In: Math
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?
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