Mean and variance. Central tendency Data:2, 3, 3, 3, 4, 6, 6, 9, 12, 13, 13...
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Transcript of Mean and variance. Central tendency Data:2, 3, 3, 3, 4, 6, 6, 9, 12, 13, 13...
![Page 1: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/1.jpg)
Mean and variance
![Page 2: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/2.jpg)
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
![Page 3: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/3.jpg)
Range
Data: 2, 3, 3, 3, 4, 6, 6, 9, 12, 13, 13
Range: 2 - 13
![Page 4: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/4.jpg)
Variance and SD
(x1 – x)2
N- 1
![Page 5: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/5.jpg)
Variance
S words
12345678
3749129114
![Page 6: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/6.jpg)
Variance
S words
12345678
3749129114
59 / 8 = 7.4 (mean)
![Page 7: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/7.jpg)
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)
![Page 8: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/8.jpg)
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)
![Page 9: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/9.jpg)
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
![Page 10: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/10.jpg)
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
![Page 11: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/11.jpg)
Variance
81.87
8 - 1= 11.7
![Page 12: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/12.jpg)
Standard Deviation
81.87
8 - 1= 3.42
![Page 13: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/13.jpg)
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
![Page 14: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/14.jpg)
z scores
Test 1 – candidate A Test 2 – candidate B
Scenario Score Mean SD Score Mean SD
1 41 49 53 49
![Page 15: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/15.jpg)
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
![Page 16: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/16.jpg)
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
![Page 17: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/17.jpg)
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
![Page 18: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/18.jpg)
z scores
x1 – x
SD
![Page 19: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/19.jpg)
z scores
S words
12345
7342365163
![Page 20: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/20.jpg)
z scores
S words
12345
7342365163
M = 265 / 5 = 53SD = 15.12
![Page 21: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/21.jpg)
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
![Page 22: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/22.jpg)
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
![Page 23: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/23.jpg)
z scores
x1 – x
SD
![Page 24: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/24.jpg)
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)?
![Page 25: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/25.jpg)
Exercise
ZA = 121 – 92 / 14 = 2.07
ZB = 177 – 143 / 21 = 1.62
![Page 26: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/26.jpg)
Coefficient of variance
SD
MeanCV =
![Page 27: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/27.jpg)
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?
![Page 28: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/28.jpg)
Coefficient of variance
Parking tickets: Mean = 90SD = 5
Fines: Mean = 5400SD = 775
CV1 = 5/90 = 0.06
CV2 = 775/5400 = 0.14
![Page 29: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/29.jpg)
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.
![Page 30: 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,](https://reader036.fdocuments.us/reader036/viewer/2022062512/55204d6149795902118b46e6/html5/thumbnails/30.jpg)
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.