In: Statistics and Probability
Use the data in Table 2.0, answer questions 1, 2, & 3. Please show all of your working.
Table 2.0 Data for a sample of 50 individual in a Cardiovascular Disease Study |
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Participant ID |
Weight (kg) |
Height (cm) |
Smoking status |
Blood glucose |
1 |
70 |
165 |
1 |
107 |
2 |
60 |
162 |
0 |
145 |
3 |
62 |
150 |
1 |
237 |
4 |
66 |
165 |
1 |
91 |
5 |
70 |
162 |
0 |
185 |
6 |
59 |
165 |
0 |
106 |
7 |
47 |
160 |
0 |
177 |
8 |
66 |
170 |
1 |
120 |
9 |
56 |
155 |
0 |
186 |
10 |
62 |
167 |
0 |
164 |
11 |
68 |
167 |
1 |
130 |
12 |
65 |
157 |
0 |
132 |
13 |
59 |
166 |
0 |
134 |
14 |
80 |
170 |
0 |
161 |
15 |
66 |
170 |
0 |
176 |
16 |
91 |
159 |
1 |
106 |
17 |
71 |
161 |
1 |
183 |
18 |
66 |
164 |
0 |
138 |
19 |
59 |
160 |
0 |
104 |
20 |
59 |
162 |
1 |
231 |
1. Use the data in Table 2.0 to prepare a stemplot of weight (kg) [5 points]
2. Calculate the standard deviation for blood glucose level. (First write out the formula and go through the steps. Show all working) [2 points]
3. Describe the distribution in terms of shape, location and spread [ 3 points] (~ 3 sentences)
1. The weights(in kgs) of sample of 20 patients are given below:
70, 60,62,66,70,59,47,66,56,62,68,65,59,80,66,91,71,66,59,59
arranging the data in ascending order we've:
47 56 59 59 59 59 60 62 62 65 66 66 66 66 68 70 70 71 80 91
Stemplot:
table:1
stem | leaf |
4 | 7 |
5 | 6,9,9,9,9 |
6 | 0,2,2,5,6,6,6,6,8 |
7 | 0,0,1 |
8 | 0 |
9 | 1 |
2.Standard deviation():
where, xi : blood glucose level of the ith individual , n=sample size
to calculate first we've to calculate the mean.
where, xi : blood glucose level of the ith individual , n=sample size
table:2(table showing necessary calculations for mean and s.d.)
Blood Glucose(xi) | (xi-mean)^2 | |
107 | 1905.3225 | |
145 | 31.9225 | |
237 | 7456.3225 | |
91 | 3558.1225 | |
185 | 1179.9225 | |
106 | 1993.6225 | |
177 | 694.3225 | |
120 | 939.4225 | |
186 | 1249.6225 | |
164 | 178.2225 | |
130 | 426.4225 | |
132 | 347.8225 | |
134 | 277.2225 | |
161 | 107.1225 | |
176 | 642.6225 | |
106 | 1993.6225 | |
183 | 1046.5225 | |
138 | 160.0225 | |
104 | 2176.2225 | |
231 | 6456.1225 | |
Total | 3031 | 32820.55 |
mean | 150.65 | - |
S.D. | 41.56197 | - |
Standard Deviation=41.56197
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