Statistics

For the following data set, approximate the sample standard deviation of commuting times per day

Commute ( in min) Frequency
50-52 5
53-55 8
56-58 12
59-61 13
62-64 11


The answer to this problem is 3.9. I have been working on this problem for 3hours trying to figure out how to get to that answer of 3.9. Need help real bad

I get 3.811685 - pretty close.

Use your standard definitions.

Pick the midpoints: 51, 54, 57, 60, 63

Calculate the mean: (51*5 + 54*8 + 57*12 + 60*13 + 63*11)/(5+8+12+13+11) = 2844/49 = 58.04082

Calculate the second moment: (51*51*5 + 54*54*8 + 57*57*12 + 60*60*13 + 63*63*11) = 165,780

Calculate the variance: (165780/49) - (58.04082)^2 = 14.52895

Calculate the Standard Deviation: sqrt(14.52895) = 3.811685

If I was allowed only one decmal place, that would be 3.9. Going smaller is unacceptable.