Question 1

The range of scores on a statistics test was 42. The lowest score was 57. What was the highest score?
A) 70.5
B) cannot be determined
C) 78
D) 99

Accepted Answer

The range is the difference between the highest and lowest scores. If the lowest score is 57 and the range is 42, then the highest score is 57 + 42 = 99.

Question 2

At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric.
What percentage of the player's serves were between 115 mph and 145 mph?
A) at most 13.5%
B) approximately 16%
C) at most 2.5%
D) at most 34%

Accepted Answer

The distribution is mound-shaped and symmetric, suggesting a normal distribution. The range 115 mph to 145 mph is one standard deviation above the mean (100 + 15 = 115) to three standard deviations above the mean (100 + 3*15 = 145). Approximately 16% of data in a normal distribution falls between one and three standard deviations above the mean.

Question 3

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the median is correct?
A) 50% of the students sampled had textbook costs equal to $425
B) 50% of the students sampled had textbook costs that were less than $425
C) The average of the textbook costs sampled was $425
D) The most frequently occurring textbook cost in the sample was $425

Accepted Answer

The median is the middle value in a data set when assorted in ascending order. In this case, 50% of the students sampled had textbook costs that were less than $425.

Question 4

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value $500. Which of the following interpretations of the 75th percentile is correct?
A) 75% of the students sampled had textbook costs that exceeded $500.
B) 75% of the students sampled had textbook costs equal to $500.
C) 25% of the students sampled had textbook costs that exceeded $500.
D) The average of the 500 textbook costs was $500.

Accepted Answer

The 75th percentile means that 75% of the students had textbook costs less than or equal to $500, so 25% had costs that exceeded $500.

Question 5

A survey was conducted to determine how people feel about the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown below. $$\begin{array} { r | l  l l l l l l l l } 
\text { Stem } & & & & & \
\hline 3 & 1 & 6 & & & & & & \
4 & 0 & 3 & 4 & 7 & 8 & 9 & 9 & 9 \
5 & 0 & 1 & 1 & 2 & 3 & 4 & 5 & \
6 & 1 & 2 & 5 & 6 & 6 & & & \
7 & 1 & 4 & & & & & \
8 & & & & & & & \
9 & 5 & & & & & &
\end{array}$$ What percentage of the respondents rated overall television quality as very good (regarded as ratings of 80 and above)?
A) 1%
B) 5%
C) 4%
D) 20%

Accepted Answer

There are 25 total ratings. Only 1 rating is 95, which is 80 and above. Therefore, the percentage is (1/25)*100 = 4%.

Question 6

By law, a box of cereal labeled as containing 24 ounces must contain at least 24 ounces of cereal. The machine filling the boxes produces a distribution of fill weights that is mound-shaped and symmetric, with a mean equal to the setting on the machine and with a standard deviation equal to 0.02 ounce. To ensure that most of the boxes contain at least 24 ounces, the machine is set so that the mean fill per box is 24.06 ounces. What percentage of the boxes do, in fact, contain at least 24 ounces?

Accepted Answer

The answer of By law, a box of cereal labeled...

Question 7

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample range for the data.
A) $98.75
B) $450
C) $99.37
D) $250

Accepted Answer

The sample range is calculated by subtracting the smallest value from the largest value in the data set: $600 - $350 = $250.

Question 8

A recent survey was conducted to compare the cost of solar energy to the cost of gas or
electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $124.00 and a standard deviation of $15.00. Assuming the distribution is mound-shaped and symmetric, would you expect to see a 3-bedroom house using gas or electric energy with a monthly utility bill of $236.50? Explain.

Accepted Answer

The answer of A recent survey was conducted to compare...

Question 9

The output below displays the mean and median for the state high school dropout rates in
year 1 and in year 5. $$\begin{array} { l r r } 
& \text { Year 1 } & \text { Year 5 } \
\text { N } & 51 & 51 \
\text { MEAN } & 28.22 & 26.56 \
\text { MEDIAN } & 27.53 & 25.18
\end{array}$$ Use the information to determine the shape of the distributions of the high school dropout rates in year 1 and year 5.

Accepted Answer

The answer of The output below displays the mean and...

Question 10

The table shows the number of each type of book found at an online auction site during arecent search.

$$\begin{array} { | l | c | } 
\hline \text { Type of Book } & \text { Number } \
\hline \text { Children's } & 51,033 \
\hline \text { Fiction } & 141,114 \
\hline \text { Nonfiction } & 253,074 \
\hline \text { Educational } & 67,252 \
\hline
\end{array}$$ a. Construct a relative frequency table for the book data.
b. Construct a pie chart for the book data.

Accepted Answer

The answer of The table shows the number of each...

