2. Central Tendency Questions
In this demonstration you will be presented with a problem.
Attempt to answer each question before you advance to
the next screen where you will be given the correct answer
along with an explanation.
4. Demo #1
Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you
construct a distribution that looks like the following:
5. Demo #1
Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you
construct a distribution that looks like the following:
6. Demo #1
Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you
construct a distribution that looks like the following:
Which would be the most appropriate measure of central
tendency and why?
7. Demo #1
Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you
construct a distribution that looks like the following:
Which would be the most appropriate measure of central
tendency and why?
A. Mean
B. Median
C. Mode
8. The Median because it is much less affected by the
outliers in the tail on the right side of the distribution.
13. Watch what happens in a positively skewed distribution to the
mean.
Median = 5 Mean = 8
14. Watch what happens in a positively skewed distribution to the
mean.
Median = 5 Mean = 8
The Mean is more influenced by outliers than is the Median.
In fact the Median is considered to be outlier resistant.
15. Let’s look at the problem again and explain to yourself the
reason behind the correct answer:
16. Let’s look at the problem again and explain to yourself the
reason behind the correct answer:
Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you
construct a distribution that looks like the following:
17. Let’s look at the problem again and explain to yourself the
reason behind the correct answer:
Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you
construct a distribution that looks like the following:
Which would be the most appropriate measure of central
tendency and why?
A. Mean
B. Median
C. Mode
18. Let’s look at the problem again and explain to yourself the
reason behind the correct answer:
Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you
construct a distribution that looks like the following:
Which would be the most appropriate measure of central
tendency and why?
A. Mean
B. Median
C. Mode
20. What if, after a one week weight loss program, you collect
data and your weight loss / weight gain distribution looks
like the following.
21. What if, after a one week weight loss program, you collect
data and your weight loss / weight gain distribution looks
like the following.
22. What if, after a one week weight loss program, you collect
data and your weight loss / weight gain distribution looks
like the following.
If someone asked how it went for your clients, which
central tendency statistic would provide the best
description of how it went?
A. Mean
B. Median
C. Mode
23. The Mode, because the mode indicates which is or are the
most frequent observation(s). In this case the most
frequent observations are 2 pounds lost and 1.5 pounds
gained. The Mean or Median of zero does not tell you
much about this distribution, neither does standard
deviation.
24. The Mode, because the mode indicates which is or are the
most frequent observation(s). In this case the most
frequent observations are 2 pounds lost and 1.5 pounds
gained. The Mean or Median of zero does not tell you
much about this distribution, neither does standard
deviation.
Note- generally you do not rely on just one statistic, but
several to help tell the story of what is going on.
25. Here is the problem again. Try to explain in your own
words why the Mode is the correct answer.
26. What if, after a one week weight loss program, you collect
data and your weight loss / weight gain distribution looks
like the following.
27. What if, after a one week weight loss program, you collect
data and your weight loss / weight gain distribution looks
like the following.
28. What if, after a one week weight loss program, you collect
data and your weight loss / weight gain distribution looks
like the following.
If someone asked how it went for your clients, which
central tendency statistic would provide the best
description of how it went?
A. Mean
B. Median
C. Mode
31. A student wants to know the highest and lowest score on
a test, to see if his score is closer to one or the other.
32. A student wants to know the highest and lowest score on
a test, to see if his score is closer to one or the other.
Which measure of spread would best answer his
question?
33. A student wants to know the highest and lowest score on
a test, to see if his score is closer to one or the other.
Which measure of spread would best answer his
question?
A. Inter Quartile Range
B. Range
C. Standard Deviation
D. Variance
35. Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you construct
a distribution that looks like the following:
36. Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you construct
a distribution that looks like the following:
37. Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you construct
a distribution that looks like the following:
Which would be the most appropriate measure of spread
and why?
A. Inter Quartile Range
B. Range
C. Standard Deviation
D. Variance
39. Let’s start from the bottom. Could it be the variance?
A. Inter Quartile Range
B. Range
C. Standard Deviation
D. Variance
40. Let’s start from the bottom. Could it be the variance?
A. Inter Quartile Range
B. Range
C. Standard Deviation
D. Variance
Well . . . the variance is the average squared deviations
from the mean. Since it uses the mean in its calculations
and since the mean moves with the tail (in this case up),
then the variance would be an inflated measure of spread.
41. How about the standard deviation?
A. Inter Quartile Range
B. Range
C. Standard Deviation
D. Variance
The standard deviation is simply the square root of the
variance, so it will also be inflated.
