Question 1

When Scholastic Achievement Test scores (SATs) are sent to test-takers, the percentiles associated with scores are also given. Suppose a test-taker scored at the 87th percentile on the verbal part of the test and at the 14th percentile on the quantitative part. Interpret these results.
A) This student performed better than 13% of the other test-takers on the verbal part and better than 14% on the quantitative part.
B) This student performed better than 87% of the other test-takers on the verbal part and better than 14% on the quantitative part.
C) This student performed better than 13% of the other test-takers on the verbal part and better than 86% on the quantitative part.
D) This student performed better than 87% of the other test-takers on the verbal part and better than 86% on the quantitative part.

Accepted Answer

The 87th percentile means the student scored better than 87% of test-takers on the verbal part, and the 14th percentile means they scored better than 14% on the quantitative part.

Question 2

Fill in the blank. __________ gives us a method of interpreting the standard deviation of any data set, regardless of the shape of the distribution.
A) The Empirical Rule
B) Chebyshev's Rule
C) both A and B
D) neither A nor B

Accepted Answer

Chebyshev's Rule gives us a general guideline for any data set, stating that regardless of the shape of the distribution, at least a certain percentage (depending on how many standard deviations away from the mean) of the data will fall within that range. The Empirical Rule specifically applies to bell-shaped, normal distributions, so it is not as versatile as Chebyshev's Rule. Therefore, the best choice is B, as it provides a method applicable to any data set.

Question 3

The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution?
A) median
B) mean
C) range
D) mode

Accepted Answer

The median is the best measure of central tendency for skewed distributions because it is not affected by extreme values, unlike the mean.

Question 4

The bar graph shows the political affiliation of 1000 registered U.S. voters. What percentage of the voters belonged to one of the traditional two parties (Democratic or Republican)?
A) 25%
B) 75%
C) 35%
D) 40%

Accepted Answer

The answer of  The bar graph shows the political...

Question 5

Percentile rankings are of practical value only with large data sets.

Accepted Answer

Percentile rankings require a large amount of data in order to provide meaningful comparisons and accurate rankings. With small data sets, there may not be enough variability to accurately rank individuals or groups.

Question 6

Which of the following statements concerning the box plot and z-score methods for detecting outliers is false?
A) The z-score method uses the mean and standard deviation as a basis for detecting outliers.
B) The z-score method is less affected by an extreme observation in the data set.
C) The box plot method uses the quartiles as a basis for detecting outliers.
D) The box plot method is less affected by an extreme observation in the data set.

Accepted Answer

The z-score method is more affected by extreme observations because it relies on the mean and standard deviation, which can be influenced by outliers.

Question 7

Calculate the range of the following data set:
 8, 8, 4, 1, 9, 12, 8, 5, 5
A) 1
B) 12
C) 13
D) 11

Accepted Answer

The range is calculated by subtracting the smallest value (1) from the largest value (12), which gives 11.

Question 8

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 97 miles per hour (mph) and the standard deviation of the serve speeds was 13 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was mound-shaped and symmetric. What proportion of the player's serves was between 110 mph and 136 mph?
A) 0.1585
B) 0.997
C) 0.317
D) 136

Accepted Answer

The z-score for 110 mph is (110 - 97) / 13 = 1.00. The z-score for 136 mph is (136 - 97) / 13 = 2.92. The proportion of the player's serves between 110 mph and 136 mph is the area under the normal curve between z = 1.00 and z = 2.92, which is 0.1585.

Question 9

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 105 miles per hour (mph) and the standard deviation of the serve speeds was 9 mph. If nothing is known about the shape of the distribution, give an interval that will contain the speeds of at least eight-ninths of the player's serves.
A) 69 mph to 141 mph
B) 132 mph to 159 mph
C) 78 mph to 132 mph
D) 87 mph to 123 mph

Accepted Answer

Using Chebyshev's theorem, at least 8/9 of the data lies within 3 standard deviations from the mean. The interval is 105 ± 3(9), which is 78 mph to 132 mph.

Question 10

The slices of a pie chart must be arranged from largest to smallest in a clockwise direction.

Accepted Answer

Pie charts do not have a strict rule requiring slices to be arranged from largest to smallest in a clockwise direction; they can be arranged in any order, although arranging them in a logical order can make them easier to read.

Question 11

The mean and the median are useful measures of central tendency for both qualitative and quantitative data.

Accepted Answer

The mean and median are measures of central tendency primarily used for quantitative data. For qualitative data, the mode is a more appropriate measure.

Question 12

An outlier may be caused by accidentally including the height of a six-year-old boy in a set of data representing the heights of 12-year-old boys.

Accepted Answer

Yes, if the height of a six-year-old boy is accidentally included in a dataset representing the heights of 12-year-old boys, it is likely to be significantly different from the other heights and could be considered an outlier.

Question 13

A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 470 with a standard deviation of 20 on a standardized test. Assuming no information concerning the shape of the distribution is known, what percentage of the students scored between 430 and 510?
A) at least 89%
B) at least 75%
C) approximately 68%
D) approximately 95%

Accepted Answer

According to Chebyshev's theorem, at least 75% of data falls within two standard deviations of the mean for any distribution shape. Here, 430 to 510 is two standard deviations from the mean (470 ± 2*20).

Question 14

Fill in the blank. __________ is a method of interpreting the standard deviation of data that have a mound-shaped, symmetric distribution.
A) The Empirical Rule
B) Chebyshev's Rule
C) both A and B
D) neither A nor B

Accepted Answer

The Empirical Rule is used for interpreting the standard deviation of data with a mound-shaped, symmetric distribution.

