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More on Z Scores and how to calculate IQR and Fences (determining cutoff points for Outliers)
Example: The following data represent the number of inches of ran in Chicago, Illinois, during the month of April for 20 randomly selected years.
|
2.47 |
3.97 |
3.94 |
4.11 |
|
1.14 |
4.02 |
3.41 |
1.85 |
|
5.22 |
0.97 |
6.14 |
2.34 |
|
3.48 |
4.77 |
2.78 |
4.00 |
|
6.28 |
5.50 |
7.69 |
5.79 |
(a) Compute the z-score corresponding to the rainfall in 1971, 0.97 inches. Interpret this result
(b) Determine the quartiles.
(c) Compute the interquartile range, IQR.
(d) Determine the lower and upper fences. Are there any outliers, according to this criterion?
Press
STAT and select 1: Edit. Clear L1 and then enter the data. Press STAT highlight
CALC, select 1:1-Var Stats, and press 2nd
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ENTER.
The sample mean and standard deviation appear on the first screen. Scroll down
to the 2nd screen to find the quartiles. Q1 is the first quartile,
Med is the 2nd quartile (or median) and Q3 is the third quartile.
(a.) To calculate the Z-score for the data point 0.97 inches, do the following calculation: (0.97-sample mean)/sample standard deviation.
(c.) The interquartile range (IQR) is Q3-Q1.
(d.) The lower fence is Q1-1.5*IQR. The upper fence is Q3+1.5*IQR.