Question

2. A sample was taken of flights arriving at a major airport to study the problem of air traffic delays. The table below shows the numbers of minutes late for a sample of 100 flights. Minutes Late Number of Flights 0-10 29 10-20 23 20-30 30-40 40-50 50-60 17 14 11 6 (a) Draw the histogram. (b) Use the mid-point assumption to estimate the sample mean number of minutes late. (c) Use the mid-point assumption to estimate the sample MAD, sample variance and standard deviation

Answer 1

interval = c("0 - 10", "10 - 20", "20 - 30", "30 - 40", "40 - 50", "50 - 60" lower_limit = c(0, 10, 20, 30, 40, 50) upper_limit = c(10, 20, 30, 40, 50, 60) mid_point = (lower_limit + upper_limit)/2 number_of_flights = c(29, 23, 17, 14, 11, 6) dataframe = data.frame(interval, lower_limit, upper_limit, mid_point, number_of_flights) ## a part of the question names (number_of_flights) = interval barplot(number_of_flights, space = 0, xlab = "Minutes Late", ylab = "Number of Flights") 25 20 15 Number of Flights 10 5 0 0 - 10 20-30 40-50 Minutes Late

Minute lauke Camilative Eug 29 52 medronclou Number of Mid - flight (ti) Point (re) 29 23 17 35 us 55 0-10 10-20 20-30 30-40 Yo-50 so-60 69 83 au 100 b) formula for mais I bill? 2230 - 2203 Ebi 100 c) Formula fae median l + h ( Z -c) la lowe day bonday of media clay ha size of the meolion class interval f= Freg, come spond to the media classe Na Ebi ea cof cumulation free of preceding media class thue au loo ohs so the median is the 50th a sith Edar obs they lie in 10-20 so Media = 10 + 10 (100 - 29) = 19.13 43

MAD formula is = Ibilx-xl Ili when yo mean afte calculating we get I filx, adil = 1339.2 A[fi= 100 MAD = 133902 - 13.392 102 Valace formand for groupled data is = [f. (x,- M ² 26 El (x - x)2 = 24301 [fr=100 - Varsan = 2437) = 243.71 100 the " Sarple s.d = I sample varian = J243.71 : 15.6112)