Download Means

Distribution Summaries
Measures of central tendency
Mean
 Median
 Mode

Measures of spread
Standard Deviation
 Interquartile Range (IQR)

Mean
Mean or Arithmetic Average or Average
is what we normally understand as the
average of a set of numbers
(observations)
Add up all the numbers and divide by
the number of numbers (n).
Example
For the observations: 21 25 32
n=3
The sum is 78
The mean is 78/3 = 26
21 22
23
24
25
26
27 28 29
30
31
32
Consider the formula
End
n
Begin
X
The
Mean
n
X
i 1
i
 Xi
i 1
n
Observation

Sigma - means
add ‘em up!
Sample Size
 X 1  X 2  X 3    X n1  X n
Subscripts
Indicating (indexing) Individuals
Characteristics of Mean
Balance point
Sum of deviations is zero
Influenced by extreme scores
Balance Point
21 22
23
24
25
26
27 28
29
30
31
32
Sum of deviations is zero
Deviation is score minus mean
 X
n
i 1
21 - 26 = -5
25 - 26 = -1
32 - 26 = 6
78
78
0
i
 X  0
Influenced by Extremes
Extreme
20 30
40
50
60
70
42 Mean
Most Cases, Typical Case
80 90
100 100 120 130
Instead of a few cases
.4
Fraction
Distribution of ages
N = 626
.2
0
18
22
26
30
34
M = 25.43
38
42
46
Self-Esteem
.2
The mean is not
the most common
Fraction
.15
N = 624
.1
.05
0
10
20
30
Rosenberg self-esteem scale
40
M = 33.3
Self-esteem by sex
.2
.1
0
10
20
30
40
M = 32.9
Females
10
20
30
40
M = 33.6
Males
How about numerically?
. tabulate sex, summ(love1)
|
Summary of Rubin Love Scale
sex |
Mean
Std. Dev.
Freq.
------------+-----------------------------------female |
86.153674
10.426731
313
male |
89.00639
8.7537514
313
------------+-----------------------------------Total |
87.580032
9.7242954
626
Another? (Depression)
. tabulate sex, summ(depres1)
| Summary of ces-d scale items s112-s123
sex |
Mean
Std. Dev.
Freq.
------------+-----------------------------------female |
13.463899
11.27072
311
male |
11.405751
8.9336186
313
------------+-----------------------------------Total |
12.431527
10.209712
624
Depression by Education
. tabulate ed1, summ(depres1)
years of
| Summary of ces-d scale items s112s123
education
|
Mean
Std. Dev.
Freq.
------------+-----------------------------------9 |
41
0
1
11 |
15.76
11.475626
25
12 |
14.608993
11.434858
93
13 |
13.592593
10.478033
27
14 |
13.887233
10.608088
183
15 |
12.14838
8.6328703
87
16 |
9.9244392
8.6261835
154
18 |
11.037037
12.270921
27
20 |
6.3703704
5.2925793
27
------------+-----------------------------------Total |
12.431527
10.209712
624
Cohabitation by income
. tabulate income1, summ( cohblnth)
|
Summary of # Months Cohabited
income1 |
Mean
Std. Dev.
Freq.
------------+-----------------------------------3.5 |
9
14.455185
43
7.5 |
9.5376344
13.7173
93
12.5 |
13.5
17.588839
114
20 |
12.284768
17.36486
151
30 |
12.722772
18.828765
101
42.5 |
15.135135
23.566881
37
62.5 |
14.916667
15.529786
12
82.5 |
0
0
1
------------+-----------------------------------Total |
12.123188
17.370189
552
Income by education
. tabulate ed1, summ(income1)
years of
|
Summary of income1
education
|
Mean
Std. Dev.
Freq.
------------+-----------------------------------11 |
11.452381
7.6483736
21
12 |
17.055556
11.563953
81
13 |
17.76087
8.5464899
23
14 |
14.876543
9.0504215
162
15 |
18.65
10.46616
80
16 |
24.960145
14.16097
138
18 |
22.204545
15.181959
22
20 |
34.5
12.788341
25
------------+-----------------------------------Total |
19.434783
12.557429
552
The formula (again)
End
n
Begin
X
The
Mean
n
X
i 1
i
 Xi
i 1
n
Observation

Sigma - means
add ‘em up!
Sample Size
 X 1  X 2  X 3    X n1  X n
Subscripts
Indicating (indexing) Individuals