Question 1

A graphical device that highlights the highest and lowest values in a data set, along with a number of other key observations in an ordered array of the data, such as the upper quartile, the middle value (or median), and the lower quartile, is called:

Accepted Answer

A boxplot displays the five-number summary of a data set, including the minimum, the lower quartile, the median, the upper quartile, and the maximum. It also highlights any outliers. Therefore, it is the best choice among the given options.

Question 2

A sample of 2,500 vehicles in Minnesota showed the following statistics related to the number of accidents per month:  Based on these data, we can infer that the distribution accidents is skewed.

Accepted Answer

The high mean and median values and a lower mode indicate a skewed distribution.

Question 3

Attendance at London Symphony concerts for the past two years showed an average of 3,000 people per performance with a standard deviation of 100 people per performance. Attendance at a randomly selected concert was found to be 3,290. If attendance data is mound-shaped, does the attendance at the selected concert appear to be unusual?
__________
Justify your conclusion.
________________________________________________________

Accepted Answer

The answer of Attendance at London Symphony concerts for the...

Question 4

If a data set has 15 values that have been sorted in ascending order, which value in the data set will be the 25^th percentile?

Accepted Answer

The 25th percentile, also known as the first quartile, divides the data set into a lower quarter and an upper three quarters. In a sorted data set of 15 values, the 25th percentile falls at the 3.75th position (0.25 * 15 = 3.75), which means we round up to the 4th value in the data set to represent the 25th percentile.

Question 5

A student took a chemistry exam where the exam scores were mound-shaped with a mean score of 90 and a standard deviation of 64. She also took a statistics exam where the scores were mound-shaped, the mean score was 70 and the standard deviation was 16. If the student's grades were 102 on the chemistry exam and 77 on the statistics exam, then:

Accepted Answer

We can compare the student's performance on each exam by converting their scores into z-scores, which tell us the number of standard deviations above or below the mean a score is. Using the formula z = (score - mean) / standard deviation, we get:
z_chemistry = (102 - 90) / 64 = 0.1875
z_statistics = (77 - 70) / 16 = 0.4375
The positive z-scores indicate that the student scored above the mean for each class, but the z-score for the statistics exam is larger than the z-score for the chemistry exam. This means that the student did relatively better on the statistics exam than on the chemistry exam compared to the other students in the two classes. Choice B is the correct answer.

Question 6

Which of the following summary measures is affected most by outliers?

Accepted Answer

The first, second, and third quartiles (which correspond to the 25th, 50th, and 75th percentiles, respectively) are measures of central tendency and spread that are less affected by outliers compared to means or ranges. The fourth quartile is not a standard term in statistics; typically, the term "third quartile" or "75th percentile" is used to describe the upper quartile. Therefore, none of these options are correct in the context of being "affected most by outliers."

Question 7

Which one of the values below represents a lower quartile for the data set 23, 24, 21, and 20?

Accepted Answer

To find the lower quartile, we need to arrange the data set in order from least to greatest: 20, 21, 23, 24. The median of the lower half of the data set is the lower quartile. The lower half of the data set is 20 and 21. The median of 20 and 21 is (20+21)/2 = 20.5. Therefore, the lower quartile is 20.5, which is closest to choice C (20.25).

Question 8

Which one of the values below represents the upper quartile of the data set 10, 12, 16, 7, 9, 7, 41, and 14?

Accepted Answer

The upper quartile (Q3) is the median of the upper half of the data set. First, order the data: 7, 7, 9, 10, 12, 14, 16, 41. The upper half (after the median) is 12, 14, 16, 41. The median of this upper half is the average of 14 and 16, which is 15.5.

Question 9

The following summary statistics were computed from a sample of size 250:  . Based on this information, which of the following statements is correct?

Accepted Answer

None of the given statements can be concluded solely based on the summary statistics provided. The measures of central tendency (mean, median) and the measures of dispersion (range, interquartile range, standard deviation) do not provide any information about the shape of the distribution or the presence of outliers. Therefore, we cannot determine whether the distribution is symmetric or right-skewed, or whether a data value of 20 is an outlier.

Question 10

If the distribution of sales is thought to be symmetric with very little variation, then:

Accepted Answer

If the distribution is symmetric with little variation, the median (second quartile) should be the center of the box in the box and whisker plot. As the distribution is symmetric, the quartiles should be equidistant from the median, resulting in the edges of the box being approximately equidistant from the median.

Question 11

An exam is given to both the fourth period class and the sixth period class. If a student's score is at the 30^th percentile in the fourth period class but at the 60^th percentile in the sixth period class, which one of the following statements is true?

