Question

The five number summary for a set of data is given below.

Min Q1 Median Q3 Max
40 69 72 79 86
Using the interquartile range, which of the following are outliers? Select all correct answers.

Answer 1

For the given data with a five-number summary, the interquartile range (IQR) is used to identify outliers. After calculating the IQR and the bounds, we identified that the minimum value of 40 is an outlier, as it is below the lower bound.

Step-by-step explanation:

The question asks us to utilize the interquartile range (IQR) to identify any potential outliers in the dataset with a given five-number summary: Min 40, Q1 69, Median 72, Q3 79, Max 86.

To calculate the IQR, we subtract the first quartile (Q1) from the third quartile (Q3): IQR = Q3 - Q1 = 79 - 69 = 10. Then, we determine the bounds for potential outliers by multiplying the IQR by 1.5 and adding it to Q3 for the upper bound, and by subtracting it from Q1 for the lower bound.

Upper Bound = Q3 + (IQR × 1.5) = 79 + (10 × 1.5) = 94

Lower Bound = Q1 - (IQR × 1.5) = 69 - (10 × 1.5) = 54

Now, we check each data value in the set against these bounds. Data values above 94 or below 54 would be considered outliers. In this set, the minimum is 40 and the maximum is 86; therefore, the minimum value of 40 falls below the lower bound and is considered an outlier. No data point exceeds the upper bound.