LECTURE 1 MATH 221 STATISTICS FOR DECISION MAKING Professor Heard Lecturer All materials © BN Heard and can not be copied without permission. Visit the Stat Cave online at www.facebook.com/statcave
Statistics for Decision Making Week 1 Lecture
Jul 04, 2015
Samples, populations, quantitative and qualitative data, random sampling, stratified sampling, systematic sampling, convenience sampling, cluster sampling, frequency distributions, class width, class boundaries, midpoints, histograms, stem and leaf plots, mean, median, mode, quartiles, outliers, etc. Using Excel for statistics and statistical analysis.
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LECTURE 1
MATH 221
STATISTICS FOR DECISION MAKINGProfessor Heard
Lecturer
All materials © BN Heard and can not be copied without permission. Visit the Stat Cave online at
www.facebook.com/statcave
35 0 30 35 30 35
35 25 35 35 33 26
34 35 35 35 34 35
25 33 25 35 15 0
20 30 20 25 18 27
The following data represents the Discussion Board assignment
scores for all of my Math 221 students. Would this be a
population or a sample?
(Scores out of 35 points)
35 0 30 35 30 35
35 25 35 35 33 26
34 35 35 35 34 35
25 33 25 35 15 0
20 30 20 25 18 27
The following data represents the Discussion Board assignment
scores for all of my Math 221 students. Would this be a
population or a sample?
(Scores out of 35 points)
This would be a population since the data is from ALL of my students.
Samples are “subsets” of populations.
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0 2 1 5 0 7
3 3 2 2 2 1
2 0 1 2 3 0
0 0 1 2 0 0
1 6 0 1 2 1
The following data represents the number of children each of my
Math 221 students have. Would this data set be qualitative or
quantitative?
(Number of Children)
0 2 1 5 0 7
3 3 2 2 2 1
2 0 1 2 3 0
0 0 1 2 0 0
1 6 0 1 2 1
The following data represents the number of children each of my
Math 221 students have. Would this data set be qualitative or
quantitative?
(Number of Children)
This would be quantitative data since we are dealing with numbers having
meaning.
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1| 0 5 5 5 8
2| 5 5 8 8 9 9
3| 0 0 2 5 5 5 5 5 5
The following data set represents the DB scores of 2 students randomly
chosen from each of a total of 10 Statistics classes. What type of data set
(or sampling) would this represent?
Know the difference in Sampling Techniques
Random (simply picking where every member has an equal chance – drawing out of a bag – generating random numbers)
Stratified (dividing your population into strata and then picking a certain number from each strata)
Systematic (picking every nth one – for example testing every 20th unit off of an assembly line)
Convenience (just asking who is available or who is listening, not making an effort to get a true sample)
Cluster (dividing the population into clusters and sampling everyone in one or two of the clusters)
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1| 0 5 5 5 8
2| 5 5 8 8 9 9
3| 0 0 2 5 5 5 5 5 5
The following data set represents the DB scores of 2 students randomly
chosen from each of a total of 10 Statistics classes. What type of data set
(or sampling) would this represent?
This would be stratified sampling since we divided the population into
Strata (classes) and then randomly selected two from each.
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row Class (Weight lbs) frequency
1 4-11 7
2 12-19 4
3 20-27 2
4 28-35 2
5 36-43 1
The following table of data represents the weight of 16 randomly selected
dogs in my neighborhood.
Looking only at row 2, determine the class width, class boundaries and
midpoint.
row Class (Weight lbs) frequency
1 4-11 7
2 12-19 4
3 20-27 2
4 28-35 2
5 36-43 1
Looking only at row 2, determine the class width, class boundaries and
midpoint.
Class
Width
12-4 = 8
You
could
have
just as
easily
said 20-
12,28-
20 or
36-28
and still
gotten
8.
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row Class (Weight lbs) frequency
1 4-11 7
2 12-19 4
3 20-27 2
4 28-35 2
5 36-43 1
Looking only at row 2, determine the class width, class boundaries and
midpoint.
The class
boundaries
for row 2
would be
11.5 and
19.5,
simply
subtract .5
from the
lower and
add .5 to
the upper.
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row Class (Weight lbs) frequency
1 4-11 7
2 12-19 4
3 20-27 2
4 28-35 2
5 36-43 1
Looking only at row 2, determine the class width, class boundaries and
midpoint.
The
midpoint for
row 2 would
be 15.5, just
add (12+19)
and divide
by 2.
Similarly the
midpoint for
row 5 would
be 39.5
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The histogram below describes the height of 25
students. Looking only at the 64-65 group, determine
the class width, class boundaries and midpoint.
53-54 55-57 58-59 60-61 62-63 64-65 66-67 68-69 70-71 72-73
The histogram below describes the height of 25
students. Looking only at the 64-65 group, determine
the class width, class boundaries and midpoint.
Class width would be 2, because 64 minus 62 is 2.
Class boundaries would be 63.5 and 65.5
Midpoint would be 64.5 because (64+65)/2 = 64.5
53-54 55-57 58-59 60-61 62-63 64-65 66-67 68-69 70-71 72-73
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1| 0 5 5 5 8
2| 5 5 8 8 9 9
3| 0 0 2 5 5 5 5 5 5
The following is a sample of discussion board scores
for a group of students. Find the first quartile, median
and third quartile
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1| 0 5 5 5 8
2| 5 5 8 8 9 9
3| 0 0 2 5 5 5 5 5 5
The following is a sample of discussion board scores
for a group of students. Find the first quartile, median
and third quartile. Input data input an Excel column, if
the data is not provided. 10
15
15
15
18
25
25
28
28
29
29
30
30
32
35
35
35
35
35
35
Etc.
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10
15
15
15
18
25
25
28
28
29
29
30
30
32
35
35
35
35
35
35
To find the first quartile use the quartile
function in Excel to get 23.25
To find the median use the median
function in Excel to get 29.00. Note this is
also the second quartile
To find the third quartile use the quartile
function in Excel to get 35.00
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20 16 12 8
18 18 20 18
20 12 20 20
16 20 20 20
The following is a random sample of
module scores for a group of students.
Find the mean, median and mode.
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20 16 12 8
18 18 20 18
20 12 20 20
16 20 20 20
The following is a random sample of module scores
for a group of students. Find the mean, median and
mode. Input data input an Excel column, if the data is
not provided. Ordering is a good idea. Use the Data
Tab, select “Sort.”8
12
12
16
16
18
18
18
20
20
20
20
20
20
20
20
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8
12
12
16
16
18
18
18
20
20
20
20
20
20
20
20
To find the mean use the “average”
function in Excel to get 17.375, if rounded
to the nearest whole number this would be
simply 17.
To find the median use the “median”
function in Excel to get 19.
To find the mode VISUALLY INSPECT
THE DATA TO FIND 20 AS THE MODE.
NOTE: WITH MULTIPLE MODES, EXCEL
WILL ONLY RETURN ONE MODE.
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20 16 12 8
18 18 20 18
20 12 20 20
16 20 20 20
The following is a random sample of
module scores for a group of students.
Find the standard deviation.
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8
12
12
16
16
18
18
18
20
20
20
20
20
20
20
20
To find the standard deviation for a
sample, use the “stdev” function in Excel
to get 3.703602 or 3.7 rounded to one
decimal place.
Note: Use “stdev” for samples and
“stdevp” for populations.
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52
58
75
78
82
88
89
92
92
92
96
96
98
98
98
98
99
99
99
100
100
100
100
100
100
The following is a random sample of exam scores for a
group of students. The mean is 91.2 and the standard
deviation is 13.0. Determine if there are any outliers,
defining an outlier as a data point outside of the mean
+/- 2 standard deviations.
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52
58
75
78
82
88
89
92
92
92
96
96
98
98
98
98
99
99
99
100
100
100
100
100
100
The following is a random sample of exam scores for a group
of students. The mean is 91.2 and the standard deviation is
13.0. Determine if there are any outliers, defining an outlier
as a data point outside of the mean +/- 2 standard deviations.
91.2 – 2(13) = 65.2 and 91.2 + 2(13) =
117.2.
The only scores outside of these bounds
are 52 and 58, thus they are the only two
outliers.
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65.2
117.2
52
58
75
78
82
88
89
92
92
92
96
96
98
98
98
98
99
99
99
100
100
100
100
100
100
The following is a random sample of exam
scores for a group of students. The mean is
91.2 and the standard deviation is 13.0. How
many standard deviations is a score of 88 from
the mean?
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52
58
75
78
82
88
89
92
92
92
96
96
98
98
98
98
99
99
99
100
100
100
100
100
100
The following is a random sample of exam
scores for a group of students. The mean is
91.2 and the standard deviation is 13.0. How
many standard deviations is a score of 88 from
the mean?
(88-92.1)/13 = -0.24615 or -0.25 rounded
to two decimal places.
This could also be described as “0.25
below the mean.”
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