Loren’s friends jump as far as they can and record their results in inches. Their results include the observations 42, 47, 50, 42, 45, 41, 49, 51, and 44. Which number, if added to the dataset, would represent an outlier in the data?
An outlier is a data point that is significantly different from the other data points in a dataset. To determine if a number would be an outlier in this dataset, we can calculate the interquartile range (IQR) and use that to identify any data points that fall more than 1.5 times the IQR above the third quartile or below the first quartile.
First, let's organize the data in ascending order:
41, 42, 42, 44, 45, 47, 49, 50, 51
Next, let's calculate the first quartile (Q1), third quartile (Q3), and the interquartile range (IQR).
Q1 = (42 + 42) / 2 = 42
Q3 = (49 + 50) / 2 = 49.5
IQR = Q3 - Q1 = 49.5 - 42 = 7.5
Now, let's determine the lower and upper bounds for identifying outliers:
Lower Bound = Q1 - 1.5 * IQR = 42 - 1.5 * 7.5 = 42 - 11.25 = 30.75
Upper Bound = Q3 + 1.5 * IQR = 49.5 + 1.5 * 7.5 = 49.5 + 11.25 = 60.75
Any data point that falls below 30.75 or above 60.75 would be considered an outlier.
Checking the data in the dataset, all numbers are between 30.75 and 60.75, so adding any number outside of this range would be considered an outlier. For example, if the number 70 were added to the dataset, it would be considered an outlier.