Question

In: Statistics and Probability

An article in the journal PLOS ONE describes a study in which the oviposition preferences of...

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

Solutions

Expert Solution

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

orchestra answered 2 years ago
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