To determine if an observation is considered an outlier when it's below a certain threshold, you can use the interquartile range (IQR) method. The IQR is the range between the first quartile (Q1) and the third quartile (Q3) of the dataset. The formula to find the IQR is:
\[IQR = Q3 - Q1\]
In your case, the five-number summary is given as 0, 7, 12, 17, 19. To find Q1 and Q3:
- Q1 is the median of the lower half of the dataset, which is the median of 0 and 7. So, \(Q1 = \frac{0 + 7}{2} = 3.5\).
- Q3 is the median of the upper half of the dataset, which is the median of 12, 17, and 19. So, \(Q3 = \frac{12 + 17 + 19}{3} = 16\).
Now, calculate the IQR:
\[IQR = Q3 - Q1 = 16 - 3.5 = 12.5\]
An observation is considered an outlier if it falls below \(Q1 - 1.5 \times IQR\). So:
\[Threshold = Q1 - 1.5 \times IQR = 3.5 - 1.5 \times 12.5 = 3.5 - 18.75 = -15.25\]
Therefore, an observation is considered an outlier if it is below -15.25 in this dataset.