42. How about the range?
A. Inter Quartile Range
B. Range
C. Standard Deviation
D. Variance
The range just tells you the survey with the highest score
(most favorable to the teacher) and the lowest score (least
favorable to the teacher).
43. How about the Inter quartile Range?
A. Inter Quartile Range
B. Range
C. Standard Deviation
D. Variance
The interquartile range divides the distribution up into
four parts.
44. The interquartile range divides the distribution up into
four parts.
Median 50% of the scores above50% of the scores below
45. The interquartile range divides the distribution up into
four parts.
Median 50% of the scores above50% of the scores below
25% of
scores
25% of
scores
25% of
scores
25% of
scores
46. The interquartile range divides the distribution up into
four parts.
And calculates where the middle 50% of the scores
are located.
Median 50% of the scores above50% of the scores below
25% of
scores
25% of
scores
25% of
scores
25% of
scores
47. The interquartile range is not affected by outliers
25% of
scores
25% of
scores
50% of the center
scores are within
the Interquartile
range
48. Answer the question again and explain in your own words
the reason behind the correct answer:
49. Answer the question again and explain in your own words
the reason behind the correct answer:
Students take a survey about the effectiveness of their
instructor’s teaching. After collecting the data you construct
a distribution that looks like the following:
Which would be the most appropriate measure of spread
and why?
A. Inter Quartile Range
B. Range
C. Standard Deviation
D. Variance
52. If most of the students do very well on an exam but only a
few do very poorly, what would the distribution look like?
A. Negatively Skewed
B. Normal
C. Positively Skewed
53. Let’s imagine the 14 students in the class got the following
scores:
54. Let’s imagine the 14 students in the class got the following
scores:
98 98 97 97 97 97 96 96 96 95 95 94 62 43
55. Let’s imagine the 14 students in the class got the following
scores:
98 98 97 97 97 97 96 96 96 95 95 94 62 43
Note that as is stated in the problem in this data set most of
the students did very well on the exam and a few did poorly.
Let’s create a distribution
56. Let’s imagine the 14 students in the class got the following
scores:
98 98 97 97 97 97 96 96 96 95 95 94 62 43
Note that as is stated in the problem in this data set most of
the students did very well on the exam and a few did poorly.
Let’s create a distribution
989796956243 94
57. Let’s imagine the 14 students in the class got the following
scores:
98 98 97 97 97 97 96 96 96 95 95 94 62 43
Note that as is stated in the problem in this data set most of
the students did very well on the exam and a few did poorly.
Let’s create a distribution
What do you think?
The direction of the skew is toward the tail.
989796956243 94
58. Since the tail is on the left or negative side, the curve is
negatively skewed.
61. Here is what the curve (a model of reality that is easier to
make sense of) would look like:
62. Here is what the curve (a model of reality that is easier to
make sense of) would look like:
63. Look at the question again and explain why the correct
answer is correct in your own words.
64. Look at the question again and explain why the correct
answer is correct in your own words.
If most of the students do very well on an exam but only a
few do very poorly, what would the distribution look like?
A. Negatively Skewed
B. Normal
C. Positively Skewed
66. If most of the students do very poorly on an exam but only
a few do very well, what would the distribution look like?
A. Negatively Skewed
B. Normal
C. Positively Skewed
67. Let’s imagine the 14 students in the class got the following
scores:
68. Let’s imagine the 14 students in the class got the following
scores:
97 78 47 46 46 45 45 45 44 44 44 44 43 43
69. Let’s imagine the 14 students in the class got the following
scores:
97 78 47 46 46 45 45 45 44 44 44 44 43 43
Let’s create a distribution
70. Let’s imagine the 14 students in the class got the following
scores:
97 78 47 46 46 45 45 45 44 44 44 44 43 43
Let’s create a distribution
977843 44 45 46 47
71. Let’s imagine the 14 students in the class got the following
scores:
97 78 47 46 46 45 45 45 44 44 44 44 43 43
Let’s create a distribution
What do you think?
977843 44 45 46 47
72. Let’s imagine the 14 students in the class got the following
scores:
97 78 47 46 46 45 45 45 44 44 44 44 43 43
Let’s create a distribution
What do you think?
The direction of the skew is toward the tail.
977843 44 45 46 47
73. Since the tail is on the right or positive side, the curve is
positively skewed.
74. 977843 44 45 46 47
Since the tail is on the right or positive side, the curve is
positively skewed.
