Question 1

What is the difference between the mean and the median, and when does each better represent a data set?

Accepted Answer

The mean is the arithmetic average of all values; the median is the middle value when data is ordered. The median better represents skewed distributions or data with outliers, while the mean is preferred for symmetric distributions.

Question 2

How is the interquartile range (IQR) calculated, and what does it measure?

Accepted Answer

The IQR is calculated as Q3 minus Q1, where Q3 is the 75th percentile and Q1 is the 25th percentile. It measures the spread of the middle 50% of the data and is resistant to outliers.

Question 3

What does the standard deviation measure, and how does it relate to the variance?

Accepted Answer

Standard deviation measures the average distance of data points from the mean. It is the square root of the variance, which is the average of the squared deviations from the mean.

Question 4

In a perfectly symmetric, bell-shaped (normal) distribution, what is the relationship among the mean, median, and mode?

Accepted Answer

In a perfectly symmetric, bell-shaped distribution, the mean, median, and mode are all equal and located at the center of the distribution.

Question 5

If every value in a data set is multiplied by a constant k, how are the mean and standard deviation affected?

Accepted Answer

Both the mean and the standard deviation are multiplied by k. Multiplying every value by a constant scales both the center and the spread of the distribution by the same factor.

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