A sample of size n = 10 n = 10 is drawn from a population. The data is shown below. 70.4 56.8 39 63.8 70.4 43.8 59.4 46.5 50.4 70.4 What is the range of this data set? range = What is the standard deviation of this data set? (Remember, it is a sample.) Please report the answer with appropriate rounding, reporting 2 more decimal places than the original data. Please, please, please do not calculate the value by hand. stdev =
SOLUTION
Part (a)
Range = maximum value – minimum value
= 70.4 - 39
= 31.4 Answer 1
Part (b)
Standard deviation = 12.463 ANSWER 2
Excel Calculations are given below:
i |
xi |
xi - avg |
(xi-avg)^2 |
|
1 |
70.4 |
13.31 |
177.1561 |
|
2 |
56.8 |
-0.29 |
0.0841 |
|
3 |
39 |
-18.09 |
327.2481 |
|
4 |
63.8 |
6.71 |
45.0241 |
|
5 |
70.4 |
13.31 |
177.1561 |
|
6 |
43.8 |
-13.29 |
176.6241 |
|
7 |
59.4 |
2.31 |
5.3361 |
|
8 |
46.5 |
-10.59 |
112.14181 |
|
9 |
50.4 |
-6.69 |
44.7561 |
|
10 |
70.4 |
13.31 |
177.1561 |
|
Total |
570.9 |
0 |
1242.6827 |
|
Average |
57.09 |
|||
Sample variance = |
1242.6827/8 |
155.335 |
||
Sample standard deviation = |
sqrt(155.335) |
|||
12.463 |
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