75. 977843 44 45 46 47
Since the tail is on the right or positive side, the curve is
positively skewed.
76. Here is what the curve (a model of reality that is easier to
make sense of) would look like:
77. Here is what the curve (a model of reality that is easier to
make sense of) would look like:
78. Look at the question again and explain why the correct
answer is correct in your own words.
79. Look at the question again and explain why the correct
answer is correct in your own words.
If most of the students do very poorly on an exam but only
a few do very well, what would the distribution look like?
A. Negatively Skewed
B. Normal
C. Positively Skewed
81. A coach of a basketball team is given the mean and the
median height of his next opponent. The mean is 6 feet 4
inches but the median height is 6 feet 6 inches. Based on
this information answer the following:
82. A coach of a basketball team is given the mean and the
median height of his next opponent. The mean is 6 feet 4
inches but the median height is 6 feet 6 inches. Based on
this information answer the following:
What is the nature of the distribution?
83. A coach of a basketball team is given the mean and the
median height of his next opponent. The mean is 6 feet 4
inches but the median height is 6 feet 6 inches. Based on
this information answer the following:
What is the nature of the distribution?
A. Negatively Skewed
B. Normal
C. Positively Skewed
84. A coach of a basketball team is given the mean and the
median height of his next opponent. The mean is 6 feet 4
inches but the median height is 6 feet 6 inches. Based on
this information answer the following:
What is the nature of the distribution?
A. Negatively Skewed
B. Normal
C. Positively Skewed
Is the team mostly taller or shorter than 6 feet 6 inches tall?
85. A coach of a basketball team is given the mean and the
median height of his next opponent. The mean is 6 feet 4
inches but the median height is 6 feet 6 inches. Based on
this information answer the following:
What is the nature of the distribution?
A. Negatively Skewed
B. Normal
C. Positively Skewed
Is the team mostly taller or shorter than 6 feet 6 inches tall?
A. Shorter
B. Taller
86. Remember that the mean and median of a normal
distribution is the same:
87. Remember that the mean and median of a normal
distribution is the same:
Normal
Distribution
88. Remember that the mean and median of a normal
distribution is the same:
Normal
Distribution
Mean = 5
Median = 5
89. Remember that the mean and median of a normal
distribution is the same:
Normal
Distribution
Scores Evenly
Distributed
Mean = 5
Median = 5
90. However, when the Mean is smaller than the Median, this
means that a score to the left of the Median has pulled the
Mean to the left or to the negative side, making the
distribution negatively skewed.
91. However, when the Mean is smaller than the Median, this
means that a score to the left of the Median has pulled the
Mean to the left or to the negative side, making the
distribution negatively skewed.
Negatively
Skewed
Distribution
92. However, when the Mean is smaller than the Median, this
means that a score to the left of the Median has pulled the
Mean to the left or to the negative side, making the
distribution negatively skewed.
Negatively
Skewed
Distribution
Mean = 3
Median = 5
93. However, when the Mean is smaller than the Median, this
means that a score to the left of the Median has pulled the
Mean to the left or to the negative side, making the
distribution negatively skewed.
Negatively
Skewed
Distribution
Mostly Higher
Scores
Mean = 3
Median = 5
94. When the Mean is calculated it takes into account the
distance of all of the scores in its calculation. That makes it
sensitive to scores that are far away from the center
(outliers).
95. When the Mean is calculated it takes into account the
distance of all of the scores in its calculation. That makes it
sensitive to scores that are far away from the center
(outliers).
The Median does not take into account the distance of the
scores from the center. It just accounts for the rank order of
the scores regardless of how far apart they are from one
another.
So an outlier like 97 will pull the mean toward it (to the left
or the negative direction) but the Median will stay the same
whether that score were 97 or 48.
96. So an outlier like 97 will pull the mean toward it (to the left
or the negative direction) but the Median will stay the same
whether that score were 97 or 48
97. So an outlier like 97 will pull the mean toward it (to the left
or the negative direction) but the Median will stay the same
whether that score were 97 or 48.
97 78 47 46 46 45 45 45 44 44 44 44 43 43
Median = 45
98. So an outlier like 97 will pull the mean toward it (to the left
or the negative direction) but the Median will stay the same
whether that score were 97 or 48.
97 78 47 46 46 45 45 45 44 44 44 44 43 43
Median = 45
48 78 47 46 46 45 45 45 44 44 44 44 43 43
Median = 45
99. One way to tell if the distribution is negatively skewed,
normal, or positively skewed is to subtract the Mean from the
Median.
