Final answer:
The correct option in the final answer for outliers in the given dataset are: c. 175, d. 0, e. 103, and f. 133. Values c. 175, d. 0, e. 103, and f. 133 are outliers in the given dataset because they fall outside the calculated range for outliers based on the interquartile range (IQR).
Step-by-step explanation:
The question pertains to identifying outliers in a dataset using the interquartile range (IQR). The given five number summary is: Min = 50, Q1 = 62, Median = 63, Q3 = 72, Max = 74. The IQR is calculated as Q3 - Q1, which is 72 - 62 = 10. Outliers are typically defined as values that fall below Q1 - (1.5 × IQR) or above Q3 + (1.5 × IQR).
To find the lower and upper bounds for outliers we calculate:
- Lower Boundary: Q1 - (1.5 × IQR) = 62 - (1.5 × 10) = 62 - 15 = 47
- Upper Boundary: Q3 + (1.5 × IQR) = 72 + (1.5 × 10) = 72 + 15 = 87
Any value outside of the range 47 to 87 is considered an outlier. Thus, from the options provided:
- a. 65 is not an outlier because it is within the range.
- b. 70 is not an outlier because it is within the range.
- c. 175 is an outlier because it is above the upper boundary.
- d. 0 is an outlier because it is below the lower boundary.
- e. 103 is an outlier because it is above the upper boundary.
- f. 133 is an outlier because it is above the upper boundary.
Therefore, the correct option in the final answer for outliers in the given dataset are: c. 175, d. 0, e. 103, and f. 133.