which of the following best represents the proportion of scores falling above 19?
- 31%
- 18%
- 41%
- 22%
The \(z\)-score may be represented as \(z=\tfrac{19-18}{2}\) or \(z=\tfrac{1}{2}\).
Using a standard \(z\)-table, the area from the mean to z is shown to be 0.1915. Subtraction of this area from 0.5 gives 0.3085. Thus, the proportion of scores falling above 19 is approximately 31%.
- Which of the following best represents the area under the curve of a normal distribution, falling between the \(z\)-scores of –0.8 and 1.2?
- 62%
- 67%
- 72%
- 77%
A standard \(z\)-table shows an area of 0.2881 between a \(z\)-score of –0.8 and the mean. It also shows an area of 0.3849 between the mean and a \(z\)-score of 1.2.
The sum of the two areas is 0.673. Thus, the area between the two \(z\)-scores is approximately 67%.
- Given the table below, which of the following best represents the probability that a student is enrolled at TAMU or prefers lattes?
- 55%
- 60%
- 65%
- 70%
The probability may be written as follows:
\(P(A \text{ or } B)= \tfrac{750}{1,650} + \tfrac{675}{1,650}-\tfrac{350}{1,650}\)
This simplifies to \(P(A \text{ or } B)= \tfrac{1,075}{1,650}\), which is approximately 65%.