STA 301(Statistics and Probability) Assignment solution Fall 2020
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Question Part 1:
STA 301 Assignment no 1 solution fall 2020
Deadline
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Assignment # 1 (Lecture 1-13)
Question
1: Marks: 10
Compute the geometric mean and Harmonic
mean for the following distribution of annual death rate.
X |
3.95 |
4.95 |
5.95 |
6.95 |
7.95 |
8.95 |
9.95 |
10.95 |
11.95 |
12.95 |
13.95 |
f |
1 |
4 |
5 |
13 |
12 |
19 |
13 |
10 |
6 |
4 |
1 |
Question
2: Marks: 10
By using the following frequency
distribution of weights of apples find.
1. Mean Deviation from Mean
2. Co-efficient of Mean Deviation from Mean
Weights |
65-84 |
85-104 |
105-124 |
124-144 |
145-164 |
165-184 |
185-204 |
f |
9 |
10 |
17 |
10 |
5 |
4 |
5 |
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Part 2:
Answer STA 301 Assignment Fall 2020
Question
1: Marks: 10
Compute the geometric mean and Harmonic
mean for the following distribution of annual death rate.
X |
3.95 |
4.95 |
5.95 |
6.95 |
7.95 |
8.95 |
9.95 |
10.95 |
11.95 |
12.95 |
13.95 |
F |
1 |
4 |
5 |
13 |
12 |
19 |
13 |
10 |
6 |
4 |
1 |
Note: Use the math type equation easily solved
Geometric means : G = antilog [Σ f log x / n] n=11
X |
f |
Log x |
F log x |
f/x |
3.95 |
1 |
0.5966 |
0.5966 |
0.2532 |
4.95 |
4 |
0.6946 |
2.7784 |
0.8081 |
5.95 |
5 |
0.7745 |
3.8726 |
0.8403 |
6.95 |
13 |
0.8420 |
10.9458 |
1.8705 |
7.95 |
12 |
0.9004 |
10.8044 |
1.5094 |
8.95 |
19 |
0.9518 |
18.0846 |
2.1229 |
9.95 |
13 |
0.9978 |
12.9717 |
1.3065 |
10.95 |
10 |
1.0394 |
10.3942 |
0.9132 |
11.95 |
6 |
1.0774 |
6.4642 |
0.5021 |
12.95 |
4 |
1.1123 |
4.4491 |
0.3069 |
12.95 |
4 |
1.1123 |
4.4491 |
0.3089 |
13.95 |
1 |
1.1446 |
1.1446 |
0.0717 |
|
N= 88 |
|
∑f log x= 82.5062 |
∑ f/x = 10.5069 |
G = antilog [Σ f log x / n]
G = antilog [82.5062/88]
G = antilog [Σ f log x]
G= 8.6616 Ans
Harmonic means: H.M = [ n/Σ (f / x) ]
H.M = [ 88/10.5069 ]
H.M = 8.375 Ans
Question
2: Marks: 10
By using the following frequency
distribution of weights of apples find.
1. Mean Deviation from Mean
2. Co-efficient of Mean Deviation from Mean
Weights |
65-84 |
85-104 |
105-124 |
124-144 |
145-164 |
165-184 |
185-204 |
f |
9 |
10 |
17 |
10 |
5 |
4 |
5 |
Solution Marks: 10
Mean
Deviation : M.D = ∑f│f - x│/ n
Class |
f |
Mid Values (x) |
f(x) |
|
|
65-84 |
9 |
74.5 |
670.5 |
48 |
432 |
85-104 |
10 |
94.5 |
945 |
28 |
280 |
105-124 |
17 |
114.5 |
1946.5 |
8 |
136 |
125-144 |
10 |
134.5 |
1345 |
12 |
120 |
145-164 |
5 |
154.5 |
772.5 |
32 |
160 |
165-184 |
4 |
174.5 |
698 |
52 |
208 |
185-204 |
5 |
194.5 |
972.5 |
72 |
360 |
|
∑f=
n= 60 |
|
∑f(x)
= 7350 |
|
1696 |
Mean
x = ∑f(x) / ∑f M.D = ∑f│x-x│/ n
x
= 7350 / 60 M.D = 1696 / 60
x = 122.5 M.D=
28.27
Co-efficient of
Mean Derivation from Mean
Formula
= M.D / x
- Co-efficient of Mean Deviation = M.D/x
- Co- efficient of mean deviation = 28.27/ 122.5
- Co-efficient of deviation = 0.23