Nice job on getting problem 1 correct.
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Problem 2
The double stem and leaf plot says we have the following data set for the men's side
- 53,54,57
- 60,61,62,63,63,64,64,66,67,67,68,69
- 70,70,70,70,70,73,76,77,77,77,77,79
- 81,82,85,86,88,88
- 90,92,93,98
Be careful to read the stem first, followed by the leaf (even though the leaf values are listed on the left side of the stem).
Notice how each row is a different stem (in this case, tens digit) to help make things more readable.
If we were to add up all of those values I listed above, then we should get the sum 2707. Divide this over n = 37 to get 2707/n = 2707/37 = 73.162 approximately. This rounds to 73 since your teacher wants you to round to the nearest whole point.
The average score for the men is 73.
You'll do the same thing for the women's side. That data set is
- 55,59
- 60,60,62,62,63,64,65,66,66,67
- 70,71,71,72,73,74,75,76,79,79
- 80,81,82,83,83,84,89
- 90,92,92,93,93,95,98
- 100
Again, it's handy to break the scores up by stem or else you'll have a long string of scores to get lost in (or it's easier to get lost in).
Adding up those 37 scores should get you 2824 which then leads to a mean of 2824/n = 2824/37 = 76.324 approximately. This rounds to 76
The average score for the women is 76.
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Problem 3
The range for the men is max - min = 98 - 53 = 45
The range for the women is max - min = 100 - 55 = 45
Both groups have the same range (which is 45)
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Problem 4
It's strongly recommended to use a spreadsheet here. Let's focus on the men's data set.
The idea is to subtract each data value from the mean 73.162, and then square the result. So each term is of the form (x-mu)^2 where mu is the mean.
For example, the data value x = 53 on the men's side will lead to
(x-mu)^2 = (53 - 73.162)^2 = 406.506
We consider this a squared error value.
You'll do this with the remaining 36 other values in the men's data set.
After doing this, you'll add up the 37 items in this new column and you should get roughly 4711.027, and this is the sum of the squared errors (SSE).
Divide this over n = 37 and we get 4711.027/37 = 127.325
Lastly, apply the square root and we arrive at sqrt(127.325) = 11.284 which rounds to 11.28
The steps for the women's standard deviation will be the same. You should get 12.30
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Answers:
Men's standard deviation = 11.28
Women's standard deviation = 12.30
These are population standard deviation values. If you don't want to use a spreadsheet, a much better option is to use online calculators that specialize in population standard deviation.
