This document discusses the difference between descriptive and inferential statistics. Descriptive statistics describe the characteristics of a whole population, using data from every member. Inferential statistics draw conclusions about a population based on a sample of data, allowing generalization to populations that are too large to measure entirely. Word problems involving descriptive statistics will refer to all or the entire group as the population, while inferential problems refer to samples that allow inferences about a broader population.

1. These slides will assist you in determining if your
problem or question is inferential or descriptive in
nature.

2. Descriptive
Inferential
These slides will assist you in determining if your
problem or question is inferential or descriptive in
nature.

3. Statistics tell a story about what is going on in
the world.

4. In general there are two types of stories that are
told using statistics:

5. In general there are two types of stories that are
told using statistics:
Descriptive Stories
Inferential Stories

6. A descriptive story describes what is going on in
a population.

7. What is a population?

8. A population is every member of a defined
group.

9. A population can be defined as ALL individuals

10. A population can be defined as ALL individuals
in a classroom.

11. A population can be defined as ALL individuals
in a classroom.

12. A population can be defined as ALL individuals
in a classroom.
30 individuals

13. A population can be defined as ALL individuals
in a school.

14. A population can be defined as ALL individuals
in a school.

15. A population can be defined as ALL individuals
in a school.
2,000 individuals

16. A population can be defined as ALL individuals
in a religion.

17. A population can be defined as ALL individuals
in a religion.

18. A population can be defined as ALL individuals
in a religion.
15,000,000 individuals

19. A population can be defined as ALL individuals in
a country.

20. A population can be defined as ALL individuals in
a country,

21. A population can be defined as ALL individuals in
a country,
350,000,000 individuals

22. A population can be defined as ALL individuals in
the world.

23. A population can be defined as ALL individuals in
the world.

24. A population can be defined as ALL individuals in
the world.
7,000,000,000 individuals

25. A population can be made up of people as in the
last examples.

26. Populations can also be made of observations.

27. An observation can be the observing of EVERY
TIME a car makes a complete stop at an
intersection.

28. An observation can be the observing of EVERY
TIME a car makes a complete stop at an
intersection.

29. Or observing ALL THE TIMES gorillas use a
specific type of sign language.

30. If the numbers you are using tell the story about
EVERYONE in a group or ALL the possible
observations in a study,

31. If the numbers you are using tell the story about
EVERYONE in a group or ALL the possible
observations in a study, then you use
descriptive statistics to tell the story about that
population.

32. Examples of Word Problems that Use
Descriptive Statistics

33. Example #1

34. Example #1
Mrs. Jones has asked you to determine the
average test score for all of the students in her
five geography classes.

35. Example #1
Mrs. Jones has asked you to determine the
average test score for all of the students in her
five geography classes.

36. Example #1
Mrs. Jones has asked you to determine the
average test score for all of the students in her
five geography classes.
This is a descriptive question because we are
describing what is happening with the entire
population (all students in Mrs. Jones
geography classes)

37. Example #2

38. Example #2
A state census shows that only 30% of all
Californians support Proposition X. You have
been asked to find out of all those who support
Prop X, what percentage would actually vote for
it.

39. Example #2
A state census shows that only 30% of all
Californians support Proposition X. You have
been asked to find out of all those who support
Prop X, what percentage would actually vote for
it.
What is the population we
want to describe?

40. Example #2
A state census shows that only 30% of all
Californians support Proposition X. You have
been asked to find out of all those who support
Prop X, what percentage would actually vote for
it.
What is the population we
want to describe?

41. Example #2
A state census shows that only 30% of all
Californians support Proposition X. You have
been asked to find out of all those who support
Prop X, what percentage would actually vote for
it.
Notice that the question is not asking
something about all Californians?

42. Example #2
A state census shows that only 30% of all
Californians support Proposition 2. You have
been asked to find out of all those who support
Prop X, what percentage would actually vote for
it.
Its asking something about the percentage
of all those who support Prop X.

