a. Calculate the sample average using ungrouped and grouped methods.
b. Calculate the sample standard deviation using ungrouped and grouped method
(a-b)
For un-grouped data:
Following table shows the calculations:
X | (x-mean)^2 | |
10 | 17.0569 | |
7 | 50.8369 | |
12 | 4.5369 | |
11 | 9.7969 | |
9 | 26.3169 | |
13 | 1.2769 | |
14 | 0.0169 | |
10 | 17.0569 | |
6 | 66.0969 | |
12 | 4.5369 | |
17 | 8.2369 | |
17 | 8.2369 | |
13 | 1.2769 | |
15 | 0.7569 | |
18 | 14.9769 | |
14 | 0.0169 | |
15 | 0.7569 | |
16 | 3.4969 | |
15 | 0.7569 | |
14 | 0.0169 | |
9 | 26.3169 | |
19 | 23.7169 | |
15 | 0.7569 | |
14 | 0.0169 | |
15 | 0.7569 | |
16 | 3.4969 | |
15 | 0.7569 | |
14 | 0.0169 | |
13 | 1.2769 | |
16 | 3.4969 | |
17 | 8.2369 | |
13 | 1.2769 | |
14 | 0.0169 | |
11 | 9.7969 | |
12 | 4.5369 | |
15 | 0.7569 | |
16 | 3.4969 | |
13 | 1.2769 | |
16 | 3.4969 | |
15 | 0.7569 | |
18 | 14.9769 | |
15 | 0.7569 | |
13 | 1.2769 | |
15 | 0.7569 | |
14 | 0.0169 | |
16 | 3.4969 | |
13 | 1.2769 | |
16 | 3.4969 | |
15 | 0.7569 | |
16 | 3.4969 | |
20 | 34.4569 | |
14 | 0.0169 | |
10 | 17.0569 | |
15 | 0.7569 | |
13 | 1.2769 | |
15 | 0.7569 | |
12 | 4.5369 | |
14 | 0.0169 | |
16 | 3.4969 | |
13 | 1.2769 | |
16 | 3.4969 | |
13 | 1.2769 | |
14 | 0.0169 | |
16 | 3.4969 | |
14 | 0.0169 | |
15 | 0.7569 | |
16 | 3.4969 | |
15 | 0.7569 | |
16 | 3.4969 | |
15 | 0.7569 | |
Total | 989 | 441.843 |
14.12857 | 2.530518077 |
Sample size: n=70
The sample mean is:
The sample standard deviation is
For grouped data:
Following table shows the calculations:
Classes | |||||
Lower limit | Upper limit | Mid Point, X | Frequency, f | fx | f(x-mean)^2 |
6 | 8.1 | 7.05 | 2 | 14.1 | 97.7202 |
8.1 | 10.2 | 9.15 | 5 | 45.75 | 119.5605 |
10.2 | 12.3 | 11.25 | 6 | 67.5 | 46.7046 |
12.3 | 14.4 | 13.35 | 21 | 280.35 | 9.9981 |
14.4 | 16.5 | 15.45 | 29 | 448.05 | 57.6549 |
16.5 | 18.6 | 17.55 | 5 | 87.75 | 61.6005 |
18.6 | 20.7 | 19.65 | 2 | 39.3 | 62.9442 |
Total | 70 | 982.8 | 456.183 |
The sample mean is
The sample standard deviation is
a. Calculate the sample average using ungrouped and grouped methods. b. Calculate the sample standard deviation...
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