Question

What can be determined about this data set before finding the range or the interquartile range? 19, 25, 35, 38, 41, 49, 50, 52, 99

Answer 1

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.

Answer 2

The data has an outlier, but the interquartile range will not change. The answer is c