Question

In: Math

Please find the range, sample standard deviation and inter-quartile range (IQR) of the following data set...

Please find the range, sample standard deviation and inter-quartile range (IQR) of the following data set using TI-84.

34 41 44 46 46 50 54 69 80 96


range = _____ (Please enter an exact answer.)
standard deviation (ss) = _______ (Please show your answer to one decimal place.)
Inter-Quartile-Range (IQR) = ________ (Please enter an exact answer.)

A new number, 112, is added to the data set above. Please find the new range, sample standard deviation and IQR of the new data set.

range = ____ (Please enter an exact answer.)
standard deviation (ss) = ______ (Please show your answer to one decimal place.)
IQR = _____ (Please enter an exact answer.)

Which measure of spread is less affected by the addition of the extreme observation?

  • IQR
  • Range
  • standard deviation

Solutions

Expert Solution

We have the Data as :

34
41
44
46
46
50
54
69
80
96

If Population standard deviation is required then the formula is :

Range = 62

Sample standard deviation = 19.5

Population standard deviation = 18.5
Inter-Quartile-Range (IQR) = Q3 - Q1 = 71.75 - 43.25 = 28.5

Now, A new number, 112, is added to the data set above

We have the Data as :

34
41
44
46
46
50
54
69
80
96
112

If Population standard deviation is required then the formula is :

Q1 = 44

Q3 = 80

Range = 78

Sample standard deviation = 25.1

Population standard deviation = 23.9
Inter-Quartile-Range (IQR) = Q3 - Q1 = 80 - 44 = 36

We can see that IQR is changed least by addition of extreme observation

Hence, measure of spread which is less affected by the addition of the extreme observation is IQR


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