In: Statistics and Probability
An article in the journal PLOS ONE describes a study in which the oviposition preferences of Tecia solanivora, the Central American potato tuberworm or Guatemalan potato moth, are compared across different varieties of Solanum tuberosum (potato).
Suppose that Paul, a plant pathologist, collects a sample of 194 potato plants. Paul records the total number of T. solanivora eggs laid on and around each plant. The egg counts are provided in the data file.
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Let ? be a random variable taking on values equal to the number of eggs laid on or around each plant.
Compute x¯ , the mean number of eggs laid on or around each plant. Report your answer to at least two decimal places of precision.
x¯=
eggs
Compute s , the sample standard deviation of the number of eggs laid on or around each plant. Report your answer to at least three decimal places of precision.
s=
eggs
"EGGCNT" 6 3 3 10 1 80 9 5 5 39 2 0 64 31 21 23 9 17 6 20 2 7 5 30 29 6 52 5 4 1 47 8 15 43 3 23 2 5 54 22 13 12 20 4 2 4 13 75 28 13 72 78 5 78 58 63 60 22 16 48 3 2 81 6 18 1 60 40 15 9 11 39 0 14 2 49 4 52 1 4 0 45 10 0 3 7 3 53 4 0 5 16 20 2 0 0 0 27 1 0 28 1 9 0 0 0 10 0 2 0 31 1 0 10 8 2 10 0 39 42 33 3 2 0 0 0 0 0 7 6 0 2 26 7 32 8 32 1 11 2 1 3 1 0 26 8 0 7 2 1 0 23 0 3 98 3 3 3 0 13 0 2 12 0 10 18 24 115 10 10 0 0 0 2 28 2 0 27 0 3 0 8 0 7 27 29 3 0 70 9 7 17 15 2
Given that Paul, a plant pathologist, collects a sample of 194 potato plants. Paul records the total number of Tecia solanivora eggs laid on and around each plant.
Given that X is a random variable taking on values equal to the number of eggs laid on or around each plant.
We need to calculate the mean and the sample standard deviation of the number of eggs laid on or around each plant.
Now the mean is given by,
The sample standard deviation is given by,
The table of calculations is provided below,
No. | x | (xi-x̄)^2 |
1 |
6 |
92.0214 |
2 | 3 | 158.5781 |
3 | 3 | 158.5781 |
4 | 10 | 31.2792 |
5 | 1 | 212.9492 |
6 | 80 | 4148.29 |
7 | 9 | 43.4647 |
8 | 5 | 112.207 |
9 | 5 | 112.207 |
10 | 39 | 547.8979 |
11 | 2 | 184.7637 |
12 | 0 | 243.1348 |
13 | 64 | 2343.2589 |
14 | 31 | 237.3824 |
15 | 21 | 29.238 |
16 | 23 | 54.8669 |
17 | 9 | 43.4647 |
18 | 17 | 1.9803 |
19 | 6 | 92.0214 |
20 | 20 | 19.4236 |
21 | 2 | 184.7637 |
22 | 7 | 73.8359 |
23 | 5 | 112.207 |
24 | 30 | 207.568 |
25 | 29 | 179.7535 |
26 | 6 | 92.0214 |
27 | 52 | 1325.4857 |
28 | 5 | 112.207 |
29 | 4 | 134.3925 |
30 | 1 | 212.9492 |
31 | 47 | 986.4135 |
32 | 8 | 57.6503 |
33 | 15 | 0.3514 |
34 | 43 | 751.1557 |
35 | 3 | 158.5781 |
36 | 23 | 54.8669 |
37 | 2 | 184.7637 |
38 | 5 | 112.207 |
39 | 54 | 1475.1145 |
40 | 22 | 41.0525 |
41 | 13 | 6.7225 |
42 | 12 | 12.9081 |
43 | 20 | 19.4236 |
44 | 4 | 134.3925 |
45 | 2 | 184.7637 |
46 | 4 | 134.3925 |
47 | 13 | 6.7225 |
48 | 75 | 3529.2178 |
49 | 28 | 153.9391 |
50 | 13 | 6.7225 |
51 | 72 | 3181.7745 |
52 | 78 | 3894.6611 |
53 | 5 | 112.207 |
