Question Help The following data represent the annual number of days over 100 a

Question

Question Help The following data represent the annual number of days over 100 a city from 1905 to 2004. Approximate the mean and standard deviation of annual number of days over 100° F. Treat the data as a population. Number of over 100°F days 0-9 10-19 20-29 30-39 40-49 50-59 60-69 Number of years 33 34 1710 3 21 = | | (Round to two decimal places as needed ) (Round to two decimal places as needed.) BOUT Media C College Privacy Your CA Terms of Genera ntellectu Enter your answer in each of the answer boxes. nvestor Corpora Enrollme

Explanation / Answer

Since the distibution is not continouous firstlt we onvert into continuous grouped distribution by using class boundaries.

Lower class boundaries= lower class limit-gap/2 and Upper class boundaries = upper class limit+gap/2

mean = mu = sum(fixi)/sum(fi)

= 1718.25/100

= 17.1825

sigma= sqrt((sum(fixi^2)/sum(fi))-(mu^2))mean =mu = sum(fixi)/sum(fi)=1710/10 = 17.10

= sqrt((46041.31/100)-(17.1825^2))

= sqrt(460.4131-295.2383)

=sqrt( 165.1747)

= 12.8520

Number of over 100 degree F Number of years (f) Mid values(xi) fi*xi fi*xi^2 0-9.5 33 4.75 156.75 744.5625 9.5-19.5 34 14.5 493 7148.5 19.5-29.5 17 24.5 416.5 10204.25 29.5-39.5 10 34.5 345 11902.5 39.5-49.5 3 44.5 133.5 5940.75 49.5-59.5 2 54.5 109 5940.5 59.5-69.5 1 64.5 64.5 4160.25 Total 100 1718.25 46041.31

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