Homework SoursePlease help to answer this question set of data 61 28 58 60
Please help to answer this question:
set of data:
61
28
58
60
14
22
55
23
13
47
71
72
34
78
14
34
34
78
67
3
19
35
8
58
62
69
6
64
42
16
a. What is the mean?
b. What is the standard deviation?
c. What is the variance?
d. What is the median?
e. What is the range?
| 61 | 28 | 58 |
| 60 | 14 | 22 |
| 55 | 23 | 13 |
| 47 | 71 | 72 |
| 34 | 78 | 14 |
| 34 | 34 | 78 |
| 67 | 3 | 19 |
| 35 | 8 | 58 |
| 62 | 69 | 6 |
| 64 | 42 | 16 |
Solution
ordering the data,
3
6
8
13
14
14
16
19
22
23
28
34
34
34
35
42
47
55
58
58
60
61
62
64
67
69
71
72
78
78
Getting the mean, X,
A)
X = Sum(x) / n
Summing the items, Sum(x) = 1245
As n = 30
Thus,
X = 41.5 [ANSWER, MEAN]
Consider the table:
b)
Thus, Sum(x - X)^2 = 16739.5
Thus, as
s^2 = Sum(x - X)^2 / (n - 1)
As n = 30
s^2 = 577.2241379
Thus,
s = 24.02548934 [ANSWER, STANDARD DEVIATION]
**************************
c)
variance = s^2 = 577.2241379 [ANSWER]
**********************************
d)
The median is the average of the two middle entries here, the 15th and 16th entries,
Median = (35+42)/2 = 38.5 [ANSWER]
*******************************
e)
Also, we have
Maximum = 78
Minimum = 3
Range = max - min = 75
| x | x - X | (x - X)^2 |
| 3 | -38.5 | 1482.25 |
| 6 | -35.5 | 1260.25 |
| 8 | -33.5 | 1122.25 |
| 13 | -28.5 | 812.25 |
| 14 | -27.5 | 756.25 |
| 14 | -27.5 | 756.25 |
| 16 | -25.5 | 650.25 |
| 19 | -22.5 | 506.25 |
| 22 | -19.5 | 380.25 |
| 23 | -18.5 | 342.25 |
| 28 | -13.5 | 182.25 |
| 34 | -7.5 | 56.25 |
| 34 | -7.5 | 56.25 |
| 34 | -7.5 | 56.25 |
| 35 | -6.5 | 42.25 |
| 42 | 0.5 | 0.25 |
| 47 | 5.5 | 30.25 |
| 55 | 13.5 | 182.25 |
| 58 | 16.5 | 272.25 |
| 58 | 16.5 | 272.25 |
| 60 | 18.5 | 342.25 |
| 61 | 19.5 | 380.25 |
| 62 | 20.5 | 420.25 |
| 64 | 22.5 | 506.25 |
| 67 | 25.5 | 650.25 |
| 69 | 27.5 | 756.25 |
| 71 | 29.5 | 870.25 |
| 72 | 30.5 | 930.25 |
| 78 | 36.5 | 1332.25 |
| 78 | 36.5 | 1332.25 |
