mean and variance. central tendency data:2, 3, 3, 3, 4, 6, 6, 9, 12, 13, 13...
TRANSCRIPT
Mean and variance
Central tendency
Data: 2, 3, 3, 3, 4, 6, 6, 9, 12, 13, 13
Mean: 2+3+3+3+4+6+6+9+12+13+13
11= 6.72
Median: 2, 3, 3, 3, 4, 6, 6, 9, 12, 13, 13 = 6
Mode: 2, 3, 3, 3, 4, 6, 6, 9, 12, 13, 13 = 3
Range
Data: 2, 3, 3, 3, 4, 6, 6, 9, 12, 13, 13
Range: 2 - 13
Variance and SD
(x1 – x)2
N- 1
Variance
S words
12345678
3749129114
Variance
S words
12345678
3749129114
59 / 8 = 7.4 (mean)
Variance
S words (=X1 – Xmean)
12345678
3749129114
3 – 7.4 7 – 7.44 – 7.49 – 7.412 – 7.49 – 7.411 – 7.44 – 7.4
59 / 8 = 7.4 (mean)
Variance
S words (=X1 – Xmean) d1
12345678
3749129114
3 – 7.4 7 – 7.44 – 7.49 – 7.412 – 7.49 – 7.411 – 7.44 – 7.4
–4.4–0.4–3.41.64.61.63.6–3.4
59 / 8 = 7.4 (mean)
Variance
S words (=X1 – Xmean) d1
12345678
3749129114
3 – 7.4 7 – 7.44 – 7.49 – 7.412 – 7.49 – 7.411 – 7.44 – 7.4
–4.4–0.4–3.41.64.61.63.6–3.4
59 / 8 = 7.4 (mean)
0 / 8 = 0
Variance
S words (=X1 – Xmean) d1 d12 (residuals)
12345678
3749129114
3 – 7.4 7 – 7.44 – 7.49 – 7.412 – 7.49 – 7.411 – 7.44 – 7.4
–4.4–0.4–3.41.64.61.63.6–3.4
19.360.1611.562.5621.162.5612.9611.56
59 / 8 = 7.4 (mean)
0 / 8 = 0 81.87
Variance
81.87
8 - 1= 11.7
Standard Deviation
81.87
8 - 1= 3.42
Standard Deviation
70% of all data points fall within 1 SD.
Mean +/- SD = range of 70% of the data
7.4 +/- 3.42 = 3.98 – 10.82 words
z scores
Test 1 – candidate A Test 2 – candidate B
Scenario Score Mean SD Score Mean SD
1 41 49 53 49
z scores
Test 1 – candidate A Test 2 – candidate B
Scenario Score Mean SD Score Mean SD
1 41 49 53 49
2 41 49 53 58
z scores
Test 1 – candidate A Test 2 – candidate B
Scenario Score Mean SD Score Mean SD
1 41 49 53 49
2 41 49 6 53 58 6
z scores
Test 1 – candidate A Test 2 – candidate B
Scenario Score Mean SD Score Mean SD
1 41 49 53 49
2 41 49 53 58
3 41 49 8 53 58 5
z scores
x1 – x
SD
z scores
S words
12345
7342365163
z scores
S words
12345
7342365163
M = 265 / 5 = 53SD = 15.12
z scores
S words (=X1 – Xmean) d1
12345
7342365163
73 – 53 42 – 5336 – 5351 – 5363 – 53
20–11–17–210
M = 265 / 5 = 53SD = 15.12
0
z scores
S Number of words (=X1 –
Xmean)
d1 z = (d1 / SD)
12345
7342365163
73 – 53 42 – 5336 – 5351 – 5363 – 53
20–11–17–210
1.32–0.73–1.12–0.130.66
265 / 5 = 53 (m)SD = 15.12
0
z scores
x1 – x
SD
Exercise
Zwei Kandidaten haben an zwei unterschiedlichen Sprachtests teilgenommen. Kandidat A hat 121 Punkte erzielt, Kandidat B hat 177 Punkte erzielt. Im ersten Test (an dem Kandidat A teilgenommen hat) lag der Mittelwert bei 92 und die Standardabweichung bei 14; im zweiten Test (an dem Kandidat B teilgenommen hat) lag der Mittelwert bei 143 und die Standardabweichung bei 21. Welcher der beiden Kandidaten hat besser abschlossen (im Vergleich zu allen übrigen Kandidaten)?
Exercise
ZA = 121 – 92 / 14 = 2.07
ZB = 177 – 143 / 21 = 1.62
Coefficient of variance
SD
MeanCV =
Coefficient of variance
Over a 4 months period a mean number of 90 parking tickets was issued. The standard deviation was 5. The tickets yielded an average of $5400 per day and the SD was $775. Where do you have more variability, in the number of parking tickets that were issued each day or in the amount of money that was generate each day?
Coefficient of variance
Parking tickets: Mean = 90SD = 5
Fines: Mean = 5400SD = 775
CV1 = 5/90 = 0.06
CV2 = 775/5400 = 0.14
SPSS
A linguist has conducted a study comparing
memory for adjectives with that for nouns. She
randomly allocates 20 participants to two
conditions. She then presents to one of the groups
of 10 participants a list of 20 adjectives and to the
other group a list of 20 nouns. Following this, she
asks each group to try to remember as many of the
words they were presented with as possible. Here
are the data.
SPSS
Adjectives: 10, 6, 7, 9, 11, 9, 8, 6, 9, 8
Nouns: 12, 13, 16, 15, 9, 7, 14, 12, 11, 13
1. What is the independent variable?
2. What is the dependent variable?
3. Is this a correlational analysis or an experiment?
4. Is this a bewteen subjects or a within subjects
design?
5. Enter the data into SPSS.