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4320BasicStatisticsVariabilityNoAudioorTransitions.pptx4320 Descriptive Statistics
Variability
1
Measures of Variability
Definition: spread of scores.
Allows for further analysis of the scores.
Range: From minimum to maximum score
Standard Deviation (s, σ, or SD): The square root of the variance
2
Standard Deviation
Most commonly used measure of variance
3
X
10
8
5
2
0
X-X
+5
+3
0
-3
-5
X-X
+2
+1
0
-1
-2
Σ =25
N =5
X=5
X
7
6
5
4
3
Standard Deviation
(X-X)^2
4
1
0
1
4
Σ =10
σ = 1.58
Σ =25
N =5
X=5
(X-X)^2
25
9
0
9
25
Σ =68
σ = 4.12
4
68%
95%
99%
7 5 3
8 5 2
10 5 0
13 5 -3
5
Example
20, 20, 21, 21, 22, 19, 20, 19, 22, 18, 18, 20, 21, 18, 19, 18, 21, 26, 30
SD = ?
6
Example
20, 20, 21, 21, 22, 19, 20, 19, 22, 18, 18, 20, 21, 18, 19, 18, 21, 26, 30
SD = 2.96
7
Work
| X | x-m | (x-m)^2 | ((x-m)^2)/(n-1) | square |
| 30 | 9.32 | 86.8624 | root | |
| 26 | 5.32 | 28.3024 | ||
| 22 | 1.32 | 1.7424 | ||
| 22 | 1.32 | 1.7424 | ||
| 21 | 0.32 | 0.1024 | ||
| 21 | 0.32 | 0.1024 | ||
| 21 | 0.32 | 0.1024 | ||
| 21 | 0.32 | 0.1024 | ||
| 20 | -0.68 | 0.4624 | ||
| 20 | -0.68 | 0.4624 | ||
| 20 | -0.68 | 0.4624 | ||
| 20 | -0.68 | 0.4624 | ||
| 19 | -1.68 | 2.8224 | ||
| 19 | -1.68 | 2.8224 | ||
| 19 | -1.68 | 2.8224 | ||
| 18 | -2.68 | 7.1824 | ||
| 18 | -2.68 | 7.1824 | ||
| 18 | -2.68 | 7.1824 | ||
| 18 | -2.68 | 7.1824 | ||
| n=19 | m=20.68 | 158.1056 | 8.783644444 | 2.963721 |
8
Standard Scores
Z-score: a standardized score
T-score: a standardized ratio
T = 50 + 10 * (Z)
Chapter 3
9
Z Score
Sit-ups (1 min)
45, 37, 36, 35, 33, 33, 32, 21, 13, 12
Push ups (1 min)
30, 25, 24, 22, 10, 9, 8, 8, 6, 5
On which test did John Doe score better on?
10
Sit Ups
Sit-ups (1 min)
45, 37, 36, 35, 33, 33, 32, 21, 13, 12
X= 29.7
s=10.2
z=(35-29.7) / 10.2 = .52
11
Push Ups
Push ups (1 min)
30, 25, 24, 22, 10, 9, 8, 8, 6, 5,
X= 15.1
s=8.22
z= (22-15.1)/8.22=.84
12
Z Score
Sit ups
Push ups
13
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50
