Question

# Choose either column D or E of the attached data set and analyze using the techniques...

Choose either column D or E of the attached data set and analyze using the techniques discussed in class up to this point. This includes the following:

Find the appropriate measure of center. Discuss why the chosen measure is most appropriate. Why did you decide against other possible measures of center?

Find the appropriate measure of variation. The measure of variation chosen here should match the measure of center chosen in Part 1.

Find the graph(s) needed to appropriately describe the data. These may be done by hand and inserted into the Word document. You can also use Excel to create a Histogram of the chosen data.

Define a random variable (X) so that your chosen data set represents values of X.

Is your chosen random variable discrete or continuous? Explain how you know.

Would the Normal or Binomial distribution be a good fit for the underlying sample distribution of X? If one of them is a good fit, state how you would approximate the distribution parameters (Use the mean and standard deviation of the data chosen)

Calculate the probability that a flight will depart early or on-time OR arrive early or on time using the empirical or relative frequency definition of probability.

Calculate the probability that a flight will arrive late OR depart late using the empirical or relative frequency definition of probability.

Assume now that the random variable X=Arrival Time is exactly normally distributed with mean m= -2.5 and standard deviation s= 23. Compute the probability of a flight arriving late based on this new information. Does this contradict your answer from Part 8?

 Year DAY_OF_MONTH DAY_OF_WEEK DEP_Delay ARR_Delay 2015 13 2 -13 -17 2015 13 2 -17 -11 2015 13 2 -14 -12 2015 13 2 -13 -13 2015 13 2 3 7 2015 13 2 -15 -23 2015 13 2 3 8 2015 13 2 11 6 2015 13 2 -20 -1 2015 13 2 -19 -12 2015 13 2 -22 0 2015 13 2 -18 -16 2015 13 2 -27 -21 2015 13 2 -27 30 2015 13 2 -25 -27 2015 13 2 -28 24 2015 13 2 -30 -29 2015 13 2 -28 24 2015 13 2 -32 -5 2015 13 2 -32 0 2015 13 2 -37 -37 2015 13 2 -37 10 2015 13 2 6 -34 2015 13 2 7 26 2015 13 2 -18 -10 2015 13 2 -20 7 2015 13 2 15 -17 2015 13 2 -13 -18 2015 13 2 -22 0 2015 13 2 -18 -16 2015 13 2 -18 -1 2015 13 2 -19 -16 2015 13 2 -27 -13 2015 13 2 -23 6 2015 13 2 -26 -11 2015 13 2 -21 -5 2015 13 2 -26 -9 2015 13 2 25 20 2015 13 2 10 0 2015 13 2 -33 -28 2015 13 2 -27 -18 2015 13 2 -33 -31 2015 13 2 3 -32 2015 13 2 12 15 2015 13 2 13 20 2015 13 2 14 12 2015 13 2 0 0 2015 13 2 -14 -3 2015 13 2 18 17 2015 13 2 -13 7 2015 13 2 12 36 2015 13 2 9 22 2015 13 2 -15 -19 2015 13 2 -24 5 2015 13 2 -20 15 2015 13 2 -26 2 2015 13 2 -28 -3 2015 13 2 -27 1 2015 13 2 9 1 2015 13 2 -29 -16 2015 13 2 -27 1 2015 13 2 -28 -3 2015 13 2 6 4 2015 13 2 -30 -7 2015 13 2 34 16 2015 13 2 -28 6 2015 13 2 18 1 2015 13 2 -33 -13 2015 13 2 -17 -11 2015 13 2 -3 -16 2015 13 2 0 -15 2015 13 2 -17 -20 2015 13 2 2 -31 2015 13 2 6 7 2015 13 2 16 14 2015 13 2 -20 -27 2015 13 2 7 24 2015 13 2 23 40 2015 13 2 -21 -16 2015 13 2 -24 -18 2015 13 2 -27 -2 2015 13 2 12 10 2015 13 2 -27 -18 2015 13 2 -32 3 2015 13 2 -31 -20 2015 13 2 -25 0 2015 13 2 -34 -20 2015 13 2 -32 -11 2015 13 2 8 -22 2015 13 2 0 0 2015 13 2 -34 -24 2015 13 2 -9 -8 2015 13 2 6 2 2015 13 2 -15 -7 2015 13 2 -11 21 2015 13 2 -20 -28 2015 13 2 -19 -27 2015 13 2 -22 6 2015 13 2 -24 -9 2015 13 2 -23 9 2015 13 2 -20 -33 2015 13 2 8 38 2015 13 2 -23 -16 2015 13 2 -26 -35 2015 13 2 -29 -30 2015 13 2 -28 -42 2015 13 2 -23 -28 2015 13 2 -31 -6 2015 13 2 -27 9 2015 13 2 -31 -12 2015 13 2 20 13 2015 13 2 -32 -12 2015 13 2 -32 -15 2015 13 2 -30 0 2015 13 2 1 -11 2015 13 2 -13 -4 2015 13 2 -14 15 2015 13 2 -19 -27 2015 13 2 1 3 2015 13 2 -12 -9 2015 13 2 -21 -4 2015 13 2 -19 -15 2015 13 2 0 -2 2015 13 2 5 7 2015 13 2 -20 -15 2015 13 2 -26 -35 2015 13 2 17 19 2015 13 2 6 2 2015 13 2 -24 -26 2015 13 2 -29 5 2015 13 2 -32 -9 2015 13 2 -30 -38 2015 13 2 -31 -34 2015 13 2 0 -34 2015 13 2 -35 -11 2015 13 2 -32 -14 2015 13 2 5 -18 2015 13 2 15 17 2015 13 2 13 13 2015 13 2 -16 -2 2015 13 2 -15 5 2015 13 2 -16 -23 2015 13 2 -17 -11 2015 13 2 14 23 2015 13 2 3 13 2015 13 2 -25 -26 2015 13 2 9 -7 2015 13 2 -25 18 2015 13 2 -25 -10 2015 13 2 0 -7 2015 13 2 -25 -30 2015 13 2 25 22 2015 13 2 -24 -6 2015 13 2 -25 -18 2015 13 2 0 -32 2015 13 2 -33 -30 2015 13 2 -32 -34 2015 13 2 24 7 2015 13 2 8 11 2015 13 2 -37 -22 2015 13 2 7 -38 2015 13 2 -17 -10 2015 13 2 -18 -1 2015 13 2 -20 -2 2015 13 2 0 -15 2015 13 2 2 1 2015 13 2 -15 13 2015 13 2 -23 -9 2015 13 2 -23 1 2015 13 2 4 -23 2015 13 2 1 3 2015 13 2 -23 20 2015 13 2 -26 8 2015 13 2 0 -7 2015 13 2 0 -12 2015 13 2 -25 -28 2015 13 2 -28 -18 2015 13 2 -33 -27 2015 13 2 -31 2 2015 13 2 -27 9 2015 13 2 23 4 2015 13 2 8 11 2015 13 2 21 17 2015 13 2 1 27 2015 13 2 4 22 2015 13 2 -16 6 2015 13 2 15 0 2015 13 2 0 24 2015 13 2 2 11 2015 13 2 -13 -16 2015 13 2 -17 -3 2015 13 2 1 0 2015 13 2 -23 -21 2015 13 2 -19 -16 2015 13 2 -25 -13 2015 13 2 -20 8 2015 13 2 -20 -24 2015 13 2 -24 -18 2015 13 2 -27 -15 2015 13 2 -23 -24 2015 13 2 -31 -18 2015 13 2 -20 -8 2015 13 2 -34 -26 2015 13 2 1 6 2015 13 2 -35 -16 2015 13 2 -36 -21 2015 13 2 -12 -21 2015 13 2 0 2 2015 13 2 -12 -10 2015 13 2 -17 -26 2015 13 2 3 4 2015 13 2 -19 -36 2015 13 2 -20 -18 2015 13 2 -17 -21 2015 13 2 -19 -42 2015 13 2 -22 -17 2015 13 2 -26 -8 2015 13 2 -24 -8 2015 13 2 -21 -9 2015 13 2 -30 -10 2015 13 2 1 1 2015 13 2 -28 -21 2015 13 2 -28 1 2015 13 2 -30 -1 2015 13 2 -21 -4 