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#1 2006-12-02 11:28:31

tboyne
Member
Registered: 2006-12-02
Posts: 2

Help to start

I need help with the following practice question: Two students analyzed the results of the science test in Mr. Nelson's class. They came up with following statistics:

Mean = 81    Median = 91   Minimum = 61   Maximum = 100   Sample Size = 11

Give a list of test scores that would result in the statistics given.

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#2 2006-12-02 15:22:00

Zhylliolom
Real Member
Registered: 2005-09-05
Posts: 412

Re: Help to start

Since the sample size is 11, you have to have 11 scores in your list. Since the minimum is 61, one of the scores in the list must be 61 and no other score may be lower than 61. Since the maximum is 100, one of the scores in the list must be 100, and no other score may be higher than 100. The mean score is the sum of all scores divided by the sample size. Then if we multiply the mean by the sample size we will know what the sum of the scores is. This value is 81*11 = 891.

We know that 61 and 100 must be in the list, as determined above. Then from the determined relation, we have a + b + c + d + e + f + g + h + i + j + k = 891 (where the letters a through k represent different test scores in the list). So we can say that j = 61 and k = 100 and subtract these values from each side to get a + b + c + d + e + f + g + h + i = 730. So now we have to find out a set of 9 remaining test scores such that the sum of the test scores is 730, when listed from least to greatest the 5th test score is 91 (since the median is 91), and the scores aren't less than 61 or greater than 100. From that last sentence we now know that one of these scores is 91, so we can say that i = 91 and subtract it from each side to get a + b + c + d + e + f + g + h = 639. Now we must be careful. Since the median was 91, four of these remaining scores must be less than 91 and four of them must be greater than 91. Any set of scores satisfying this and a + b + c + d + e + f + g + h = 639 will work then. These values may be found by "guessing": let the last four scores be 95 (which is greater than 91 so we can choose this). Then subtract these four 95's from each side to get a + b + c + d = 259. Now we must find four scores greater than 61 but less than 91 that sum up to 259. If 3 of these scores are 65 and one is 64, then we have 65 + 65 + 65 + 64 = 259, so these values work.

Then one list of test scores that would result in the statistics given is 61, 64, 65, 65, 65, 91, 95, 95, 95, 95, 100. Hopefully you could follow my reasoning somewhat. Also note that this isn't the only possible list, you can easily find others.

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