Question

In: Statistics and Probability

17, 18, 18, 18, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22,...

17, 18, 18, 18, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 23,23, 24,24,24,24,24,24,24,24,25,26,26,26,26,26,26,27,27,27,27,27,28,28,29,31,31,32,32,34,35,38 use the data to do the following: 1. sample mean 2. median 3. mode 4. standard deviation

Solutions

Expert Solution

The answers are:

1. Sample Mean 24.66667
2. Median 24
3. Mode 24
4. Standard Deviation 4.594199

Calculations:

Consider the following table:

Data Frequency Data * Frequency (X - Mean) * Frequency (X - Mean)^2 * Frequency
17 1 17 -7.6667 58.7778
18 3 54 -20.0000 133.3333
19 1 19 -5.6667 32.1111
20 4 80 -18.6667 87.1111
21 4 84 -14.6667 53.7778
22 6 132 -16.0000 42.6667
23 2 46 -3.3333 5.5556
24 8 192 -5.3333 3.5556
25 1 25 0.3333 0.1111
26 6 156 8.0000 10.6667
27 5 135 11.6667 27.2222
28 2 56 6.6667 22.2222
29 1 29 4.3333 18.7778
31 2 62 12.6667 80.2222
32 2 64 14.6667 107.5556
34 1 34 9.3333 87.1111
35 1 35 10.3333 106.7778
38 1 38 13.3333 177.7778
Total 51 1258 0.00 1,055.3333

Median is corresponding to the 26th position element = 24

Mode = Most common observation = 24

Hence

Please do upvote if you are satisfied! Let me know in the comments if anything is not clear. I will reply ASAP!

orchestra answered 2 years ago
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