When do you prefer mean over median? Can you walk me through an example?

Question Analysis

This question is asking you to demonstrate your understanding of two fundamental statistical measures: the mean and the median. The interviewer wants to see if you know when it is appropriate to use one over the other, based on the characteristics of the data set. This involves recognizing the impact of outliers and skewed data on these measures. Additionally, providing an example will showcase your ability to apply theoretical knowledge to practical situations.

Answer

When to Prefer Mean Over Median:

• Symmetrical Distribution: The mean is preferred when the data is symmetrically distributed. In such cases, the mean provides a central value that represents the dataset effectively.

• Data Without Outliers: If a dataset does not contain significant outliers, the mean is a reliable measure of central tendency, as it considers all data points.

• Quantitative Analysis: The mean is useful when conducting further statistical analysis, such as calculating the variance or standard deviation, which rely on the mean.

Example:

Consider a scenario where you are analyzing the test scores of a class of students. Suppose the scores are: 78, 82, 85, 89, 90, 93, 95.

• Symmetric Distribution: The scores are fairly symmetric without extreme values, meaning the mean will give an accurate representation of the data.

• Mean Calculation: The mean is calculated by adding all the scores and dividing by the number of scores:

  [
  \text{Mean} = \frac{78 + 82 + 85 + 89 + 90 + 93 + 95}{7} = 87.43
  ]

In this case, the mean provides a good representation of the students’ performance because the data distribution is symmetrical and there are no outliers. Thus, using the mean is appropriate and gives a clear picture of the average performance of the class.