The document presents 7 practice problems about calculating different statistics from data sets. The problems involve comparing average cyberbullying incidents between grade levels, comparing test score ranges between therapy groups, calculating average blood pressure, examining exam score distributions, determining income variation across a school district, and describing comfort level distributions for different faculty groups. Central tendency, spread, and symmetry are the key statistical concepts addressed.

1. Central Tendency, Spread, & Symmetry
PRACTICE PROBLEMS

2. PROBLEM #1

3. You want to compare the average number of
cyberbullying incidents among freshmen,
sophomores, juniors, and seniors.
Central Tendency Spread
Symmetry Kurtosis
Which type of statistic is strongly associated with this problem?

4. You want to compare the average number of
cyberbullying incidents among freshmen,
sophomores, juniors, and seniors.
Central Tendency Spread
Symmetry Kurtosis

5. You want to compare the average number of
cyberbullying incidents among freshmen,
sophomores, juniors, and seniors.
Central Tendency Spread
Symmetry Kurtosis

7. You want to compare the average number of
cyberbullying incidents among freshmen,
sophomores, juniors, and seniors.
Central Tendency Spread
Symmetry Kurtosis

8. PROBLEM #2

9. A study was undertaken to determine the impact of a new
therapy on troubled teens in a particular school. All 50
students participated in the study. 24 teenagers who were
given this therapy were compared with 26 teenagers who
were given a traditional therapy. Both are tested for
evidence of improvement using a 50 point index.
First, you explore your data by finding out the difference
between the lowest and highest index scores for each group.
Central Tendency Spread
Symmetry Kurtosis
Which type of statistic is strongly associated with this problem?

10. A study was undertaken to determine the impact of a new
therapy on troubled teens in a particular school. All 50
students participated in the study. 24 teenagers who were
given this therapy were compared with 26 teenagers who
were given a traditional therapy. Both are tested for
evidence of improvement using a 50 point index.
First, you explore your data by finding out the difference
between the lowest and highest index scores for each group.
Central Tendency Spread
Symmetry Kurtosis

11. A study was undertaken to determine the impact of a new
therapy on troubled teens in a particular school. All 50
students participated in the study. 24 teenagers who were
given this therapy were compared with 26 teenagers who
were given a traditional therapy. Both are tested for
evidence of improvement using a 50 point index.
First, you explore your data by finding out the difference
between the lowest and highest index scores for each group.
Central Tendency Spread
Symmetry Kurtosis

13. A study was undertaken to determine the impact of a new
therapy on troubled teens in a particular school. All 50
students participated in the study. 24 teenagers who were
given this therapy were compared with 26 teenagers who
were given a traditional therapy. Both are tested for
evidence of improvement using a 50 point index.
First, you explore your data by finding out the difference
between the lowest and highest index scores for each group.
Central Tendency Spread
Symmetry Kurtosis

14. PROBLEM #3

15. The director of a health clinic has asked you to help her
analyze data from the results of patient systolic blood
pressure readings.
You decide to compute the mean systolic pressure for just
this data set.
Central Tendency Spread
Symmetry Kurtosis
Which type of statistic is strongly associated with
this problem?

16. The director of a health clinic has asked you to help her
analyze data from the results of patient systolic blood
pressure readings.
You decide to compute the mean systolic pressure for just
this data set.
Central Tendency Spread
Symmetry Kurtosis

17. The director of a health clinic has asked you to help her
analyze data from the results of patient systolic blood
pressure readings.
You decide to compute the mean systolic pressure for just
this data set.
Central Tendency Spread
Symmetry Kurtosis

19. The director of a health clinic has asked you to help her
analyze data from the results of patient systolic blood
pressure readings.
You decide to compute the mean systolic pressure for just
this data set.
Central Tendency Spread
Symmetry Kurtosis

20. PROBLEM #4

21. You have been told that an entrance exam for mechanical
engineers at your school is very difficult.
If it is very difficult you would expect most of the scores to
bunched up on the lower end of the score distribution with a
few high scores.
You decide to test this hypothesis.
Central Tendency Spread
Symmetry Kurtosis
Which type of statistic is strongly associated with this problem?

