Homework One : Note answers are bolded
2.4 THE MEDIAN WOULD BE MULTIPLIED BY THE CONSTANT (C)
2.5 THE MODE WOULD BE MULTIPLIED BY THE CONSTANT (C)
2.6 THE GEOMETRIC MEAN WOULD BE MULTIPLIED BY THE CONSTANT (C)
2.7 THE RANGE WILL BE MULTIPLIED BY THE CONSTANT (C)
CHECK THE EXAMPLE FROM THE FIRST DAY OF CLASS!
2.8
|
Range |
midpoint |
X |
frequency |
= |
Bin Sums |
|
0.0-less than 2 |
0.075 |
X |
458 |
= |
34.35 |
|
.2-.3 |
0.25 |
X |
268 |
= |
67 |
|
.4-.5 |
0.45 |
X |
151 |
= |
67.95 |
|
. 6-1.0 |
0.8 |
X |
79 |
= |
63.2 |
|
1.1-2.0 |
1.55 |
X |
44 |
= |
68.2 |
|
2.1-3.0 |
2.55 |
X |
19 |
= |
48.45 |
|
3.1-4.0 |
3.55 |
X |
9 |
= |
31.95 |
|
4.1-5.0 |
4.55 |
X |
3 |
= |
13.65 |
|
5.1-6.0 |
5.55 |
X |
2 |
= |
11.1 |
|
1033 |
405.85 |
The arithmatic mean is 405.85/1033 = .39
2.9
|
frequency |
( |
midpoint |
- |
mean |
) |
squared |
= |
|
|
458 |
( |
0.075 |
- |
0.39 |
) |
= |
45.44505 |
|
|
268 |
( |
0.25 |
- |
0.39 |
) |
= |
5.2528 |
|
|
151 |
( |
0.45 |
- |
0.39 |
) |
= |
0.5436 |
|
|
79 |
( |
0.8 |
- |
0.39 |
) |
= |
13.2799 |
|
|
44 |
( |
1.55 |
- |
0.39 |
) |
= |
59.2064 |
|
|
19 |
( |
2.55 |
- |
0.39 |
) |
= |
88.6464 |
|
|
9 |
( |
3.55 |
- |
0.39 |
) |
= |
89.8704 |
|
|
3 |
( |
4.55 |
- |
0.39 |
) |
= |
51.9168 |
|
|
2 |
( |
5.55 |
- |
0.39 |
) |
= |
53.2512 |
|
|
1033 |
407.41255 |
Variance= Sum of Squares/(N-1) 407.41/10 32= .395
Standard Deviation = sqrt of variance sqrt .395= .63
2.10
2.15
2.18
|
Rec syst |
Stand syst |
Difference |
Rec Dia |
Stand Dia |
Difference |
|
|
1 |
99 |
105 |
-6 |
71 |
79 |
-8 |
|
2 |
126 |
124 |
2 |
74 |
76 |
-2 |
|
3 |
108 |
102 |
6 |
72 |
68 |
4 |
|
4 |
122 |
114 |
8 |
68 |
72 |
-4 |
|
5 |
104 |
96 |
8 |
64 |
62 |
2 |
|
6 |
108 |
96 |
12 |
60 |
56 |
4 |
|
7 |
116 |
106 |
10 |
70 |
70 |
0 |
|
8 |
106 |
106 |
0 |
74 |
76 |
-2 |
|
9 |
118 |
120 |
-2 |
82 |
90 |
-8 |
|
10 |
92 |
88 |
4 |
58 |
60 |
-2 |
|
11 |
110 |
102 |
8 |
78 |
80 |
-2 |
|
12 |
138 |
124 |
14 |
80 |
76 |
4 |
|
13 |
120 |
118 |
2 |
70 |
84 |
-14 |
|
14 |
142 |
136 |
6 |
88 |
90 |
-2 |
|
15 |
118 |
92 |
26 |
58 |
58 |
0 |
|
16 |
134 |
126 |
8 |
76 |
68 |
8 |
|
17 |
118 |
108 |
10 |
72 |
68 |
4 |
|
18 |
126 |
114 |
12 |
78 |
76 |
2 |
|
19 |
108 |
94 |
14 |
78 |
70 |
8 |
|
20 |
136 |
144 |
-8 |
86 |
88 |
-2 |
|
21 |
110 |
100 |
10 |
78 |
64 |
14 |
|
22 |
120 |
106 |
14 |
7 4 |
70 |
4 |
|
23 |
108 |
94 |
14 |
74 |
74 |
0 |
|
24 |
132 |
128 |
4 |
92 |
88 |
4 |
|
25 |
102 |
96 |
6 |
68 |
64 |
4 |
|
26 |
118 |
102 |
16 |
70 |
68 |
2 |
|
27 |
116 |
88 |
28 |
76 |
60 |
16 |
|
28 |
118 |
100 |
18 |
80 |
84 |
-4 |
|
29 |
110 |
96 |
14 |
74 |
70 |
