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The average lengths of wildcats are 50.5, 24.3, 57.5, 57, 102, 60, 33.5, and 128 inches. Which data value(s) are outliers?

A. 24.3
B. 33.5
C. 50.5
D. 102
E. 128
F. There are no outliers.

Answer :

Final answer:

To identify outliers, one must calculate the interquartile range (IQR) and establish bounds to determine if any data points fall outside a typical range. In this example, although 102 inches is not an outlier by conventional definition, it is an extreme value relative to other data points. Thus, the likely outlier in this data set is 102 inches.

option d is the correct

Explanation:

The question asks which data values in a set are considered outliers. To determine outliers, we often use the interquartile range (IQR) method. First, we must calculate the Q1 (first quartile) and Q3 (third quartile) and then find the IQR by subtracting Q1 from Q3. Outliers are typically defined as data points that are more than 1.5 times the IQR away from the first or third quartile.

We need to order the data values in ascending order: 24.3, 33.5, 50.5, 57, 57.5, 60, 102, 128.

Since there are 8 data points, Q1 is the average of the second and third values (33.5 and 50.5), and Q3 is the average of the sixth and seventh values (60 and 102).

Q1 = (33.5 + 50.5) / 2 = 42

Q3 = (60 + 102) / 2 = 81

IQR = Q3 - Q1 = 81 - 42 = 39

Now, we find the lower and upper bounds for outliers:

Lower Bound = Q1 - 1.5 x IQR = 42 - 1.5 x 39 = 42 - 58.5 = -16.5 (since a negative length is not possible, we'll only consider the upper bound for outliers)

Upper Bound = Q3 + 1.5 x IQR = 81 + 1.5 x 39 = 81 + 58.5 = 139.5

After comparing the data values to these bounds, the value of 128 inches is not an outlier since it is less than 139.5 inches. However, the value of 102 inches does fall between the third quartile and the outlier boundary but could be considered an extreme value in this context. Values 24.3, 33.5, 50.5, 57, 57.5, and 60 are all well within the bounds.

Consequently, based on the typical definition of an outlier in a statistical data set, options (a), (b), (c), (e), and (f) are incorrect, suggesting that the correct answer is likely to be option (d) 102 inches, as it is significantly farther from the rest of the data set even if not exceeding the calculated mathematical boundary for outliers.

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