2015 13 2 13 -26 2015 13 2 -31 -28 2015 13 2 -30 -11 2015 13 2 7 5 2015 13 2 2 12 2015 13 2 6 14 2015 13 2 19 16 2015 13 2 11 -32 2015 13 2 13 6 2015 13 2 -22 -20 2015 13 2 -19 -36 2015 13 2 -23 3 2015 13 2 0 2 2015 13 2 -18 -25 2015 13 2 8 0 2015 13 2 -21 -24 2015 13 2 -28 -3 2015 13 2 7 6 2015 13 2 -22 -3 2015 13 2 5 2 2015 13 2 30 4 2015 13 2 15 19 2015 13 2 23 6 2015 13 2 7 6 2015 13 2 11 12 2015 13 2 2 -24 2015 13 2 -37 -26 2015 13 2 -10 22 2015 13 2 5 0 2015 13 2 5 13 2015 13 2 9 -11 2015 13 2 0 -23 2015 13 2 -15 7 2015 13 2 -21 22 2015 13 2 5 -33 2015 13 2 3 -32 2015 13 2 7 28 2015 13 2 12 10 2015 13 2 -26 -24 2015 13 2 -29 -20 2015 13 2 -25 -17 2015 13 2 -21 11 2015 13 2 17 14 2015 13 2 -29 -38 2015 13 2 -27 -13 2015 13 2 -31 -7 2015 13 2 -35 -7 2015 13 2 28 7 2015 13 2 -33 -4 2015 13 2 -38 6 2015 13 2 15 6 2015 13 2 -14 0 2015 13 2 14 10 2015 13 2 0 -20 2015 13 2 -16 9 2015 13 2 -13 -22 2015 13 2 -19 -18 2015 13 2 14 15 2015 13 2 1 28 2015 13 2 1 -29 2015 13 2 -26 -21 2015 13 2 -28 3 2015 13 2 29 11 2015 13 2 17 29 2015 13 2 -30 7 2015 13 2 -25 -37 2015 13 2 -31 -38 2015 13 2 -34 -29 2015 13 2 10 9 2015 13 2 4 -39 2015 13 2 -28 -28 2015 13 2 -36 -17 2015 13 2 -36 -8 2015 13 2 -9 -7 2015 13 2 -18 -18 2015 13 2 8 -18 2015 13 2 -11 5 2015 13 2 -16 9 2015 13 2 13 10 2015 13 2 6 13 2015 13 2 -20 4 2015 13 2 2 -19 2015 13 2 -23 -18 2015 13 2 -17 -29 2015 13 2 -24 -21 2015 13 2 -27 -15 2015 13 2 24 19 2015 13 2 -24 -33 2015 13 2 -26 -18 2015 13 2 -27 -17 2015 13 2 -30 -24 2015 13 2 -34 2 2015 13 2 1 -37 2015 13 2 -28 -33 2015 13 2 -35 5 2015 13 2 -31 -31 2015 13 2 17 23 2015 13 2 -15 2 2015 13 2 -15 -9 2015 13 2 0 2 2015 13 2 -16 -9 2015 13 2 -21 8 2015 13 2 -18 -10 2015 13 2 22 5 2015 13 2 11 8 2015 13 2 16 -23 2015 13 2 -25 -19 2015 13 2 -26 -21 2015 13 2 -25 -17 2015 13 2 -22 -16 2015 13 2 -27 -20 2015 13 2 -30 -28 2015 13 2 -30 -26 2015 13 2 28 21 2015 13 2 2 -31 2015 13 2 -35 -29 2015 13 2 27 23 2015 13 2 9 3 2015 13 2 0 -26 2015 13 2 3 18 2015 13 2 0 4 2015 13 2 -13 -34 2015 13 2 -17 -38 2015 13 2 -17 -32 2015 13 2 -17 -18 2015 13 2 -17 -4 2015 13 2 -18 -5 2015 13 2 9 -17 2015 13 2 0 -19 2015 13 2 -22 7 2015 13 2 -24 -10 2015 13 2 14 11 2015 13 2 22 5 2015 13 2 -30 -8 2015 13 2 -30 -16 2015 13 2 -27 -14 2015 13 2 -27 -22 2015 13 2 3 10 2015 13 2 -33 6 2015 13 2 0 14 2015 13 2 -34 6 2015 13 2 2 -27 2015 13 2 -9 -13 2015 13 2 -11 -20 2015 13 2 3 5 2015 13 2 5 23 2015 13 2 -15 6 2015 13 2 -22 0 2015 13 2 -17 -33 2015 13 2 -21 -23 2015 13 2 -25 -22 2015 13 2 -21 -43 2015 13 2 -24 -16 2015 13 2 14 12 2015 13 2 -26 -13 2015 13 2 -22 -10 2015 13 2 17 -21 2015 13 2 -23 7 2015 13 2 -32 -19 2015 13 2 -31 -15 2015 13 2 -28 -5 2015 13 2 1 -25 2015 13 2 -27 -10 2015 13 2 -35 -16 2015 13 2 -36 2 2015 13 2 -16 12 2015 