Question 15

A study was designed to investigate the effects of two variables - (1) a student's level of mathematical anxiety and (2) teaching method - on a student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 390 with a standard deviation of 30 on a standardized test. Assuming a non-mound-shaped distribution, what percentage of the students scored over 480?
A) at most 11%
B) at least 89%
C) approximately 2.5%
D) at most 5.5%

Accepted Answer

The non-mound-shaped distribution means that the data is not normally distributed. Therefore, we cannot use the normal distribution to calculate the percentage of students who scored over 480. However, we can use the Chebyshev's theorem to calculate the minimum percentage of students who scored over 480. Chebyshev's theorem states that for any data set, at least 1 - 1/k^2 of the data will fall within k standard deviations of the mean. In this case, k = (480 - 390) / 30 = 3. Therefore, at least 1 - 1/3^2 = 89% of the students scored over 480.

Question 16

A frequency table displays the proportion of observations falling into each class.

Accepted Answer

A frequency table displays the count of observations falling into each class, not the proportion.

Question 17

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 $90 and a standard deviation of $15. If nothing is known about the shape of the distribution, what percentage of homes will have a monthly utility bill of less than $60?
A) at least 88.9%
B) at most 11.1%
C) at most 25%
D) at least 75%

Accepted Answer

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

Question 18

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 8 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: 72 mph, 108 mph, and 116 mph

A) 72, 108, and 116 are all outliers.
B) None of the three speeds is an outlier.
C) 72 is the only outlier.
D) 72 and 108 are both outliers, but 116 is not.

Accepted Answer

A z-score greater than 2 or less than -2 is typically considered an outlier. The z-score for 72 mph is -3.5, making it an outlier. The z-scores for 108 mph and 116 mph are 1 and 2, respectively, which are not considered outliers.

Question 19

By law, a box of cereal labeled as containing 36 ounces must contain at least 36 ounces of cereal. The machine filling the boxes produces a distribution of fill weights 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 36 ounces, the machine is set so that the mean fill per box is 36.06 ounces.
Assuming nothing is known about the shape of the distribution, what can be said about the proportion of cereal boxes that contain less than 36 ounces.
A) The proportion is at most 11%.
B) The proportion is at least 89%.
C) The proportion is less than 2.5%.
D) The proportion is at most 5.5%.

Accepted Answer

Using Chebyshev's inequality, which applies regardless of the distribution's shape, at least 75% of the data lies within 2 standard deviations from the mean. Since the mean is 36.06 and the standard deviation is 0.02, 36 ounces is 3 standard deviations below the mean. Therefore, at most 1/9 (about 11%) of the boxes can contain less than 36 ounces.

Question 20

For any quantitative data set, $$\sum ( x - \bar { x } ) = 0$$

Accepted Answer

The sum of deviations of each data point from the mean ($\bar{x}$) is always zero because the mean is the balance point of the data set.

Quiz 2: Methods for Describing Sets of Data

When Scholastic Achievement Test scores (SATs) are sent to test-takers, the percentiles associated with scores are also given. Suppose a test-taker scored at the 87th percentile on the verbal part of the test and at the 14th percentile on the quantitative part. Interpret these results.

Fill in the blank. __________ gives us a method of interpreting the standard deviation of any data set, regardless of the shape of the distribution.

The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution?

The bar graph shows the political affiliation of 1000 registered U.S. voters. What percentage of the voters belonged to one of the traditional two parties (Democratic or Republican) ?

Percentile rankings are of practical value only with large data sets.

Which of the following statements concerning the box plot and z-score methods for detecting outliers is false?

Calculate the range of the following data set: 8, 8, 4, 1, 9, 12, 8, 5, 5

The slices of a pie chart must be arranged from largest to smallest in a clockwise direction.

The mean and the median are useful measures of central tendency for both qualitative and quantitative data.

An outlier may be caused by accidentally including the height of a six-year-old boy in a set of data representing the heights of 12-year-old boys.

Fill in the blank. __________ is a method of interpreting the standard deviation of data that have a mound-shaped, symmetric distribution.

A frequency table displays the proportion of observations falling into each class.

For any quantitative data set, $\sum ( x - \bar { x } ) = 0$

Quiz 2: Methods for Describing Sets of Data

When Scholastic Achievement Test scores (SATs) are sent to test-takers, the percentiles associated with scores are also given. Suppose a test-taker scored at the 87th percentile on the verbal part of the test and at the 14th percentile on the quantitative part. Interpret these results.

Fill in the blank. __________ gives us a method of interpreting the standard deviation of any data set, regardless of the shape of the distribution.

The distribution of salaries of professional basketball players is skewed to the right. Which measure of central tendency would be the best measure to determine the location of the center of the distribution?

The bar graph shows the political affiliation of 1000 registered U.S. voters. What percentage of the voters belonged to one of the traditional two parties (Democratic or Republican) ?

Percentile rankings are of practical value only with large data sets.

Which of the following statements concerning the box plot and z-score methods for detecting outliers is false?

Calculate the range of the following data set: 8, 8, 4, 1, 9, 12, 8, 5, 5

The slices of a pie chart must be arranged from largest to smallest in a clockwise direction.

The mean and the median are useful measures of central tendency for both qualitative and quantitative data.

An outlier may be caused by accidentally including the height of a six-year-old boy in a set of data representing the heights of 12-year-old boys.

Fill in the blank. __________ is a method of interpreting the standard deviation of data that have a mound-shaped, symmetric distribution.

A frequency table displays the proportion of observations falling into each class.

For any quantitative data set, ∑(x−xˉ)=0\sum ( x - \bar { x } ) = 0∑(x−xˉ)=0

For any quantitative data set, $\sum ( x - \bar { x } ) = 0$