4 |
|
30 |
122 |
118 < /TD> |
4 |
72 |
78 |
-6 |
|
31 |
106 |
94 |
12 |
62 |
56 |
6 |
|
32 |
146 |
138 |
8 |
90 |
94 |
-4 |
|
N=32 |
282 |
30 |
Arithmatic Mean = Total Diffs/N
Systolic Difference mean = 282/32 = 8.8 mm Hg
Diastolic Difference Mean = 30/32 = .9 mm Hg
In order to compute the Median, you must sort the values:
|
Syst Diff |
Dia Diff |
|
28 |
16 |
|
26 |
14 |
|
18 |
8 |
|
16 |
8 |
14 |
6 |
|
14 |
4 |
|
14 |
4 |
|
14 |
4 |
|
14 |
4 |
|
12 |
4 |
|
12 |
4 |
|
12 |
4 |
|
10 |
4 |
|
10 |
2 |
|
10 |
2 |
|
8 |
2 |
|
8 |
0 |
|
8 |
0 |
|
8 |
0 |
|
8 |
-2 |
|
6 |
-2 |
|
6 |
-2 |
|
6 |
-2 |
|
4 |
-2 |
|
4 |
-2 |
|
4 |
-4 |
|
2 |
-4 |
|
2 |
-4 |
|
0 |
-6 |
|
-2 |
-8 |
|
-6 |
-8 |
|
-8 |
-14 |
The median is the average of the 16th & 17th largest values
Systolic median = (8 + 8)/2 = 8 mm Hg
Diastolic median = (0 + 2)/2 = 1 mm Hg
2.19
|
Systolic Stem & Leaf |
Diastolic Stem & Leaf |
|||
|
2 |
86 |
1 |
6 |
|
|
2 |
1 |
4 |
||
|
1 |
86 |
0 |
886 |
|
|
1 |
4 444422000 |
0 |
44444444222000 |
|
|
0 |
88888666 |
0 |
222222444 |
|
|
0 |
44422 |
0 |
688 |
|
|
0 |
2 |
-1 |
4 |
|
|
0 |
68 |
|||
2.20
It seems that the position (standing v supine) has an impact on systolic pressure such that systolic pressure measures higher in the recumbant position than in the standing. There doesn’t appear to be a positional impact on diastolic pressure.
2.34
|
I |
( |
Ind. Pod |
- |
Mean |
) |
squared |
= |
|
|
1 |
( |
1.76 |
- |
1.63 |
) |
= |
0.0169 |
|
|
2 |
( |
1.45 |
- |
1.63 |
) |
= |
0.0324 |
|
|
3 |
( |
1.03 |
- |
1.63 |
) |
= |
0.36 |
|
|
4 |
( |
1.53 |
- |
1.63 |
) |
= |
0.01 |
|
|
5 |
( |
2.34 |
- |
1.63 |
) |
= |
0.5041 |
|
|
6 |
( |
1.96 |
< P ALIGN="CENTER">- |
1.63 |
) |
= |
0.1089 |
|
|
7 |
( |
1.79 |
- |
1.63 |
) |
= |
0.0256 |
|
|
8 |
( |
1.21 |
- |
1.63 |
) |
= |
0. 1764 |
|
|
N=8 |
13.07 |
1.2343 |
Arithmatic Mean for I plants is 13.07/8 = 1.63
Variance = 1.2342/(8-1) = 1.76
Standard Deviation = sqrt 1.76 = .42
|
U |
( |
Ind. Pod |
- |
Mean |
) |
squared |
= |
|
|
1 |
( |
0.49 |
- |
1.08 |
) |
0.3481 |
||
|
2 |
( |
0.85 |
- |
1.08 |
) |
0.0529 |
||
|
3 |
( |
1 |
- |
1.08 |
) |
0.0064 |
||
|
4 |
( |
1.54 |
- |
1.08 |
) |
0.2116 |
||
|
5 |
( |
1.01 |
- |
) |
0.0049 |
|||
|
6 |
( |
0.75 |
- |
1.08 |
) |
0.1089 |
||
|
7 |
( |
2.11 |
- |
1.08 |
) |
1.0609 |
||
|
8 |
( |
0.92 |
- |
1.08 |
) |
0.0256 |
||
|
N=8 |
8.67 |
1.8193 |
Arithmatic Mean for U plants is 8.67/8 = 1.08
Variance = 1.8193/(8-1) = .26
Standard Deviation = sqrt .26 = .51
2.35
Many graphical options. My favorite:
2.36
It appears that the I plants are generally heavier than the U plants.