Given:
19, 25, 35, 38, 41, 49, 50, 52, 99
Just upon looking at the data set, I can determine that there is an OUTLIER. An outlier is a point that is distant from other points.
The outlier in this data set is number 99.
These data set has the following five number summary:
1) minimum number - 19
2) 1st quartile - 30
3) 2nd quartile or median - 41
4) 3rd quartile - 51
5) maximum number - 99
Interquartile range = q3 - q1 → 51 - 30 = 21
To determine if an observation point is an outlier, we need to determine the lower fence and the upper fence.
lower fence = q1 - 1.5(iqr)
lower fence = 30 - 1.5(21) → 30 - 31.5 = -1.5
upper fence = q3 + 1.5(iqr)
upper fence = 51 + 1.5(21) → 51 + 31.5 = 82.50
Any number outside the lower fence, -1.5, and upper fence, 82.50, is an OUTLIER.
99 is beyond the upper fence. Thus, it is an outlier.