13 2 -17 6 2015 13 2 3 4 2015 13 2 -10 -6 2015 13 2 -16 -24 2015 13 2 -21 -9 2015 13 2 -19 -18 2015 13 2 -24 -37 2015 13 2 -22 -29 2015 13 2 -20 -18 2015 13 2 -27 10 2015 13 2 11 3 2015 13 2 -25 3 2015 13 2 -30 5 2015 13 2 -23 -11 2015 13 2 -27 -16 2015 13 2 -26 -4 2015 13 2 -27 -10 2015 13 2 -30 -6 2015 13 2 -24 -4 2015 13 2 -34 -12 2015 13 2 -33 -8 2015 13 2 -36 4 2015 13 2 -11 -7 2015 13 2 -13 -25 2015 13 2 2 -27 2015 13 2 4 -24 2015 13 2 -17 -18 2015 13 2 -13 -23 2015 13 2 20 5 2015 13 2 -17 -16 2015 13 2 -21 -31 2015 13 2 -25 -34 2015 13 2 -27 -25 2015 13 2 17 -13 2015 13 2 -27 -30 2015 13 2 -26 -27 2015 13 2 -29 -39 2015 13 2 3 -16 2015 13 2 -31 1 2015 13 2 -24 -17 2015 13 2 3 0 2015 13 2 23 7 2015 13 2 -33 -6 2015 13 2 -34 -10 2015 13 2 -34 1 2015 13 2 -6 -6 2015 13 2 7 7 2015 13 2 -13 -3 2015 13 2 -18 -15 2015 13 2 -17 -17 2015 13 2 -19 -12 2015 13 2 -15 -16 2015 13 2 -22 -19 2015 13 2 -21 -18 2015 13 2 -16 -18 2015 13 2 27 19 2015 13 2 11 7 2015 13 2 -24 -16 2015 13 2 -26 1 2015 13 2 -29 -27 2015 13 2 -28 -27 2015 13 2 -31 -33 2015 13 2 -32 28 2015 13 2 28 18 2015 13 2 12 -37 2015 13 2 30 14 2015 13 2 -33 -35 2015 13 2 -34 -13 2015 13 2 0 -14 2015 13 2 -15 -14 2015 13 2 -19 -11 2015 13 2 -15 -5 2015 13 2 12 4 2015 13 2 15 20 2015 13 2 3 12 2015 13 2 19 17 2015 13 2 22 19 2015 13 2 -25 -20 2015 13 2 -22 -27 2015 13 2 -28 -1 2015 13 2 -27 0 2015 13 2 -25 9 2015 13 2 3 -32 2015 13 2 -21 0 2015 13 2 -25 -14 2015 13 2 10 9 2015 13 2 -33 3 2015 13 2 -34 -31 2015 13 2 -35 1 2015 13 2 0 -31 2015 13 2 3 -32 2015 13 2 -6 -34 2015 13 2 -18 -35 2015 13 2 6 -40 2015 13 2 9 5 2015 13 2 -12 -3 2015 13 2 -21 -17 2015 13 2 -20 2 2015 13 2 -21 11 2015 13 2 20 20 2015 13 2 -26 5 2015 13 2 -16 -19 2015 13 2 -27 -23 2015 13 2 -21 -5 2015 13 2 26 13 2015 13 2 -29 -17 2015 13 2 -28 -19 2015 13 2 -28 -17 2015 13 2 -31 -15

above table calculated in excel via Data tab -> Data Analysis Tool pack -> Descriptive Statistics

1)Measures of central tendency are mean, median , mode,

since the data is skewed in both dep_delay and ARR_DELAY

we will use median as Measures of central tendency

2)among standrd devaition and interquartile range(IQR)

IQR is  best measure of dispersion(also we use median as measure of central tendency)

3)DEP_DELAY box plot

number of departures on early(excel formula)

=countif(-13,-17,-14............,"<0")

=334

number of departures on time(excel formula)

=countif(-13,-17,-14............,"=0")

=22

number of departures late(excel formula)

=countif(-13,-17,-14............,">0")

=144

total departures,n=144+22+334=500

probability that a flight will depart early or on-time=(334+22)/500=0.712

probability that a flight will depart late=144/500=0.288

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