43. Here are some words to look for in your word
problem to determine if it is descriptive:

44. • All
• Everyone
• The entire group
• Population
• Leaving no one out
• Etc.
Here are some words to look for in your word
problem to determine if it is descriptive:

45. • All
• Everyone
• The entire group
• Population
• Leaving no one out
• Etc.
Remember to always define the population
in your word problem
Here are some words to look for in your word
problem to determine if it is descriptive:

46. • All
• Everyone
• The entire group
• Population
• Leaving no one out
• Etc.
Is it defined as broadly as
all the people living in
Japan?
Here are some words to look for in your word
problem to determine if it is descriptive:

47. • All
• Everyone
• The entire group
• Population
• Leaving no one out
• Etc. Or is it defined as narrowly
as all the real estate
lawyers in Sidney,
Australia?
Here are some words to look for in your word
problem to determine if it is descriptive:

48. Are you ready to make your decision?

49. Is your word problem descriptive?

50. Is your word problem descriptive?
Descriptive
Inferential

51. Now let’s determine how to tell if your
word problem tells an inferential story.

52. Because it is not feasible to collect information
about everyone in a country, state, or school,
nor would it be possible to look at all
observations, we can take a smaller sample and
then generalize it to a larger population.
The methods used to do this are called
inferential statistics

53. Because it is not feasible to collect information
about everyone in a country, state, or school,
nor would it be feasible to look at all
observations, we can take a smaller sample and
then generalize it to a larger population.
The methods used to do this are called
inferential statistics

54. Because it is not feasible to collect information
about everyone in a country, state, or school,
nor would it be feasible to look at all
observations, we can take a smaller sample and
then generalize it to a larger population.
The methods used to do this are called
inferential statistics

55. Because it is not feasible to collect information
about everyone in a country, state, or school,
nor would it be feasible to look at all
observations, we can take a smaller sample and
then generalize it to a larger population.
The methods used to do this are called
inferential statistics.

56. Inferential statistics use information about a
sample (a group within a population) to tell a
story about a population.

57. Inferential statistics use information about a
sample (a group within a population) to tell a
story about a population.
The word inferential means we are inferring
something about a population based on information
from a smaller but representative sample

58. Consider the following inferential problem:

59. Using a sample of 5th grade student verbal acuity
scores, determine the average scores of 5th
graders in the state of Montana.
Consider the following inferential problem:

60. The population is defined as all of the fifth
grader verbal acuity scores in the state of
Montana.

61. The population is defined as all of the fifth
grader verbal acuity scores in the state of
Montana.

62. Let’s take a random
sample of a 100 fifth
grade students scores
from across the entire
state.

63. 100 Fifth Grade
Verbal Acuity
Scores
Let’s take a random
sample of a 100 fifth
grade students scores
from across the entire
state.

64. 100 Fifth Grade
Verbal Acuity
Scores
Average
Score of
Sample = 34

65. 100 Fifth Grade
Verbal Acuity
Scores
Average
Score of
Sample = 34
We generalize by
saying there is a
strong probability
that Montana 5th
graders averaged a
34 on their verbal
acuity test

66. 100 Fifth Grade
Verbal Acuity
Scores
Average
Score of
Sample = 34
We generalize by
saying there is a
strong probability
that Montana 5th
graders averaged a
34 on their verbal
acuity test
The generalizing from a
sample (100 Fifth Graders) to
the population (all Fifth
Graders in Montana) is an
example of what we call -
Inferential Statistics

67. Once again, with inferential statistics, we are
telling the story about a sample

68. Once again, with inferential statistics, we are
telling the story about a sample
Story
about a
Sample

69. Once again, with inferential statistics, we are
telling the story about a sample and then
generalizing that story to a larger population.

70. Once again, with inferential statistics, we are
telling the story about a sample and then
generalizing that story to a larger population.
Story
about a
Sample

71. Once again, with inferential statistics, we are
telling the story about a sample and then
generalizing that story to a larger population.
Story
about a
Sample
Generalizing to a

72. Once again, with inferential statistics, we are
telling the story about a sample and then
generalizing that story to a larger population.
Story
about a
Sample
Larger Population
Generalizing to a

73. Let’s look at an example of an
inferential statistic word problem

74. Skating rink officials want to know if teenagers
in PoDunk Town prefer rink skating better than
park skate boarding. They ask a sample of
teenagers and record their responses.
versus

75. Skating rink officials want to know if teenagers
in PoDunk Town prefer rink skating better than
park skate boarding. They ask a sample of
teenagers and record their responses.
It will most likely be
an inferential
question if you see
the word sample

76. Skating rink officials want to know if teenagers
in PoDunk Town prefer rink skating better than
park skate boarding. They ask a sample of
teenagers and record their responses.
that generalizes to a
population

77. Here are some words to look for in your word
problem to determine if it is inferential:

78. • sample
• some
• several
• random
• generalize
• Etc.
Here are some words to look for in your word
problem to determine if it is inferential:

79. Would you classify the problem you are working
on as inferential?

80. Would you classify the problem you are working
on as inferential?
Descriptive
Inferential