Question

Many standard statistical methods that you will study in Part II of this book are intended for use with distributions that are symmetric and have no outliers. These methods start with the mean and standard deviation, x and s. For example, standard methods would typically be used for the IQ and GPA data here data457.dat.

(a) Find x and s for the IQ data. (Round your answers to two decimal places.)

x	=
s	=

(b) Find the median IQ score. It is, as we expect, close to the mean.


(c) Find the mean and median for the GPA data. The two measures of center differ a bit. (Round your answers to two decimal places.)

mean	=
median	=

What feature of the data (make a stemplot or histogram to see) explains the difference?

obs     gpa     iq      gender  concept
1       10.38   111     2       67
2       3.53    101     2       43
3       9.37    96      2       52
4       8.83    117     2       66
5       9.06    109     1       58
6       10.41   104     2       51
7       9.04    127     2       71
8       4.45    119     2       51
9       9.66    67      1       49
10      9.43    104     2       51
11      8.49    132     1       35
12      10.93   70      1       54
13      9.96    104     2       54
14      8.19    131     1       64
15      7.17    93      1       56
16      10.53   83      1       69
17      6.39    115     1       55
18      7.67    88      1       65
19      4.75    63      2       40
20      6.64    106     1       66
21      8.27    88      2       55
22      5.21    75      2       20
24      7.47    91      1       56
26      9.05    70      2       68
27      8.99    103     1       69
28      6.76    80      2       70
29      6.72    107     2       80
30      10.69   112     2       53
31      7.49    103     2       65
32      9.35    125     1       67
33      9.49    80      1       62
34      9.49    112     1       39
35      8.94    84      2       71
36      10.75   100     2       59
37      8.96    85      1       60
38      8.35    106     2       64
39      9.78    109     2       71
40      7.72    84      1       72
41      10.98   83      1       54
43      10.75   111     2       64
44      8.06    98      2       58
45      10.25   87      2       70
46      7.43    119     2       72
47      10.06   114     2       70
48      7.05    77      2       47
50      6.53    113     2       52
51      7.17    89      1       46
52      6.8     113     2       66
53      5.67    68      2       67
54      7.84    137     2       63
55      8.68    98      2       53
56      8.9     123     2       67
57      10.41   111     2       61
58      9.62    96      1       54
59      8.77    99      1       60
60      10.72   95      1       60
61      3.49    105     2       63
62      10.02   92      2       30
63      4.01    97      2       54
64      7.52    94      2       66
65      4.12    94      2       44
68      9.06    113     2       49
69      10.23   94      1       44
71      10.57   89      2       67
72      4.4         83  1       64
74      9.99    107     2       73
76      10.17   122     2       59
77      9.64    113     1       37
78      10.54   121     1       63
79      9.88    112     2       36
80      7.32    88      1       64
83      8.3     76      2       42
84      10.92   91      1       28
85      4.48    79      1       60
86      9.93    111     1       70
87      7.77    102     2       51
88      9.19    86      1       21
89      9.87    107     2       56

Answer 1

Many standard statistical methods that you will study in Part II of this book are intended for use with distributions that are symmetric and have no outliers. These methods start with the mean and standard deviation, x and s. For example, standard methods would typically be used for the IQ and GPA data here data457.dat.

Descriptive statistics
	gpa	iq
count	78	78
mean	8.4035	99.50
sample standard deviation	1.9835	16.51
sample variance	3.9343	272.69
minimum	3.49	63
maximum	10.98	137
range	7.49	74
1st quartile	7.3475	88.00
median	8.9500	100.50
3rd quartile	9.9525	111.75
interquartile range	2.6050	23.75
mode	9.0600	111.00

(a) Find x and s for the IQ data. (Round your answers to two decimal places.)

x	=99.50
s	=16.51

(b) Find the median IQ score. It is, as we expect, close to the mean.

Median= 100.50

(c) Find the mean and median for the GPA data. The two measures of center differ a bit. (Round your answers to two decimal places.)

mean	=8.40
median	=8.95

What feature of the data (make a stemplot or histogram to see) explains the difference?

Stem and Leaf plot for	gpa
stem unit =	1
leaf unit =	0.1
Frequency	Stem	Leaf
2	3	4 5
6	4	0 1 4 4 4 7
2	5	2 6
6	6	3 5 6 7 7 8
12	7	0 1 1 3 4 4 4 5 6 7 7 8
13	8	0 1 2 3 3 4 6 7 8 9 9 9 9
19	9	0 0 0 0 1 3 3 4 4 4 6 6 6 7 8 8 9 9 9
18	10	0 0 1 2 2 3 4 4 5 5 5 6 7 7 7 9 9 9
Total =78

The distribution of GPA is negatively skewed. Therefore mean is less tha median.

Stem and Leaf plot for	iq
stem unit =	10
leaf unit =	1
Frequency	Stem	Leaf
3	6	3 7 8
6	7	0 0 5 6 7 9
15	8	0 0 3 3 3 4 4 5 6 7 8 8 8 9 9
14	9	1 1 2 3 4 4 4 5 6 6 7 8 8 9
16	10	0 1 2 3 3 4 4 4 5 6 6 7 7 7 9 9
16	11	1 1 1 1 2 2 2 3 3 3 3 4 5 7 9 9
5	12	1 2 3 5 7
3	13	1 2 7
Total = 78