Accepted Answer

Since the student's score is at a lower percentile in the fourth period class compared to sixth period class, it means that there were more students who scored higher in the fourth period class than in the sixth period class. Therefore, students in the fourth period class generally performed better on the exam than students in the sixth period class. Option A is false because it is the reverse of the right answer. Option B is false because it assumes a linear relationship between the percentiles in both classes, which may not be the case. Option C is false because it assumes an incorrect inverse relationship between the percentiles in both classes.

Question 12

Consider the following set of measurements: 6, 3, 5, 14, 2, 6, 0, and 8. a. Find the 25^th percentile: ______________, Find the 50^th percentile: ______________, Find the 75^th percentile: ______________. b. What is the value of the interquartile range? ______________

Accepted Answer

The answer of Consider the following set of measurements: 6,...

Question 13

A sample of 600 values produced the following summary statistics:  Based on this information, the lower fence on a box and whisker plot is:

Accepted Answer

The lower fence on a box and whisker plot is given by:

Lower fence = Q1 - 1.5(IQR)

where Q1 is the first quartile and IQR is the interquartile range.

From the summary statistics provided, we can see that the first quartile (Q1) is 43.00 and the interquartile range (IQR) is 29.40 - 43.00 = 13.40.

Plugging these values into the formula gives:

Lower fence = 43.00 - 1.5(13.40) = -4.60

Therefore, the lower fence on the box and whisker plot is -4.60, which corresponds to choice B.

Question 14

Expressed in percentiles, the interquartile range is the difference between the:

Accepted Answer

The interquartile range is the range of the middle 50% of a dataset. This means it goes from the 25th percentile to the 75th percentile. Therefore, the best choice is C, which gives the difference between the 25% and 75% values.

Question 15

A sample of 50 values produced the following summary statistics:  Based on this information, the left and right ends of the box in a box and whisker plot are, respectively,

Accepted Answer

The box in a box and whisker plot represents the middle 50% of the data, which is the interquartile range (IQR). The IQR can be calculated as the difference between the third quartile (Q3) and the first quartile (Q1). From the given summary statistics, Q1 is 10 and Q3 is 16.7. Therefore, the left end of the box is 10 and the right end of the box is 16.7.

Question 16

The percentage of all observations in a data set that lies between the 30^th percentile and the third quartile:

Accepted Answer

The 30th percentile means 30% of the data is below this point. The third quartile (75th percentile) means 75% of the data is below this point. Therefore, the percentage of data between the 30th percentile and the third quartile is 75% - 30% = 45%.

Question 17

Which of the following randomly selected measurements, x, might be considered a potential outlier (i.e., an unusual measurement) if it was selected from the given population?

Accepted Answer

The answer of Which of the following randomly selected measurements,...

Question 18

The following data represent the number of small cracks per bar for a sample of eight steel bars:
4 6 10 1 3 1 25 8
Which, if any, of the observations appear to be outliers? Justify your answer.
____________________________

Accepted Answer

The answer of The following data represent the number of...

Question 19

A sample of 600 values produced the following summary statistics:  Based on this information, upper fence on a box and whisker plot is:

Accepted Answer

To find the upper fence on a box and whisker plot, we need to calculate the interquartile range (IQR) and then add 1.5 times the IQR to the third quartile (Q3). 
From the summary statistics provided, we can see that Q1 = 24.80, Q2 (median) = 36.00, and Q3 = 49.00. 
Using these values, we can calculate the IQR as:
IQR = Q3 - Q1 = 49.00 - 24.80 = 24.20 
Then, the upper fence would be:
Upper fence = Q3 + 1.5(IQR) = 49.00 + 1.5(24.20) = 102.60 
Therefore, the best choice is D, with an upper fence of 102.60.

Question 20

Lily recently took a biochemistry test, and it was reported back to her that her score placed her at the 97^th percentile. Therefore:

Accepted Answer

Lily scored as high or higher than 97% of the students who took the test. This is indicated by the fact that her score placed her at the 97th percentile. The other answer choices are incorrect: 
A) cannot be determined from the given information 
B) contradicts the fact that Lily was in the top 3% of the students who took the test 
D) and E) suggest that there were only 97 students who took the test, but this cannot be determined from the given information.

Quiz 2: Describing Data With Numerical Measures

A graphical device that highlights the highest and lowest values in a data set, along with a number of other key observations in an ordered array of the data, such as the upper quartile, the middle value (or median) , and the lower quartile, is called:

A sample of 2,500 vehicles in Minnesota showed the following statistics related to the number of accidents per month: Based on these data, we can infer that the distribution accidents is skewed.

If a data set has 15 values that have been sorted in ascending order, which value in the data set will be the 25^th percentile?

