The manager of a local fast food restaurant is interested in improving the servi
ID: 1143280 • Letter: T
Question
The manager of a local fast food restaurant is interested in improving the service provided to customers who use the restaurant's drive up window. the manager ask his assistant to record the time(in minutes) it takes to serve 200 customers at the final window in the facility's drive up system. the following 50 customer service times are observed for an hour in the day.
Chapter Three Sry Seatintia 62 0.0774 0.09530.13380.1645 0.1788 0.1880 0.2041 0.22400.2303 0.2426 0.2641 0.27150.27980.29900.30190.31810.3374 0.3475 0.3534 0.3538 0.3734 0.37460.37980.3799 0.3845 0.3996 0.4029 0.4145 0.4152 0.4184 042330.42570.4259 0.4434 0.4573 0.4629 0.46290.47140.48410.5007 0.50710.5117 0.5162 0.5168 0.51770.5179 0.5219 0.5227 0.53430.5344 a. Compute the summary statistic that hest measures the central tendency or norm in these data b. Compute the summary statisticis) that best measures the variation in these data c. Show whether there are any outliers in these data. d. What is the 9uüth percentile of these data?Explanation / Answer
a).
Consider the given problem here the best measure of “central tendency” is given by the “mean of these observation”.
=> Mean = (1/n)*summation(Xi) = (18.5668/50) = 0.3713.
b).
Now, the summary statisitics that best measures the variance in these data is given by “standard deviation” of these data.
=> standard deviation = square root[(1/n)*summation(Xi - X bar)^2] = square root[0.7712/50].
=> Standard Deviation = 0.1242.
c).
So, here the “1st quartile” is given by, “Q1 = (1/4)*50 = 12.5 = 13th term is “Q1=0.2798”.
Similarly, the “3rd quartile” is given by, “Q3 = (3/4)*50 = 37.5 = 38th term is “Q3=0.4714”.
So, the “IQR” is given by “Q3-Q1=0.1916”. Now, any numbers lower than “Q1-1.5*IQR” and more than “Q3+1.5*IQR”, will be consider as an “outlier”.
=> Q1 - 1.5*IQR = 0.2798 - 1.5*0.1916 = (-0.0076).
=> Q3 + 1.5*IQR = 0.4714 + 1.5*0.1916 = 0.7588.
So, any observation outside the range from “(-0.0076) to 0.7588” will be considered as an “outlier”.
d).
Now, the “90th” per centile is given by.
=> “90/100*50 = 45th term will be the “90th” percentile, => “90th percentile” is given by “0.5177”.
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