Question

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?(1 point)
Responses

40
40

44
44

72
72

52

Answer 1

To determine which number would represent an outlier in the data, we need to calculate the interquartile range (IQR) and identify any values that fall outside of the range.

First, we need to arrange the data in ascending order:

41, 42, 42, 44, 45, 47, 49, 50, 51

Next, we can calculate the first quartile (Q1), third quartile (Q3), and the IQR:

Q1 = 42
Q3 = 49
IQR = Q3 - Q1 = 49 - 42 = 7

Using the IQR, we can identify any values that fall outside of the range:

Lower fence = Q1 - (1.5 * IQR) = 42 - (1.5 * 7) = 31.5
Upper fence = Q3 + (1.5 * IQR) = 49 + (1.5 * 7) = 59.5

Any value that is less than the lower fence or greater than the upper fence would be considered an outlier.

Comparing the given options:
1. 40 falls within the range and is not an outlier.
2. 44 is already included in the dataset and is not an outlier.
3. 72 is greater than the upper fence and would be considered an outlier.
4. 52 falls within the range and is not an outlier.

Therefore, the number that would represent an outlier in the data is 72.