SOLUTION: The average weekly overtime earnings from a sample of workers from a particular
service industry were recorded as follows:
Average weekly overtime earnings ($):
Under 1
1 but
Algebra.Com
Question 1205386: The average weekly overtime earnings from a sample of workers from a particular
service industry were recorded as follows:
Average weekly overtime earnings ($):
Under 1
1 but under 2
2 but under 5
5 but under 10
10 or more
Number of workers
19
29
17
12
3
Total= 80
Do average weekly overtime earnings follow a Normal distribution?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
as your data has an open category at the end, you have a dilemma because you want to find the midpoint of the different categories and the last category has a beginning of 10 but does not have an endpoint shown.
in real life, you would have to look at the data to determine what the endpoint of the 10 and up category would be.
if you couldn't find the data, you would need to make up some assumptions about what that endpoint could possibly be so that you could determine a midpoint.
the data is assumed to be discrete because the smallest unit is most likely a penny.
0 < 1 gives a width of 1 minus 0 = 1 minus .01 = .99
divide that by 2 and add it to 0 to get 0 + .99/2 to get a midpoint of .495.
1 < 2 gives a width of 2 minus 1 = 1 minus .01 = .99.
divide that by 2 and add it to 1 to get 1 + .99/2 to get a midpoint of 1.495.
2 < 5 gives a width of 5 - 2 = 3 minus .01 = 2.99.
divide that by 2 and add it to 2 to get 2 + 1.495 to get a midpoint of 3.495.
5 < 10 give a width of 10 - 5 = 5 minus .01 = 4.99.
divide that by 2 and add it to 5 to get 5 + 4.99/2 to get a midpoint of 7.495.
for 10 or greater, you need to make some assumptions.
your answer would be dependent on those assumptions, so they would need to be described when providing the total average because the total would be based on what assumptions you used.
since your current week only has 3 occurrences in the 10 and over category, you would need to look at the individual values and come up with the maximum number of hours so you could determine a midpoint.
for example, if the 3 occurrences were 12, 15, and 19, then your greatest value is 19 and your formula for the midterm would be 10 + (19-10)/2 = 14.5.
based on that, your last category of 10 or greater would be assumed to have a midpoint of 14.5.
you would then be able to calculate the mean by using the midpoint of the categories and the number of occurrences for those categories.
i used the calculator at https://stats.libretexts.org/Learning_Objects/02%3A_Interactive_Statistics/08%3A_Mean_and_Standard_Deviation_for_Grouped_Frequency_Tables_Calculator to calculate the mean of the grouped data.
the overall mean of overtime dollars per week was calculated to be 3.0703 which can be rounded to 3.07.
that's an average of 3 dollars and 7 cents in overtime dollars for the week.
the results from the use of the calculator are shown below.
once again, that last category was based on assumptions and those assumptions would need to be communicated when presenting the results.
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