Question 11

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample standard deviation for the data.
A) $450
B) $250
C) $98.75
D) $99.37

Accepted Answer

To calculate the sample standard deviation, first find the mean of the data: (400 + 350 + 600 + 525 + 450) / 5 = 465. Then, calculate the squared differences from the mean, sum them, and divide by (n-1) where n is the sample size: [(400-465)² + (350-465)² + (600-465)² + (525-465)² + (450-465)²] / 4 = 9875. Finally, take the square root of this result to get the sample standard deviation: √9875 ≈ 99.37.

Question 12

Which of the following is a measure of the variability of a distribution?
A) skewness
B) range
C) sample size
D) median

Accepted Answer

Range is a measure of the variability of a distribution. It is the difference between the maximum and minimum values in a distribution.

Question 13

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the standard deviation of the expenditures was calculated to be $100. Suppose a randomly selected student reported that their textbook expenditure was $700. Calculate the z-score for this student's textbook expenditure.
A) -2
B) -3
C) +2
D) +3

Accepted Answer

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. Here, z = (700 - 500) / 100 = +2.

Question 14

Parking at a university has become a problem. University administrators are interested in determining the average time it takes a student to find a parking spot. An administrator inconspicuously followed 90 students and recorded how long it took each of them to find a parking spot. Which of the following types of graphs should not be used to display information concerning
The students parking times?
A) box plot
B) stem-and-leaf display
C) pie chart
D) histogram

Accepted Answer

A pie chart is not suitable for displaying continuous data like parking times, as it is typically used for categorical data to show proportions of a whole.

Question 15

A dot plot of the speeds of a sample of 50 cars passing a policeman with a radar gun is shown below. 
 What proportion of the motorists were driving above the posted speed limit of 55 miles per hour?
A) 0.64
B) 0.50
C) 0.14
D) 7

Accepted Answer

The answer of A dot plot of the speeds of...

Question 16

Explain how using a scale break on the vertical axis of a histogram can be misleading.

Accepted Answer

The answer of Explain how using a scale break on...

Question 17

At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player's serve speeds?

Speeds: 50 mph, 80 mph, and 105 mph

A) 50 is the only outlier.
B) 50, 80, and 105 are all outliers.
C) 50 and 80 are both outliers, 105 is not.
D) None of the three speeds are outliers.

Accepted Answer

A z-score is calculated as (X - mean) / standard deviation. A common rule is that a z-score beyond ±2 or ±3 indicates an outlier. For 50 mph, the z-score is (50-100)/15 = -3.33, which is an outlier. For 80 mph, the z-score is (80-100)/15 = -1.33, and for 105 mph, it is (105-100)/15 = 0.33. Neither 80 mph nor 105 mph have z-scores beyond ±2, so they are not outliers.

Question 18

The z-score for a value x is -2.5. State whether the value of x lies above or below the mean and by how many standard deviations.

Accepted Answer

The answer of The z-score for a value x is...

Question 19

The temperature fluctuated between a low of 73°F and a high of 89°F. Which of the following could be calculated using just this information?
A) variance
B) median
C) standard deviation
D) range

Accepted Answer

The range can be calculated using the high and low temperatures by subtracting the low from the high (89°F - 73°F).

Question 20

The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what percentage of these commuting times are between 30 and 110 minutes?
A) at least 75%
B) at least 89%
C) at least 0%
D) at least 95%

Accepted Answer

According to Chebyshev's theorem, at least 75% of data lies within two standard deviations of the mean for any distribution. Here, 30 to 110 minutes is within two standard deviations (70 ± 2*20).

Quiz 2: Methods for Describing Sets of Data

The range of scores on a statistics test was 42. The lowest score was 57. What was the highest score?

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. The mean expenditure was calculated to be $500 and the median expenditure was calculated to be $425. Which of the following interpretations of the median is correct?

The amount spent on textbooks for the fall term was recorded for a sample of five hundred university students. It was determined that the 75th percentile was the value $500. Which of the following interpretations of the 75th percentile is correct?

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample range for the data.

The amount spent on textbooks for the fall term was recorded for a sample of five university students - $400, $350, $600, $525, and $450. Calculate the value of the sample standard deviation for the data.

Which of the following is a measure of the variability of a distribution?

A dot plot of the speeds of a sample of 50 cars passing a policeman with a radar gun is shown below. What proportion of the motorists were driving above the posted speed limit of 55 miles per hour?

Explain how using a scale break on the vertical axis of a histogram can be misleading.

The z-score for a value x is -2.5. State whether the value of x lies above or below the mean and by how many standard deviations.

The temperature fluctuated between a low of 73°F and a high of 89°F. Which of the following could be calculated using just this information?