math

can someone please help me solve this?
the u.s weather bureau has provided the following information about the total annual rainfall (in inches) in hawaii for the years 1965 to 1984.
15 12 31.5 17 11.2 13 12.4 16.3 14.6 10 12.8 14.1 14.7 10.7 15.2 10.9 18.4 12 15.9 10
a) use Chebyshev's theorem to find an interval centered about the mean for the annual rain fall in which you would expect at least 88.9% of the years to fall.

b)use Chebyshev's theorem to find an interval centered about the mean for the annual rain fall in which you would expect at least 75% of the years to fall.

c)for the data given above find the median and the coefficent of variation.

I will try to keep this simple add all the rainfall numbers up (287.7) divide by how many parts you had (20)=14.385 this is your mean.

Make a chart with three columns the first will be each individual rainfall amount. Second column will be each amount with the mean subtracted from it. Third column will be the number in column 2 squared.

ex:
15 .615 .378
12 -2.385 5.688
31.5 17.115 292
17 2.615 6.838

do this for all 20.
add up column 3 you should get 417.1855

now you divide that total (417.1855) by n-1 (20-1=19) 417.1855/19=21.957 this is your variance. take the square root of the variance and you get standard deviation (4.686).
Finally part of the answer take standard deviation/mean to get coeffecient of variation (4.686/14.385= .325756) so 32.57%

Cheby just puts bounds on how much data must lie close to the mean. Here comes the whole 1-(1/k^2). k has to be 3.3333 to equal 88.9% and k has to be 2 to equal 75%.
Now we take the mean (14.385)and subtract k (3.3333)*standard dev(4.686)
14.385-15.61998=-1.235 to get the bottom of the interval. to get the top add 3.3333*standard dev to the mean 14.385+15.61998=30.005.
the 75 % question is just making k=2
14.385- (2)(4.686)=5.013
14.385+ (2)(4.686)=23.757.

to get the medain sort all your dat in order 10, 10, 10.7, 10.9, 11.2, 12, 12, 12.4,12.8, 13, 14, 14.6, 14.7,15, 15.2, 15.9, 16.3, 17, 18.4, 31.5. cross off the two end numbers until you get to the middle 10 gone 31.5 gone 10 gone 18.4 gone etc... if you have an odd number that middle one is the median in this case you have an even amount so you take the average of 13 and 14 to get13.5. Hope this helped

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