22. You have been told that an entrance exam for mechanical
engineers at your school is very difficult.
If it is very difficult you would expect most of the scores to
bunched up on the lower end of the score distribution with a
few high scores.
You decide to test this hypothesis.
Central Tendency Spread
Symmetry Kurtosis

23. You have been told that an entrance exam for mechanical
engineers at your school is very difficult.
If it is very difficult you would expect most of the scores to
bunched up on the lower end of the score distribution with a
few high scores.
You decide to test this hypothesis.
Central Tendency Spread
Symmetry Kurtosis

25. You have been told that an entrance exam for mechanical
engineers at your school is very difficult.
If it is very difficult you would expect most of the scores to
bunched up on the lower end of the score distribution with
few high scores.
You decide to test this hypothesis.
Central Tendency Spread
Symmetry Kurtosis

26. PROBLEM #5

27. You are working with a newly formed school district. Before
you begin your work as a school psychologist you want to
learn more about the nature of the families and those living in
the boundaries. You go to the department of vital statistics
and are given census data regarding the socio-economic
conditions of families in the new district.
You decide to determine how much income varies across the
district.
Central Tendency Spread
Symmetry Kurtosis
Which type of statistic is strongly associated with this problem?

28. You are working with a newly formed school district. Before
you begin your work as a school psychologist you want to
learn more about the nature of the families and those living in
the boundaries. You go to the department of vital statistics
and are given census data regarding the socio-economic
conditions of families in the new district.
You decide to determine how much income varies across the
district.
Central Tendency Spread
Symmetry Kurtosis

29. You are working with a newly formed school district. Before
you begin your work as a school psychologist you want to
learn more about the nature of the families and those living in
the boundaries. You go to the department of vital statistics
and are given census data regarding the socio-economic
conditions of families in the new district.
You decide to determine how much income varies across the
district.
Central Tendency Spread
Symmetry Kurtosis

31. You are working with a newly formed school district. Before
you begin your work as a school psychologist you want to
learn more about the nature of the families and those living in
the boundaries. You go to the department of vital statistics
and are given census data regarding the socio-economic
conditions of families in the new district.
You decide to determine how much income varies across the
district.
Central Tendency Spread
Symmetry Kurtosis

32. PROBLEM #6

33. You wish to find out the comfort level seasoned faculty
have with emerging educational technologies. You
survey 15 faculty who have taught more than 25 years.
Two select “no comfort”, twelve select “minimal comfort”
and two select moderate comfort.
Which statistic would be most relevant to describing the
nature of this distribution?
Central Tendency Spread
Symmetry Kurtosis
1
2
3
4
5
6
7
8
9
10
11
12
1
2
1
2

34. You wish to find out the comfort level seasoned
faculty have with emerging educational technologies.
You survey 15 faculty who have taught more than 25
years. Two select “no comfort”, twelve select
“minimal comfort” and two select moderate comfort.
Central Tendency Spread
Symmetry Kurtosis
1
2
3
4
5
6
7
8
9
10
11
12
1
2
1
2

36. You wish to find out the comfort level seasoned
faculty have with emerging educational technologies.
You survey 15 faculty who have taught more than 25
years. Two select “no comfort”, twelve select
“minimal comfort” and two select moderate comfort.
Central Tendency Spread
Symmetry Kurtosis
1
2
3
4
5
6
7
8
9
10
11
12
1
2
1
2

37. PROBLEM #7

38. You wish to find out the comfort level mid-career faculty
with emerging educational technologies. You survey 15
faculty who have taught more than ten and less than 25
years. Five select “no comfort”, five select “minimal
comfort” and five select moderate comfort.
Which statistic would be most relevant to describing the
nature of this distribution?
Central Tendency Spread
Symmetry Kurtosis
1
2
3
4
5
1
2
1
2
3
4
5
3
4
5

39. You wish to find out the comfort level mid-career faculty
with emerging educational technologies. You survey 15
faculty who have taught more than ten and less than 25
years. Five select “no comfort”, five select “minimal
comfort” and five select moderate comfort.
Which statistic would be most relevant to describing the
nature of this distribution?
Central Tendency Spread
Symmetry Kurtosis
1
2
3
4
5
1
2
1
2
3
4
5
3
4
5

40. You wish to find out the comfort level mid-career faculty
with emerging educational technologies. You survey 15
faculty who have taught more than ten and less than 25
years. Five select “no comfort”, five select “minimal
comfort” and five select moderate comfort.
Which statistic would be most relevant to describing the
nature of this distribution?
Central Tendency Spread
Symmetry Kurtosis
1
2
3
4
5
1
2
1
2
3
4
5
3
4
5

42. You wish to find out the comfort level mid-career faculty
with emerging educational technologies. You survey 15
faculty who have taught more than ten and less than 25
years. Five select “no comfort”, five select “minimal
comfort” and five select moderate comfort.
Which statistic would be most relevant to describing the
nature of this distribution?
Central Tendency Spread
Symmetry Kurtosis
1
2
3
4
5
1
2
1
2
3
4
5
3
4
5

43. So, does is the research question dealing with central
tendency, spread or symmetry (or kurtosis)?