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The most appropriate measure of center of this data set would be the median, or the arithmetic average. The median would be more suitable because the mean is more heavily influenced by outliers. In a skewed distribution, the mean would be pulled more towards the tail of the data where outliers exist, and the average value would be greater than that of the median. In this case, using the 1.5 x IQR rule, any departure time less than 19.5 or greater than 16.5 is an outlier. Hence, with multiple outliers present in the data, the median would not be influenced as heavily as the mean by outliers, and would give a more accurate representation of the average value of the set. (Refer to spreadsheet). The measure of variation that corresponds with*…show more content…*

If a point value is indicated by an equal or positive sign, this shows that the flight departed on time or late. The chosen random variable would be discrete. Although the data set is a large sample size of 500 values, it is still possible to list out all the outcomes of the data as a fixed set and assign probabilities to them. The values for departure delay times are also inputted as whole positive and negative integers with no decimal values. Decimal values are characteristic of a continuous random variable for an infinite sample space. Therefore, this another indicator that a discrete random variable would be ideal for a finite sample space. The binomial distribution would be suitable for the underlying distribution of X because a data point must either lie within or outside of the interval of a delayed departure. Hypothetically, if a value lies outside the range of -10 and 130, then this would mean that the flight will cancelled. A flight cannot depart to its destination too early or too late, as it would be considered an unreliable flight. Therefore, any time of departure that exceeds -10 or 130 cannot exist. The probability that a flight will depart early or on-time is 71.0%. The probability that a flight will arrive late is 36.0%. The probability that a flight departs late or arrives early is 83.4%. Compared to each individual events’ probabilities of departing early or on-time or arriving late, this percentage indicates that the chances of a

If a point value is indicated by an equal or positive sign, this shows that the flight departed on time or late. The chosen random variable would be discrete. Although the data set is a large sample size of 500 values, it is still possible to list out all the outcomes of the data as a fixed set and assign probabilities to them. The values for departure delay times are also inputted as whole positive and negative integers with no decimal values. Decimal values are characteristic of a continuous random variable for an infinite sample space. Therefore, this another indicator that a discrete random variable would be ideal for a finite sample space. The binomial distribution would be suitable for the underlying distribution of X because a data point must either lie within or outside of the interval of a delayed departure. Hypothetically, if a value lies outside the range of -10 and 130, then this would mean that the flight will cancelled. A flight cannot depart to its destination too early or too late, as it would be considered an unreliable flight. Therefore, any time of departure that exceeds -10 or 130 cannot exist. The probability that a flight will depart early or on-time is 71.0%. The probability that a flight will arrive late is 36.0%. The probability that a flight departs late or arrives early is 83.4%. Compared to each individual events’ probabilities of departing early or on-time or arriving late, this percentage indicates that the chances of a

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