Question
Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X...
Forty randomly selected students were asked the number of pairs of sneakers they owned. Let X = the number of pairs of sneakers owned. The results are as follows:
| X | Frequency | Relative Frequency | Cumulative Relative Frequency |
|---|---|---|---|
| 1 | 3 | ||
| 2 | 3 | ||
| 3 | 7 | ||
| 4 | 13 | ||
| 5 | 13 | ||
| 6 | 1 |
Find the sample standard deviation, s. (Round your answer to two decimal places.) please show work
Homework Answers
Answer #1
We make the table first
| X | Frequency | Relative Frequency | Cumulative Relative Frequency |
| 1 | 3 | 0.075 | 0.075 |
| 2 | 3 | 0.075 | 0.15 |
| 3 | 7 | 0.175 | 0.325 |
| 4 | 13 | 0.325 | 0.65 |
| 5 | 13 | 0.325 | 0.975 |
| 6 | 1 | 0.025 | 1 |
| Total | 40 | 1 | N/A |
Now we make another table to find sample standard deviation
| X | Frequency(f) | Xf | (Xi- )2f |
| 1 | 3 | 3 | 23.941875 |
| 2 | 3 | 6 | 9.991875 |
| 3 | 7 | 21 | 4.764375 |
| 4 | 13 | 52 | 0.398125 |
| 5 | 13 | 65 | 17.948125 |
| 6 | 1 | 6 | 4.730625 |
| Total | 40 | 153 | 61.775 |
The mean is obtained as
Now the sample SD with divisor 40 is given by
The sample SD with divisor 39 is given by
Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, give it a like. Thanks.
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