100. One way to tell if the distribution is negatively skewed,
normal, or positively skewed is to subtract the Mean from the
Median.
• If the result is negative than the distribution is negatively
skewed and most of the scores are on the upper end of the
distribution.
101. One way to tell if the distribution is negatively skewed,
normal, or positively skewed is to subtract the Mean from the
Median.
• If the result is negative than the distribution is negatively
skewed and most of the scores are on the upper end of the
distribution.
• If the result is positive than the distribution is positively
skewed and most of the scores are on the lower end of the
distribution.
102. • If the result is negative than the distribution is negatively
skewed and most of the scores are on the upper end of the
distribution.
• If the result is positive than the distribution is positively
skewed and most of the scores are on the lower end of the
distribution.
Negatively
Skewed
Distribution
Mean = 3
Median = 5
-2
103. • If the result is negative than the distribution is negatively
skewed and most of the scores are on the upper end of the
distribution.
• If the result is positive than the distribution is positively
skewed and most of the scores are on the lower end of the
distribution.
Negatively
Skewed
Distribution
Normal
Distribution
Mean = 3
Median = 5
Mean = 5
Median = 5
-2 0
104. • If the result is negative than the distribution is negatively
skewed and most of the scores are on the upper end of the
distribution.
• If the result is positive than the distribution is positively
skewed and most of the scores are on the lower end of the
distribution.
Negatively
Skewed
Distribution
Normal
Distribution
Positively
Skewed
Distribution
Mean = 3
Median = 5
Mean = 5
Median = 5
Mean = 7
Median = 5
-2 0 2
105. • If the result is negative than the distribution is negatively
skewed and most of the scores are on the upper end of the
distribution.
• If the result is positive than the distribution is positively
skewed and most of the scores are on the lower end of the
distribution.
Negatively
Skewed
Distribution
Normal
Distribution
Positively
Skewed
Distribution
Mean = 3
Median = 5
Mean = 5
Median = 5
Mean = 7
Median = 5
-2 0 2
106. So a basketball team with the Mean (6’4”) smaller than
the Median (6’6”) will have most of the players
bunched up by the median with a few outliers below
(e.g., 5’6” or 5’8”). This is negatively skewed because
the mean is pulled toward the tail.
107. So a basketball team with the Mean (6’4”) smaller than
the Median (6’6”) will have most of the players
bunched up by the median with a few outliers below
(e.g., 5’6” or 5’8”). This is negatively skewed because
the mean is pulled toward the tail.
What is the nature of the distribution?
108. So a basketball team with the Mean (6’4”) smaller than
the Median (6’6”) will have most of the players
bunched up by the median with a few outliers below
(e.g., 5’6” or 5’8”). This is negatively skewed because
the mean is pulled toward the tail.
What is the nature of the distribution?
A. Negatively Skewed
B. Normal
C. Positively Skewed
109. So a basketball team with the Mean (6’4”) smaller than
the Median (6’6”) will have most of the players
bunched up by the median with a few outliers below
(e.g., 5’6” or 5’8”). This is negatively skewed because
the mean is pulled toward the tail.
What is the nature of the distribution?
A. Negatively Skewed
B. Normal
C. Positively Skewed
110. So a basketball team with the Mean (6’4”) smaller than
the Median (6’6”) will have most of the players
bunched up by the median with a few outliers below
(e.g., 5’6” or 5’8”). This is negatively skewed because
the mean is pulled toward the tail.
What is the nature of the distribution?
A. Negatively Skewed
B. Normal
C. Positively Skewed
Is the team mostly taller or shorter than 6 feet 6 inches
tall?
111. So a basketball team with the Mean (6’4”) smaller than
the Median (6’6”) will have most of the players
bunched up by the median with a few outliers below
(e.g., 5’6” or 5’8”). This is negatively skewed because
the mean is pulled toward the tail.
What is the nature of the distribution?
A. Negatively Skewed
B. Normal
C. Positively Skewed
Is the team mostly taller or shorter than 6 feet 6 inches
tall?
A. Shorter
B. Taller
112. So a basketball team with the Mean (6’4”) smaller than
the Median (6’6”) will have most of the players
bunched up by the median with a few outliers below
(e.g., 5’6” or 5’8”). This is negatively skewed because
the mean is pulled toward the tail.
What is the nature of the distribution?
