Ampling and Exploratory Data Analysis Assignment 2022

Name: ____________________ ID number: ________________________
MASSEY UNIVERSITY
College of Sciences
School of Fundamental Sciences (Statistics)
Introductory Biostatistics 161.130
Assignment 1: Sampling and Exploratory Data Analysis
Due date: Friday 16th August 2019
Total marks: 45 Assessment value: 12%
The population data
The population we are considering for this assignment are the 10,000
kuku (New Zealand green–lipped mussels) growing in a mussel farm in
the Marlborough Sounds. Variables of interest are the length of the
kuku (in millimetres), grade (small, medium or large) and sex (male or
female).
Each kuku (mussel) has a unique ID. The population consists of:
 1948 large kuku with ID numbers from 1 to 1948.
 4457 medium kuku with ID numbers from 1949 to 6405
 3595 small kuku with ID numbers from 6406 to 10000.
You do not have access to the population data. You will generate a sample of ID numbers and then
we will give you a file containing information on the length, grade and sex for each of the kuku
identified in your sample.
Part A: Sampling method [9 marks]
 You are to use Excel to create a representative sample (size 100) of the population. Your
sample will consist of 100 ID numbers.
 Ensure all 100 ID numbers are in a single column.
 Click on the following link to open a Shiny app and copy your 100 ID numbers into the
“Sample row identifiers” box.
 http://shiny.massey.ac.nz/jcmarsha/student_data/?p=161120&y=2019&a=1
 This will generate a file containing ID, length, grade and sex for each of the kuku in your
sample. This is your sample data.
 Keep an electronic copy of your sample data for use in Assignments 2 and 3.
 Use your sample data to answer the following questions in the answer spaces provided.
(You can re-size the answer spaces.)
1. What type of sampling method have you chosen to use? [1 mark]
Simple random sampling technique
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2. What other sampling methods could you have used and why is the method that you chose
better? [3 marks]
Stratified random sampling
3. Describe how you used Excel to create your sample. [4 marks]
To generate random values in excel, a person uses an inbuilt function RANDBETWEEN.
Therefore;
i. select a cell and type =RANDBETWEEN(1,10000)
ii. Use the autofill (+) to generate the 100 sample ID
4. Attach a copy of your sample to the Appendix. [1 mark]
Part B: Exploring your sample data [36 marks]
Use Excel and incorporate the output into your report.
1. Descriptive analysis of kuku grades according to sex.
a. Produce a contingency table of kuku grades according to sex. [2 marks]
Sex
Grade Total
Large Medium Small
Female 6 22 22 50
Male 9 24 17 50
Total 15 46 39 100
b. Draw a suitable graph of the distribution of kuku grades according to sex. [2 marks]
Large Medium Small
Grade
0
5
10
15
20
25
30
Kuku Grades according to Sex
Female Male
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Name: ____________________ ID number: ________________________
c. Describe the important features of the distribution of kuku grades according to sex for
your sample. [4 marks]
The graph above exhibits that there are more males than females in both Large and Medium grade.
However, there are more female than male in small grade.
2. Descriptive analysis of kuku lengths.
a. Draw a suitable plot(s) to show the distribution of kuku lengths. [2 marks]
40 60 80 100 120 140 160 180 200 220 240
0
5
10
15
20
25
Histogram showing frequency Distribution
b. Produce summary statistics of kuku lengths. Include the sample size, mean, standard
deviation and the five-number summary. [2 marks]
Descriptive statistics for Length
Mean 98.445
Standard Error 4.430075443
Median 92.05
Mode 122.3
Standard Deviation 44.30075443
Sample Variance 1962.556843
Kurtosis 0.364050039
Skewness 0.792390479
Range 202.2
Minimum 20.6
Maximum 222.8
Sum 9844.5
Count 100
c. Describe the important features of kuku lengths in your sample. [4 marks]
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Name: ____________________ ID number: ________________________
As evident, the mean length of kuku is 98.445 with a standard deviation of 44.3. Moreover, the
maximum length of kuku is 222.8 whereas the minimum length is 20.6.
3. Descriptive analysis of kuku lengths according to sex.
a. Draw side by side boxplots of kuku lengths for the different sexes. [2 marks]
Female Male
0
50
100
150
200
250
Side by Side Box plot
b. Produce summary statistics of kuku lengths for the different sexes. Include the
sample size, mean, standard deviation and the five number summary for each sex.
HINT: you may find it easier to do this if you use the filter in Excel to unstack the
lengths according to sex (see Excel Tour Guide B). [2 marks]
Female Male
Mean
93.8224489
8 Mean 100.908
Standard Error
6.32294457
6 Standard Error 6.00096716
Median 81.3 Median 96.95
Standard
Deviation
44.2606120
3
Standard
Deviation 42.43324573
Sample Variance
1959.00177
7 Sample Variance 1800.580343
Kurtosis
1.47040301
4 Kurtosis -0.180181434
Skewness
1.16887547
1 Skewness 0.436795439
Range 194.2 Range 184.4
Minimum 28.6 Minimum 20.6
Maximum 222.8 Maximum 205
Sum 4597.3 Sum 5045.4
Count 49 Count 50
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Name: ____________________ ID number: ________________________
c. Describe the important features of kuku lengths of males and females in your sample.
[4 marks]
As evident, the mean length of female kuku is 93.822 with a standard deviation of 44.261.
Moreover, the maximum length of female kuku is 222.8 whereas the minimum length is 28.6. On
the other side, the mean length of male kuku is 100.908 with a standard deviation of 42.433.
Besides, the maximum length of male kuku is 205 whereas the minimum length is 20.6.