54 | 78 | 3894.6611 |
55 | 58 | 1798.3723 |
56 | 63 | 2247.4445 |
57 | 60 | 1972.0012 |
58 | 22 | 41.0525 |
59 | 16 | 0.1658 |
60 | 48 | 1050.2279 |
61 | 3 | 158.5781 |
62 | 2 | 184.7637 |
63 | 81 | 4278.1044 |
64 | 6 | 92.0214 |
65 | 18 | 5.7947 |
66 | 1 | 212.9492 |
67 | 60 | 1972.0012 |
68 | 40 | 595.7124 |
69 | 15 | 0.3514 |
70 | 9 | 43.4647 |
71 | 11 | 21.0936 |
72 | 39 | 547.8979 |
73 | 0 | 243.1348 |
74 | 14 | 2.5369 |
75 | 2 | 184.7637 |
76 | 49 | 1116.0423 |
77 | 4 | 134.3925 |
78 | 52 | 1325.4857 |
79 | 1 | 212.9492 |
80 | 4 | 134.3925 |
81 | 0 | 243.1348 |
82 | 45 | 864.7846 |
83 | 10 | 31.2792 |
84 | 0 | 243.1348 |
85 | 3 | 158.5781 |
86 | 7 | 73.8359 |
87 | 3 | 158.5781 |
88 | 53 | 1399.3001 |
89 | 4 | 134.3925 |
90 | 0 | 243.1348 |
91 | 5 | 112.207 |
92 | 16 | 0.1658 |
93 | 20 | 19.4236 |
94 | 2 | 184.7637 |
95 | 0 | 243.1348 |
96 | 0 | 243.1348 |
97 | 0 | 243.1348 |
98 | 27 | 130.1247 |
99 | 1 | 212.9492 |
100 | 0 | 243.1348 |
101 | 28 | 153.9391 |
102 | 1 | 212.9492 |
103 | 9 | 43.4647 |
104 | 0 | 243.1348 |
105 | 0 | 243.1348 |
106 | 0 | 243.1348 |
107 | 10 | 31.2792 |
108 | 0 | 243.1348 |
109 | 2 | 184.7637 |
110 | 0 | 243.1348 |
111 | 31 | 237.3824 |
112 | 1 | 212.9492 |
113 | 0 | 243.1348 |
114 | 10 | 31.2792 |
115 | 8 | 57.6503 |
116 | 2 | 184.7637 |
117 | 10 | 31.2792 |
118 | 0 | 243.1348 |
119 | 39 | 547.8979 |
120 | 42 | 697.3413 |
121 | 33 | 303.0113 |
122 | 3 | 158.5781 |
123 | 2 | 184.7637 |
124 | 0 | 243.1348 |
125 | 0 | 243.1348 |
126 | 0 | 243.1348 |
127 | 0 | 243.1348 |
128 | 0 | 243.1348 |
129 | 7 | 73.8359 |
130 | 6 | 92.0214 |
131 | 0 | 243.1348 |
132 | 2 | 184.7637 |
133 | 26 | 108.3102 |
134 | 7 | 73.8359 |
135 | 32 | 269.1969 |
136 | 8 | 57.6503 |
137 | 32 | 269.1969 |
138 | 1 | 212.9492 |
139 | 11 | 21.0936 |
140 | 2 | 184.7637 |
141 | 1 | 212.9492 |
142 | 3 | 158.5781 |
143 | 1 | 212.9492 |
144 | 0 | 243.1348 |
145 | 26 | 108.3102 |
146 | 8 | 57.6503 |
147 | 0 | 243.1348 |
148 | 7 | 73.8359 |
149 | 2 | 184.7637 |
150 | 1 | 212.9492 |
151 | 0 | 243.1348 |
152 | 23 | 54.8669 |
153 | 0 | 243.1348 |
154 | 3 | 158.5781 |
155 | 98 | 6790.9499 |
156 | 3 | 158.5781 |
157 | 3 | 158.5781 |
158 | 3 | 158.5781 |
159 | 0 | 243.1348 |
160 | 13 | 6.7225 |
161 | 0 | 243.1348 |
162 | 2 | 184.7637 |
163 | 12 | 12.9081 |
164 | 0 | 243.1348 |
165 | 10 | 31.2792 |
166 | 18 | 5.7947 |
167 | 24 | 70.6813 |
168 | 115 | 9881.7954 |
169 | 10 | 31.2792 |
170 | 10 | 31.2792 |
171 | 0 | 243.1348 |
172 | 0 | 243.1348 |
173 | 0 | 243.1348 |
174 | 2 | 184.7637 |
175 | 28 | 153.9391 |
176 | 2 | 184.7637 |
177 | 0 | 243.1348 |
178 | 27 | 130.1247 |
179 | 0 | 243.1348 |
180 | 3 | 158.5781 |
181 | 0 | 243.1348 |
182 | 8 | 57.6503 |
183 | 0 | 243.1348 |
184 | 7 | 73.8359 |
185 | 27 | 130.1247 |
186 | 29 | 179.7535 |
187 | 3 | 158.5781 |
188 | 0 | 243.1348 |
189 | 70 | 2960.1456 |
190 | 9 | 43.4647 |
191 | 7 | 73.8359 |
192 | 17 | 1.9803 |
193 | 15 | 0.3514 |
194 | 2 | 184.7637 |
Total | 3025 | 89618.8299 |
Mean
Sample Standard Deviation