Q10. Use the following outputs regarding the lengths (in minutes) of 50 surgerie

Question

Q10. Use the following outputs regarding the lengths (in minutes) of 50 surgeries to answer the following questions. (Note: they are all whole numbers) 6 449 01112334444555555666778899 80011122233346899 9 0024 10 / 120 Stabistics 80 33653 eness a) What is the minimum? b) What is the maximum? c) What is the range? d) What is the interquartile range (IQR)? e) Why might a researcher prefer to report the IQR instead of the range? 1) How should one calculate whether a value is an outier g) What are the two cutoff values that determine whether a value is an outlier in this distribution? What is the z-score of the person with the highest valye? What is the z-score of the person with the lowest value? What would happen to the SD if we removed the highest value? h) i)

Explanation / Answer

Q 10 ) The given output is of Stem and leaf chart

The Left side values denotes the Stem and the Right side values denotes the leaf

So , In the given data

First value is 6 / 449 corresponds to values 64 , 64 and 69 respectively

In above example 6 denotes the Stem and 4 , 4 , 9 are leaves

So, from the given output we get the data as below

a ) Minimum : By using excel command we can calculate the minimum value as

Put all the data in excel then use command  

=MIN ( select all the data )

We get the minimum = 64 .............( answer )

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B ) Maximum : By using excel command we can calculate the maximum value as

Put all the data in excel then use command  

=MAX ( select all the data )

We get the Maximum = 120 .............( answer )

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C ) Range = Maximum - minimum = 120 - 64 = 56   .............( answer )

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D ) Interquartile range : It can be calculated as

IQR = Q3 - Q1

Where Q3 = Third Quartile and

Q1 = First Quartile

Q1 and Q3 both are calculated by using excel as

Put all the data in excel worksheet then use command

For Q1 =Quartile(Array,1)

For Q3   =Quartile(Array,3)

We get First Quartile = Q1 = 74

and Third Quartile = Q3 = 82.75

we get IQR = Q3 - Q1 = 82.75 - 74 = 8.75 .............( Answer ).

Data 64 64 69 70.00 71 71 71 72 73 73 74 74 74 74 75 75 75 75 75 75 76 76 76 77 77 78 78 79 79 80 80 81 81 81 82 82 82 83 83 83 84 86 88 89 89 90 90 92 94 120

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