A. Negatively Skewed
B. Normal
C. Positively Skewed
Is the team mostly taller or shorter than 6 feet 6 inches
tall?
A. Shorter
B. Taller
113. Look at the question again and explain why the correct
answer is correct in your own words.
114. Look at the question again and explain why the correct
answer is correct in your own words.
A coach of a basketball team is given the mean and the
median height of his next opponent. The mean is 6 feet 4
inches but the median height is 6 feet 6 inches. Based on
this information answer the following:
What is the nature of the distribution?
A. Negatively Skewed
B. Normal
C. Positively Skewed
Is the team mostly taller or shorter than 6 feet 6 inches tall?
A. Shorter
B. Taller
117. What is the nature of the distributions of each of the
data sets below?
118. What is the nature of the distributions of each of the
data sets below?
Data Set A - 1 1 1 2 2 2 2 3 3 6 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
119. What is the nature of the distributions of each of the
data sets below?
Data Set B - 1 2 3 4 5 6 7 8 9 10 11
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
120. What is the nature of the distributions of each of the
data sets below?
Data Set C - 6 6 6 6 6 7 7 7 7 7 7
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
121. What is the nature of the distributions of each of the
data sets below?
Data Set D - 3 4 5 5 6 6 6 7 7 8 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
122. Let’s see each distribution graphed –
Data Set A - 1 1 1 2 2 2 2 3 3 6 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
123. Let’s see each distribution graphed –
Data Set A - 1 1 1 2 2 2 2 3 3 6 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed 1 2 3 4 5 6 7 8 9 10 11
1
1
2
2
1 2
3
3
2
6 9
124. Let’s see each distribution graphed –
Data Set A - 1 1 1 2 2 2 2 3 3 6 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed 1 2 3 4 5 6 7 8 9 10 11
1
1
2
2
1 2
3
3
2
6 9
125. Let’s see each distribution graphed –
Data Set A - 1 1 1 2 2 2 2 3 3 6 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed 1 2 3 4 5 6 7 8 9 10 11
1
1
2
2
1 2
3
3
2
6 9
126. Let’s see each distribution graphed –
Data Set B - 1 2 3 4 5 6 7 8 9 10 11
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
127. Let’s see each distribution graphed –
Data Set B - 1 2 3 4 5 6 7 8 9 10 11
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed 1 2 3 4 5 6 7 8 9 10 11
1 102 11873 4 5 6 9
128. Let’s see each distribution graphed –
Data Set B - 1 2 3 4 5 6 7 8 9 10 11
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed 1 2 3 4 5 6 7 8 9 10 11
1 102 11873 4 5 6 9
129. Let’s see each distribution graphed –
Data Set C - 6 6 6 6 6 7 7 7 7 7 7
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
130. Let’s see each distribution graphed –
Data Set C - 6 6 6 6 6 7 7 7 7 7 7
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed 1 2 3 4 5 6 7 8 9 10 11
6
6
7
7
6 7
6 7
7
6 7
131. Let’s see each distribution graphed –
Data Set C - 6 6 6 6 6 7 7 7 7 7 7
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed 1 2 3 4 5 6 7 8 9 10 11
6
6
7
7
6 7
6 7
7
6 7
132. Let’s see each distribution graphed –
Data Set D - 3 4 5 5 6 6 6 7 7 8 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
133. Let’s see each distribution graphed –
Data Set D - 3 4 5 5 6 6 6 7 7 8 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed 1 2 3 4 5 6 7 8 9 10 11
5
5
6
6
9
6
4 83 7
7
134. Let’s see each distribution graphed –
Data Set D - 3 4 5 5 6 6 6 7 7 8 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed 1 2 3 4 5 6 7 8 9 10 11
5
5
6
6
9
6
4 83 7
7
136. What is the nature of the distributions of each of the
data sets below?
137. What is the nature of the distributions of each of the
data sets below?
Data Set A - 1 1 1 2 2 2 2 3 3 6 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
138. What is the nature of the distributions of each of the
data sets below?
Data Set B - 1 2 3 4 5 6 7 8 9 10 11
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
139. What is the nature of the distributions of each of the
data sets below?
Data Set C - 6 6 6 6 6 7 7 7 7 7 7
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed
140. What is the nature of the distributions of each of the
data sets below?
Data Set D - 3 4 5 5 6 6 6 7 7 8 9
A. Leptokurtic
B. Mesokurtic (Normal)
C. Negatively Skewed
D. PlatoKurtic
E. Positively Skewed