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.