Which of the following summary measures is affected most by outliers?

Which one of the values below represents a lower quartile for the data set 23, 24, 21, and 20?

Which one of the values below represents the upper quartile of the data set 10, 12, 16, 7, 9, 7, 41, and 14?

The following summary statistics were computed from a sample of size 250: . Based on this information, which of the following statements is correct?

If the distribution of sales is thought to be symmetric with very little variation, then:

An exam is given to both the fourth period class and the sixth period class. If a student's score is at the 30^th percentile in the fourth period class but at the 60^th percentile in the sixth period class, which one of the following statements is true?

Consider the following set of measurements: 6, 3, 5, 14, 2, 6, 0, and 8. a. Find the 25^th percentile: , Find the 50^th percentile: , Find the 75^th percentile: . b. What is the value of the interquartile range?

A sample of 600 values produced the following summary statistics: Based on this information, the lower fence on a box and whisker plot is:

Expressed in percentiles, the interquartile range is the difference between the:

A sample of 50 values produced the following summary statistics: Based on this information, the left and right ends of the box in a box and whisker plot are, respectively,

The percentage of all observations in a data set that lies between the 30^th percentile and the third quartile:

Which of the following randomly selected measurements, x, might be considered a potential outlier (i.e., an unusual measurement) if it was selected from the given population?

The following data represent the number of small cracks per bar for a sample of eight steel bars: 4 6 10 1 3 1 25 8 Which, if any, of the observations appear to be outliers? Justify your answer. ____________________________

A sample of 600 values produced the following summary statistics: Based on this information, upper fence on a box and whisker plot is:

Lily recently took a biochemistry test, and it was reported back to her that her score placed her at the 97^th percentile. Therefore:

Quiz 2: Describing Data With Numerical Measures

A graphical device that highlights the highest and lowest values in a data set, along with a number of other key observations in an ordered array of the data, such as the upper quartile, the middle value (or median) , and the lower quartile, is called:

A sample of 2,500 vehicles in Minnesota showed the following statistics related to the number of accidents per month: Based on these data, we can infer that the distribution accidents is skewed.

If a data set has 15 values that have been sorted in ascending order, which value in the data set will be the 25th percentile?

Which of the following summary measures is affected most by outliers?

Which one of the values below represents a lower quartile for the data set 23, 24, 21, and 20?

Which one of the values below represents the upper quartile of the data set 10, 12, 16, 7, 9, 7, 41, and 14?

The following summary statistics were computed from a sample of size 250: . Based on this information, which of the following statements is correct?

If the distribution of sales is thought to be symmetric with very little variation, then:

An exam is given to both the fourth period class and the sixth period class. If a student's score is at the 30th percentile in the fourth period class but at the 60th percentile in the sixth period class, which one of the following statements is true?

Consider the following set of measurements: 6, 3, 5, 14, 2, 6, 0, and 8. a. Find the 25th percentile: ______________, Find the 50th percentile: ______________, Find the 75th percentile: ______________. b. What is the value of the interquartile range? ______________

A sample of 600 values produced the following summary statistics: Based on this information, the lower fence on a box and whisker plot is:

Expressed in percentiles, the interquartile range is the difference between the:

A sample of 50 values produced the following summary statistics: Based on this information, the left and right ends of the box in a box and whisker plot are, respectively,

The percentage of all observations in a data set that lies between the 30th percentile and the third quartile:

Which of the following randomly selected measurements, x, might be considered a potential outlier (i.e., an unusual measurement) if it was selected from the given population?

The following data represent the number of small cracks per bar for a sample of eight steel bars: 4 6 10 1 3 1 25 8 Which, if any, of the observations appear to be outliers? Justify your answer. ____________________________

A sample of 600 values produced the following summary statistics: Based on this information, upper fence on a box and whisker plot is:

Lily recently took a biochemistry test, and it was reported back to her that her score placed her at the 97th percentile. Therefore:

If a data set has 15 values that have been sorted in ascending order, which value in the data set will be the 25^th percentile?

An exam is given to both the fourth period class and the sixth period class. If a student's score is at the 30^th percentile in the fourth period class but at the 60^th percentile in the sixth period class, which one of the following statements is true?

Consider the following set of measurements: 6, 3, 5, 14, 2, 6, 0, and 8. a. Find the 25^th percentile: , Find the 50^th percentile: , Find the 75^th percentile: . b. What is the value of the interquartile range?

The percentage of all observations in a data set that lies between the 30^th percentile and the third quartile:

Lily recently took a biochemistry test, and it was reported back to her that her score placed her at the 97^th percentile. Therefore: