Starting out with Statistics
What do we do with statistics?
• Describe a group using numbers
– Descriptive Statistics
• Infer about how a larger group of data
would behave based on a smaller subset.
– Inferential Statistics
– A set of rules that help us make a decision
about how good an inference we can make.
Some terms to start off
• Population:
– All the data points that could be considered
• Sample:
– The data points that are being evaluated
• Usually less than the population (a subset of the
population)
• Often a good representation of the population
Some terms to start off
• Variable
– A particular piece of information that can take on
different values across the data that is being evaluated.
• Dependent variable:
– Typically what the investigator is interested in
measuring
• Independent variable:
– Typically the way in which the data is grouped, or what
is being manipulated.
Frequency Table
• A column for the variable
(test scores)
• A column for frequency
(number of subjects who received a particular
score)
grades
f
30
3
29.5
5
29
5
28.5
2
28
10
27.5
5
27
6
26.5
5
26
6
25
2
24.5
3
24
4
23.5
1
23
5
22.5
4
22
1
21.5
2
21
1
20
3
Frequency Table
• Cummulative frequency
– Number of subjects who have a particular score
or any that are lower (or higher)
grades
f
cf
30
3
29.5
5
29
5
28.5
2
28
10
27.5
5
27
6
26.5
5
26
6
25
2
24.5
3
24
4
23.5
1
23
5
22.5
4
22
1
21.5
2
21
1
20
3
3
grades
f
cf
30
3
29.5
5
29
5
28.5
2
28
10
27.5
5
27
6
26.5
5
26
6
25
2
24.5
3
24
4
23.5
1
23
5
22.5
4
22
1
21.5
2
21
1
4
20
3
3
grades
f
cf
30
3
29.5
5
29
5
28.5
2
28
10
27.5
5
27
6
26.5
5
26
6
25
2
24.5
3
24
4
23.5
1
23
5
22.5
4
22
1
7
21.5
2
6
21
1
4
20
3
3
grades
f
cf
30
3
73
29.5
5
70
29
5
65
28.5
2
60
28
10
58
27.5
5
48
27
6
43
26.5
5
37
26
6
32
25
2
26
24.5
3
24
24
4
21
23.5
1
17
23
5
16
22.5
4
11
22
1
7
21.5
2
6
21
1
4
20
3
3
n or N : Symbol for the total number of
data points
What is N for this data set?
grades
f
cf
30
3
73
29.5
5
70
29
5
65
28.5
2
60
28
10
58
27.5
5
48
27
6
43
26.5
5
37
26
6
32
25
2
26
24.5
3
24
24
4
21
23.5
1
17
23
5
16
22.5
4
11
22
1
7
21.5
2
6
21
1
4
20
3
3
If you wanted to find  X
what would you do?
grades
f
30
3
29.5
5
29
5
28.5
2
28
10
27.5
5
27
6
26.5
5
26
6
25
2
24.5
3
24
4
23.5
1
23
5
22.5
4
22
1
21.5
2
21
1
20
3
 X  20  20  20  21  21.5  21.5  ...
grades
 X  fX
f
fX
30
3
29.5
5
29
5
28.5
2
28
10
27.5
5
27
6
26.5
5
26
6
25
2
24.5
3
24
4
23.5
1
23
5
22.5
4
22
1
21.5
2
21
1
20
3
90
grades
 X  fX
f
fX
30
3
90
29.5
5
147.5
29
5
28.5
2
28
10
27.5
5
27
6
26.5
5
26
6
25
2
24.5
3
24
4
23.5
1
23
5
22.5
4
22
1
21.5
2
21
1
20
3
grades
 X  fX
 X  90  147.5  145  ...
f
fX
30
3
90
29.5
5
147.5
29
5
145
28.5
2
57
28
10
280
27.5
5
137.5
27
6
162
26.5
5
132.5
26
6
156
25
2
50
24.5
3
73.5
24
4
96
23.5
1
23.5
23
5
115
22.5
4
90
22
1
22
21.5
2
43
21
1
21
20
3
60
 X  1901.5
ƒ
Test scores
Symmetric Distribution:
A distribution in which the
left and right halves are
mirror images.
Frequency
how many
Scores
Symmetric
frequency
scores
Skewed Distribution:
The majority of the scores
in the distribution fall
to one end. At the
opposite end of the
distribution is a tail.
frequency
scores
frequency
scores