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PS_1_Solution

# Observe thatpercentcalculationrequiresorderingthedata

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Unformatted text preview: 3,00% 23,00% 5,10% 5,10% 5,10% 5,10% 5,10% 5,10% 5,10% 0,00% 0,00% 02 March 2011 • In Excel follow the route Data ‐> Data Analysis ‐> Rank and Percentile • Select the data as “Input Range” • Select a free cell for “Output Range” and click “OK” You will obtain a summary result as given here. Observe that percent calculation requires ordering the data. Note: If we do not have any information about the distribution of the population, we can still calculate quartiles from sample roughly. In this case, follow these steps: • Order your data from smallest to largest. Let s be the smallest data and L be the largest data in the sample. In this example, s = 110 and L= 558. • Calculate sample median. This will be the 50th percentile (second quartile). In this example, it is 117. • Divide the data into two as o Case 1: even sample size first part is from s to the largest data smaller than median second part is from smallest data larger than median to L o Case 2: odd sample size first part is from s to median second part is from median to L • Calculate the median of the first part. This will be the 25th percentile (first quartile). In this example, it is 112. • Calculate the median of the first part. This will be the 75th percentile (third quartile). In this example, it is 123,5. We will use this method when we are preparing a box plot for our sample. 02 March 2011 (b) Construct a histogram and a pareto chart for the data set. Set up a relative frequency distribution and give a relative frequency histogram. To construct a histogram: • In Excel follow the route Data ‐> Data Analysis ‐> Histogram • Select the data as “Input Range” • Select a free cell for “Output Range” • Mark “Chart Output” and click “OK” You will obtain a histogram and the underlying frequency distribution as follows: Histogram Frequency Bin Frequency 110 2 184,6667 37 259,3333 0 334 0 408,6667 0 483,3333 0 More 1 40 30 20 10 0 Frequency Bin Remember that the number of bins in a histogram is important. If there are too many and too few bins, you may not reveal the patterns of your data in the histogram. You can find the tips to build an effective histogram in document “CH1 Descriptive Statistics.pdf” loaded in moodle. To construct a pareto chart: • In Ex...
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