Final answer:
After calculating the IQR and determining the bounds for potential outliers, the only outlier in the given dataset {79, 76, 82, 83, 84, 86, 85, 84, 84, 85, 88} is the value 76.
Step-by-step explanation:
To determine if there are any outliers in the data set {79, 76, 82, 83, 84, 86, 85, 84, 84, 85, 88}, we can use the interquartile range (IQR) test. First, we arrange the data in ascending order and then find the first quartile (Q1) and third quartile (Q3). The IQR is the difference between Q3 and Q1, and outliers are typically defined as those data points that fall below Q1 - 1.5*IQR or above Q3 + 1.5*IQR.
Arranged data: {76, 79, 82, 83, 84, 84, 84, 85, 85, 86, 88}
Q1 (1st quartile): 82
Q3 (3rd quartile): 85
IQR: Q3 - Q1 = 85 - 82 = 3
Lower bound for outliers: Q1 - 1.5*IQR = 82 - (1.5*3) = 77.5
Upper bound for outliers: Q3 + 1.5*IQR = 85 + (1.5*3) = 89.5
Since 76 is below our lower bound of 77.5, it is an outlier. However, 88 is not an outlier since it is less than our upper bound of 89.5. Thus, the outlier in this dataset is 76.