Final answer:
In the data provided, the number '27' is identified as an outlier using the interquartile range method; values below 60.5 or above 104.5 would be considered outliers in this data set.
Step-by-step explanation:
You have a question about identifying outliers in a given set of data. The data set represents the number of laps completed by members of a swim team: 27, 76, 77, 80, 82, 83, 86, 88, 88, 90. To identify outliers, we can use the interquartile range (IQR) method. First, we order the data from smallest to largest, which you've provided. Next, we find the median (the middle value) of the upper and lower halves of the data to determine the first and third quartiles (Q1 and Q3).
The data is already ordered, so our next step is to find Q1 and Q3. Q1 is the median of the first half: 27, 76, 77, 80, 82, which is 77. Q3 is the median of the second half: 83, 86, 88, 88, 90, which is 88. Now, calculate the IQR: Q3 - Q1 = 88 - 77 = 11. Next, we calculate the boundaries for potential outliers by multiplying the IQR by 1.5 and adding this figure to Q3 for the upper bound and subtracting from Q1 for the lower bound. That gives us: Lower Bound = Q1 - 1.5(IQR) = 77 - 1.5(11) = 60.5, and Upper Bound = Q3 + 1.5(IQR) = 88 + 1.5(11) = 104.5.
Any number below 60.5 or above 104.5 is considered an outlier. In this set, the number 27 is below the lower bound, so it is considered an outlier.