4. Descriptive analysis of kuku lengths according to grade.
a. Draw side by side boxplots of kuku lengths for the different grades. [2 marks]
Large Medium Small
0
10
20
30
40
50
60
70
80
90
100
Side by Side Box plot
b. Produce summary statistics of kuku lengths for the different grades. Include the
sample size, mean, standard deviation and the five number summary for each grade.
HINT: you may find it easier to do this if you use the filter in Excel to unstack the
lengths according to grade (see Excel Tour Guide B). [2 marks]
Large Medium Small
Mean 177.9533333 Mean 104.9804348 Mean 60.15641
Standard Error 7.031066211 Standard Error 3.026535813 Standard Error 2.722867
Median 167.2 Median 107.2 Median 63.3
Standard Deviation 27.23120234 Standard Deviation 20.52696459 Standard Deviation 17.0043
Sample Variance 741.538381 Sample Variance 421.3562754 Sample Variance 289.1462
Kurtosis -0.836533708 Kurtosis 0.016781541 Kurtosis -0.32787
Skewness 0.207279048 Skewness -0.712626603 Skewness -0.2844
Range 93.2 Range 90.8 Range 76.5
Minimum 129.6 Minimum 47.9 Minimum 20.6
Maximum 222.8 Maximum 138.7 Maximum 97.1
Sum 2669.3 Sum 4829.1 Sum 2346.1
Count 15 Count 46 Count 39
c. Describe the important features of kuku lengths for the different grades in your
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Name: ____________________ ID number: ________________________
sample. [4 marks]
As evident, the mean length of large kuku is 177.95 with a standard deviation of 27.23. Moreover,
the maximum length of large kuku is 222.8 whereas the minimum length is 129. On the other side,
the mean length of medium kuku is 104.98 with a standard deviation of 20.53. Besides, the
maximum length of medium kuku is 138.7 whereas the minimum length is 47.9. Consequently, the
mean length of small kuku is 60.16 with a standard deviation of 17.00. Besides, the maximum
length of small kuku is 97.1 whereas the minimum length is 20.6
5. Conclusions (4 marks)
What does the descriptive analysis of your sample tell you about the population of kuku. i.e.
what can you conclude about the 10000 kuku on the Marlborough Sounds mussel farm?
Generally, mean length of kuku is 98.445 with a standard deviation of 44.3. However, the males
tend to record a higher mean length (100.908) as compared to female (93.822)
Is it reasonable to generalise these conclusion(s) to other populations? Explain.
It is reasonable to generalise the conclusion to other population since the sample used to infer the
population was selected randomly, thus it is unbiased.
+ + + + + + + +
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Name: ____________________ ID number: ________________________
Appendix:
ID Lengt
h
Grade Sex
37 201.8 Large Female
176 167.2 Large Male
202 153.7 Large Male
331 158.7 Large Male
574 205 Large Male
579 220.2 Large Female
827 156.7 Large Male
896 222.8 Large Female
902 177.7 Large Male
932 195.2 Large Female
1014 161.2 Large Female
1163 159.4 Large Female
1447 195.7 Large Male
1500 164.4 Large Male
1766 129.6 Large Male
2048 105.3 Medium Female
2052 90.7 Medium Male
2069 122.3 Medium Male
2080 128.7 Medium Female
2132 124.7 Medium Male
2149 107.2 Medium Female
2421 80.8 Medium Male
2543 125.5 Medium Male
2584 82.2 Medium Male
2753 106.8 Medium Female
2908 126.5 Medium Male
3011 122.4 Medium Male
3111 120.7 Medium Female
3132 128 Medium Male
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3171 93.3 Medium Male
3217 101.4 Medium Male
3243 81.4 Medium Female
3262 93.4 Medium Female
3566 95.7 Medium Female
3743 126.5 Medium Female
3752 114.1 Medium Female
3836 113.3 Medium Female
3844 115.5 Medium Female
3902 117 Medium Male
3973 95.5 Medium Female
4080 118.9 Medium Male
4104 116.9 Medium Male
4122 87.1 Medium Male
4233 102.3 Medium Male
4256 127.1 Medium Male
4310 90.8 Medium Female
4378 113.1 Medium Male
4489 126.8 Medium Female
4831 138.7 Medium Female
4904 96.8 Medium Male
5028 102.3 Medium Female
5130 128.3 Medium Female
5238 107.2 Medium Male
5338 114.4 Medium Male
5436 86.9 Medium Male
5443 122.3 Medium Female
5595 81.3 Medium Female
6204 71.2 Medium Female
6245 66.9 Medium Female
6251 47.9 Medium Male
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Name: ____________________ ID number: ________________________
6338 63 Medium Male
6499 86.1 Small Male
6600 77.7 Small Female
6638 97.1 Small Male
6709 77.3 Small Male
6730 77.4 Small Male
6911 75.5 Small Female
6917 79.5 Small Female
7045 75.3 Small Female
7074 76.3 Small Female
7142 48 Small Female
7306 70 Small Male
7552 60.8 Small Female
7948 47 Small Male
8075 56.6 Small Female
8149 70.2 Small Male
8163 35.8 Small Female
8238 46 Small Female
8377 73.8 Small Female
8415 20.6 Small Male
8432 64.5 Small Female
8506 54.3 Small Male
8726 74.8 Small Female
8760 38.7 Small Male
8817 53.1 Small Female
8825 58.3 Small Female
8943 57.4 Small Female
8981 52.3 Small Male
9184 38.5 Small Female
9240 28.6 Small Female
9345 63.3 Small Female
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Name: ____________________ ID number: ________________________
9379 43 Small Male
9448 64.6 Small Female
9473 65.2 Small Male
9584 41.5 Small Female
9624 65.3 Small Male
9668 35.4 Small Male
9671 69 Small Male
9881 71.4 Small Male
9908 55.9 Small Female
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