Question 1

Here is a set of scores: 18, 99, 14, 16, 31, 43, 12, 14, 13, 51, 12.Which score is considered to be an outlier?

Accepted Answer

There are different ways to identify outliers, but one of the most common methods is to use the Interquartile Range (IQR). To do this, we need to find the first quartile (Q1) and the third quartile (Q3) of the data set.

Q1 is the middle number between the smallest number and the median of the data set (ignoring the median if it is an odd number). In this case, the smallest number is 12, and the median is (14+14)/2 = 14. So Q1 = 12.

Q3 is the middle number between the largest number and the median of the data set (ignoring the median if it is an odd number).  In this case, the largest number is 99, and the median is (31+43)/2 = 37. So Q3 = 51.

The IQR is the difference between Q3 and Q1, so IQR = Q3 - Q1 = 51 - 12 = 39.

According to the IQR rule, any data point that is less than Q1 - 1.5×IQR or greater than Q3 + 1.5×IQR is considered an outlier.

In this case, the lower limit is 12 - 1.5×39 = -27, which does not make sense in the context of the data. Therefore, we ignore it and focus on the upper limit, which is 51 + 1.5×39 = 108. Any score that is greater than 108 is an outlier.

The only score that meets this condition is 99. Therefore, the answer is D: 99 is considered to be an outlier.

Question 2

Around the end-of-year holidays, such as Thanksgiving, a great amount of meat is purchased.To be prepared for the increased demand, a local grocery store manager wants to know the typical amount of ham sold at medium-sized stores around Thanksgiving.But even more than that, he wants to know how sales tend to vary around that typical amount because he wants to be prepared to sell as many hams as possible.His interest in how much sales vary will require a measure of:

Accepted Answer

The manager's interest in how much sales vary requires a measure of variability, which is the spread or dispersion of the data. The other options (central tendency, parameters, and statistics) do not focus on the variation of the data, but rather on the center or characteristics of the data.

Question 3

The concept of variability is best described as:

Accepted Answer

Variability refers to the extent to which data values are spread out or dispersed. It is typically measured by the range, variance, or standard deviation of the data. Therefore, option A, which defines variability as the spread of the distribution of data, is the best choice. Options B, C, and D are not accurate descriptions of variability.

Question 4

In a sample of data that has several extremely high scores, creating positive skew, the mean will be _____ the median.

Accepted Answer

The mean is influenced by extreme values, so in a sample with several extremely high scores, the mean will be pulled in the direction of the extreme values, creating positive skew. The median, on the other hand, is not influenced by extreme values, so it will remain relatively stable. Therefore, the mean will be greater than the median.

Question 5

Professor Kellogg calculates the grades on the first exam for her statistics class.She finds that students did either really well or really poorly.What kind of distribution does Prof.Kellogg have?

Accepted Answer

If the students did really well or really poorly, it suggests that there are two modes or peaks in the distribution of scores. This means that the distribution is likely bimodal.

Question 6

In a distribution that is skewed by a few extreme outliers, what would be the best choice for a measure of central tendency?

Accepted Answer

The median is the best choice in a skewed distribution because it is not affected by extreme values or outliers, whereas the mean is heavily influenced by them. The mode may also be affected by outliers, making the median a more reliable measure of central tendency in this situation. The range is not a measure of central tendency, but rather a measure of dispersion.

Question 7

Katrina observes and records the number of people who purchase a meal at the school cafeteria during each operating hour.The cafeteria is open from 6:00 a.m.to 9:00 p.m.and students typically eat breakfast, lunch, and dinner.What type of distribution should Katrina expect to see in her data?

Accepted Answer

Katrina is likely to observe a multimodal distribution because students typically eat meals at different times of the day, creating peaks during breakfast, lunch, and dinner times.

Question 8

A multimodal distribution has _____ mode(s).

Accepted Answer

The answer of A multimodal distribution has _____ mode(s).
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Question 9

In a sample of data that has several extremely low scores, creating negative skew, the mean will be _____ the median.

Accepted Answer

The mean is more affected by extreme scores than the median, so in a data set with negative skew (due to several extremely low scores), the mean will be pulled toward those low scores and be lower than the median.

Question 10

The median is preferred over the mean for _____ distributions.

Accepted Answer

The median is preferred over the mean for skewed distributions because the median is not affected by extreme outliers, unlike the mean. Skewed distributions have a tail that extends further in one direction, which can result in extreme outliers that significantly affect the mean, making it less representative of the true center of the data. Therefore, the median is a better measure of central tendency for skewed distributions.

Question 11

A bimodal distribution has _____ mode(s).

Accepted Answer

A bimodal distribution has two distinct peaks or modes, indicating that there are two distinct groups or categories within the data.

Question 12

If you knew nothing about your data except that it is a scale variable, which measure of central tendency would be the "safest bet"?

Accepted Answer

The median is the "safest bet" as it is not affected by extreme values, unlike the mean which can be heavily influenced by outliers. The mode, on the other hand, may not provide a good representation of the central tendency if there are multiple modes or if the data is relatively evenly distributed. The term "center" is vague and not a common measure of central tendency.

Question 13

In a sample of data that has several extremely high scores, creating positive skew, the mean:

Accepted Answer

In a positively skewed distribution, the mean will be pulled towards the higher extreme scores, causing it to be greater than the median. The mode may or may not be equal to the mean or median, as it depends on the exact shape of the distribution. However, since the question states that there are several extremely high scores, it is unlikely that the mode will be equal to either the mean or median.

Question 14

_____ is affected by outliers because it takes the actual value of each data point into consideration.

Accepted Answer

The mean is affected by outliers because it takes the actual value of each data point into consideration. The median and mode are less affected by outliers, as they only consider the middle value or most frequent value, respectively.

Question 15

A unimodal distribution has _____ mode(s).

Accepted Answer

A unimodal distribution has only one mode, which is the value that appears most frequently in the distribution.

Question 16

If you wanted to know whether judges in your state are typically male or female, what measure of central tendency would you use to describe the typical judge?

Accepted Answer

The mode is the most appropriate measure of central tendency for determining the most common category (in this case, male or female) among judges in your state.

Question 17

The most frequently occurring score in a distribution is the:

Accepted Answer

The mode is defined as the most frequently occurring score in a distribution.

Question 18

In a sample of data that has several extremely low scores, creating negative skew, the mean:

Accepted Answer

In a negatively skewed distribution, the mean is pulled towards the lower end (extremely low scores), making it less than the median.

Question 19

Sixteen college freshmen were asked to record the number of alcoholic drinks they typically consume in a week.Here are their data: 2, 4, 6, 0, 1, 10, 9, 0, 6, 3, 6, 8, 5, 4, 6, 2.What is the mode of this distribution?

Accepted Answer

The mode is the value that appears most frequently in the data set. In this case, the number 6 appears the most frequently, so the mode is 6. Choice D is the correct answer.

Question 20

Here is a set of data: 31, 54, 26, 42, 39, 45, 38, 42.What is the mode?

Accepted Answer

The mode is the value that appears most frequently in the set. In this case, 42 appears twice, which is more than any other value. Therefore, the mode is 42.

Quiz 4: Central Tendency and Variability