Download History of the English Language

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
1
2
3
4
5
6
7
8
3
7
4
9
12
9
11
4
Variance
S
words
1
2
3
4
5
6
7
8
3
7
4
9
12
9
11
4
 59 / 8
= 7.4 (mean)
Variance
S
words
(=X1 – Xmean)
1
2
3
4
5
6
7
8
3
7
4
9
12
9
11
4
3 – 7.4
7 – 7.4
4 – 7.4
9 – 7.4
12 – 7.4
9 – 7.4
11 – 7.4
4 – 7.4
 59 / 8
= 7.4 (mean)
Variance
S
words
(=X1 – Xmean)
d1
1
2
3
4
5
6
7
8
3
7
4
9
12
9
11
4
3 – 7.4
7 – 7.4
4 – 7.4
9 – 7.4
12 – 7.4
9 – 7.4
11 – 7.4
4 – 7.4
–4.4
–0.4
–3.4
1.6
4.6
1.6
3.6
–3.4
 59 / 8
= 7.4 (mean)
Variance
S
words
(=X1 – Xmean)
d1
1
2
3
4
5
6
7
8
3
7
4
9
12
9
11
4
3 – 7.4
7 – 7.4
4 – 7.4
9 – 7.4
12 – 7.4
9 – 7.4
11 – 7.4
4 – 7.4
–4.4
–0.4
–3.4
1.6
4.6
1.6
3.6
–3.4
 59 / 8
= 7.4 (mean)
0/8=0
Variance
S
words
(=X1 – Xmean)
d1
d12 (residuals)
1
2
3
4
5
6
7
8
3
7
4
9
12
9
11
4
3 – 7.4
7 – 7.4
4 – 7.4
9 – 7.4
12 – 7.4
9 – 7.4
11 – 7.4
4 – 7.4
–4.4
–0.4
–3.4
1.6
4.6
1.6
3.6
–3.4
19.36
0.16
11.56
2.56
21.16
2.56
12.96
11.56
0/8=0
 81.87
 59 / 8
= 7.4 (mean)
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
Scenario Score
Mean
1
49
41
SD
Test 2 – candidate B
Score
Mean
53
49
SD
z scores
Test 1 – candidate A
Scenario Score
Mean
1
41
2
41
SD
Test 2 – candidate B
Score
Mean
49
53
49
49
53
58
SD
z scores
Test 1 – candidate A
Scenario Score
Mean
1
41
49
2
41
49
SD
6
Test 2 – candidate B
Score
Mean
53
49
53
58
SD
6
z scores
Test 1 – candidate A
Scenario Score
Mean
1
41
2
3
SD
Test 2 – candidate B
Score
Mean
49
53
49
41
49
53
58
41
49
53
58
8
SD
5
z scores
x1 – x
SD
z scores
S
words
1
2
3
4
5
73
42
36
51
63
z scores
S
words
1
2
3
4
5
73
42
36
51
63
M = 265 / 5 = 53
SD = 15.12
z scores
S
words
(=X1 – Xmean) d1
1
2
3
4
5
73
42
36
51
63
73 – 53
42 – 53
36 – 53
51 – 53
63 – 53
M = 265 / 5 = 53
SD = 15.12
20
–11
–17
–2
10
0
z scores
S
Number of words
(=X1 –
Xmean)
d1
z = (d1 / SD)
1
2
3
4
5
73
42
36
51
63
73 – 53
42 – 53
36 – 53
51 – 53
63 – 53
20
–11
–17
–2
10
1.32
–0.73
–1.12
–0.13
0.66
 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
CV =
SD
Mean
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:
Fines:
Mean = 90
SD = 5
Mean = 5400
SD = 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:
Nouns:
10, 6, 7, 9, 11, 9, 8, 6, 9, 8
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.