Final answer:
To identify outliers in a data set represented by quartiles, calculate the interquartile range (Q3 - Q1), then use the formula for upper and lower bounds. Any value outside the bounds is an outlier. In this case, the value 83 is an outlier.
Step-by-step explanation:
To determine which value in the data set is an outlier, we need to understand the concept of outliers. An outlier is a data point that is significantly different from other values in the data set. In this case, the first quartile (Q1) is 41 and the third quartile (Q3) is 57.
To identify outliers, we can use the formula:
Upper Bound = Q3 + 1.5 * IQR
Lower Bound = Q1 - 1.5 * IQR
Where IQR is the interquartile range (Q3 - Q1).
Using the given information, we can calculate the interquartile range:
IQR = 57 - 41 = 16
Then, we can calculate the upper bound:
Upper Bound = 57 + 1.5 * 16 = 57 + 24 = 81
And the lower bound:
Lower Bound = 41 - 1.5 * 16 = 41 - 24 = 17
Any value in the data set that is less than 17 or greater than 81 is considered an outlier. Therefore, the value 83 is an outlier.