Answering a question on Statistics course for 2nd year B.Sc. student at Department of Fisheries, University of Chittagong, Chattogram 4331, Bangladesh. Submission data: 27th August, 2020.

1. Page | 1
Assignment on
Statistics
Course No. :- FISH:301
Submitted to:
Md. Rashed-Un-Nabi Rafi
Professor
Department of Fisheries
University of Chittagong
Submitted by:
Mishal Roy
ID No. : 17207017
Department of Fisheries
University of Chittagong
Submission date: 27-08-2020

2. Page | 2
Question:
Finding items:
1. Arithmetic mean
2. Geometric mean
3. Harmonic mean
4. Median
5. Mode
6. Coefficient of range
7. Coefficient of quartile deviation
8. Coefficient of quartile mean deviation
9. Standard deviation
10. Coefficient of variation
11. First moment
12. Second moment
13. Third moment
14. Fourth moment
15. Measure of Skewness (using all formulas)
16. Measure of Kurtosis (using all formulas)
Class
Frequency
(f)
x fx f(x-μ) f(x-μ)
2
f(x-μ)
3
f(x-μ)
4
25-30 1
30-35 8
35-40 18
40-45 27
45-50 25
50-55 16
55-60 7
60-65 2
Sum 104

3. Page | 3
Answer:
1. Arithmetic mean:
Class
Frequency
(f)
x fx
25-30 1 27.5 27.5
30-35 8 32.5 260
35-40 18 37.5 675
40-45 27 42.5 1147.5
45-50 25 47.5 1187.5
50-55 16 52.5 840
55-60 7 57.5 402.5
60-65 2 62.5 125
Sum 104 360 4665
̅
̅
∑
∑
̅
2. Geometric mean:
Class
Frequency
(f)
x f * log(x)
25-30 1 27.5 1.439332694
30-35 8 32.5 12.09506689
35-40 18 37.5 28.33256282
40-45 27 42.5 43.96650111
45-50 25 47.5 41.91734024
50-55 16 52.5 27.52254885
55-60 7 57.5 12.31767491
60-65 2 62.5 3.591760035
Sum 104 360 171.1827876

4. Page | 4
( )
3. Harmonic mean:
Class
Frequency
(f)
X f/x
25-30 1 27.5 0.036363636
30-35 8 32.5 0.246153846
35-40 18 37.5 0.48
40-45 27 42.5 0.635294118
45-50 25 47.5 0.526315789
50-55 16 52.5 0.304761905
55-60 7 57.5 0.12173913
60-65 2 62.5 0.032
Sum 104 360 2.382628425
4. Median:
Class
Frequency
(f)
x c.f
25-30 1 27.5 1
30-35 8 32.5 9
35-40 18 37.5 27
40-45 27 42.5 54
45-50 25 47.5 79
50-55 16 52.5 95
55-60 7 57.5 102
60-65 2 62.5 104
Sum 104 360 471

5. Page | 5
5. Mode:
6. Coefficient of range:
Class
Frequency
(f)
25-30 1
30-35 8
35-40 18
40-45 27
45-50 25
50-55 16
55-60 7
60-65 2
Sum 104
SL
SL
rangeoftCoefficien




6. Page | 6
7. Coefficient of quartile deviation
N/4 = 104/4 = 26; lies in the group 35-40
N/2 = 104/2 = 52; lies in the group 40-45
N/3 = 104/3 = 34.67; lies in the group 40-45
Class
Frequency
(f)
x c.f
25-30 1 27.5 1
30-35 8 32.5 9
35-40 18 37.5 27
40-45 27 42.5 54
45-50 25 47.5 79
50-55 16 52.5 95
55-60 7 57.5 102
60-65 2 62.5 104
Sum 104 360 471
𝑄 𝐿
𝑁
× 𝑐 𝑓
𝑓
× 𝑖
𝑄 𝐿
𝑁
× 𝑐 𝑓
𝑓
× 𝑖
𝑄 𝐿
𝑁
× 𝑐 𝑓
𝑓
× 𝑖
13
13
..
QQ
QQ
DQoftcoefficien




7. Page | 7
8. Coefficient of mean deviation:
Class
Frequency
(f)
x ‾x f*|x-‾x|)
25-30 1 27.5
44.86
17.36
30-35 8 32.5 98.85
35-40 18 37.5 132.40
40-45 27 42.5 63.61
45-50 25 47.5 66.11
50-55 16 52.5 122.31
55-60 7 57.5 88.51
60-65 2 62.5 35.29
Sum 104 360 44.86 624.44
9. Standard deviation:
√
Class
Frequency
(f)
x ‾x f*(x-‾x)2
25-30 1 27.5
44.86
301.3696
30-35 8 32.5 9771.3225
35-40 18 37.5 17529.76
40-45 27 42.5 4046.2321
45-50 25 47.5 4370.5321
50-55 16 52.5 14959.7361
55-60 7 57.5 7834.0201
60-65 2 62.5 1245.3841
Sum 104 360 44.86 60058.36
x
xxf
nMDoftCoefficien
i 

1
  
21
xxf
N
SD ii

8. Page | 8
10. Coefficient of variation:
11. First moment:
Class
Frequency
(f)
X f*x f*x2 f*x3 f*x4
25-30 1 27.5 27.5 756.25 20796.875 571914.0625
30-35 8 32.5 260 8450 274625 8925312.5
35-40 18 37.5 675 25312.5 949218.75 35595703.13
40-45 27 42.5 1147.5 48768.75 2072671.875 88088554.69
45-50 25 47.5 1187.5 56406.25 2679296.875 127266601.6
50-55 16 52.5 840 44100 2315250 121550625
55-60 7 57.5 402.5 23143.75 1330765.625 76519023.44
60-65 2 62.5 125 7812.5 488281.25 30517578.13
Sum 104 360 4665 214750 10130906.25 489035312.5
12. Second moment:
13. Third moment:
14. Fourth moment:
%100.. 






x
SD
VC
N
fx
N
xf  


1
1
N
xf
N
xxf
22
2
)(  



N
xf
N
xxf  



33
3
)(

N
xf
N
xxf
44
4
)(  




9. Page | 9
15. Measure of skewness:
a) Karl Pearson’s Coefficient of Skewness:
b) Coefficient of skewness based on central moments:
c) Bowley’s Coefficient of Skewness
16. Measure of Kurtosis:
2
2
4
2


 