Final answer:
The z-score calculation is an effective method for identifying outliers, particularly when dealing with data that is expected to be normally distributed. The IQR method is also useful, especially in the context of skewed data distributions. Outliers should be examined contextually and can be removed or retained depending on the nature and purpose of the study.
Step-by-step explanation:
When trying to identify outliers, one of the best statistical approaches is the z-score calculation. This method determines how many standard deviations a data point is from the mean. If a data point's z-score is above 3 or below -3, it is commonly considered an outlier. Additionally, identifying outliers can also be done using the Interquartile Range (IQR), which involves calculating the first and third quartiles (Q1 and Q3) and then finding the range between them. Any data point that lies more than 1.5 times the IQR above Q3 or below Q1 is typically classified as an outlier.
For example, in the dataset provided (3, 4, 5, 7, 9), to use the IQR approach, one would calculate the median (5), then find Q1 (3.5) and Q3 (7.5), and the IQR would be Q3 - Q1 (4). Multiplying the IQR by 1.5 gives us 6, so any data point greater than Q3 + 6 (13.5) or less than Q1 - 6 (-2.5) would be considered an outlier. There are no such values in this dataset.
If a data value is identified as an outlier, it should be carefully examined. It could be removed if it is a mistake or an anomaly that does not represent the situation being studied. However, if the outlier is a result of natural variability in the data or is an important part of the population being studied, it should be kept. In case an outlier is removed, its impact on the analysis (like changes in the mean, variance or regression models) should be well understood and documented.
Comparing these methods, the z-score is best suited for normally distributed data, while the IQR method is more robust for skewed distributions.