Loren's friends jump as far as they can and record their results in inches.

Question

Their results include the observations 42, 47, 50, 42, 45,41,49,51,44
Which number, 72, 44, 40, 52, if added to the dataset would represent an outlier in the data?

Answer 1

The number 72 would be considered an outlier in the data set.

To determine if a number is an outlier, we can use the formula for finding outliers which is:

1. Calculate the Interquartile Range (IQR) by finding the difference between the Upper Quartile (Q3) and the Lower Quartile (Q1).
2. Multiply the IQR by 1.5.
3. Add this result to Q3 to find the upper bound, and subtract it from Q1 to find the lower bound.
4. Any number outside of these bounds would be considered an outlier.

Using the dataset provided:
Q1 = 42.5
Q3 = 49
IQR = 49 - 42.5 = 6.5
1.5 * IQR = 9.75

Lower bound = Q1 - 1.5 * IQR = 42.5 - 9.75 = 32.75
Upper bound = Q3 + 1.5 * IQR = 49 + 9.75 = 58.75

Since 72 is greater than the upper bound of 58.75, it would be considered an outlier in the dataset.