Question

How is the mean deviation calculated for a given dataset?

• A. Adding all the values of the given dataset.
• B. Dividing the sum of all the values of the given dataset by the number of observations in the dataset.
• C. Dividing the sum of all the deviations from the mean by the number of observations in the dataset.
• D. Dividing the sum of squares of all the deviations from mean by the number of observations in the dataset.

Hint:

Keep the key statistical definitions straight:

\textbf{Mean:} Sum of values / Number of values.
\textbf{Mean Deviation:} Sum of absolute deviations from mean / Number of values.
\textbf{Variance:} Sum of squared deviations from mean / Number of values (or N-1 for sample). \end{itemize}

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The question asks for the definition or method of calculating the mean deviation. Mean deviation (or mean absolute deviation) is a measure of the average distance between each data point and the mean of the dataset.

Step 2: Analyzing the options:
- (A) Adding all the values of the given dataset. This gives the sum of the data, not a measure of deviation.
- (B) Dividing the sum of all the values... by the number of observations... This is the definition of the arithmetic mean.
- (C) Dividing the sum of all the deviations from the mean... by the number of observations... This is the definition of mean deviation. It's important to note that "deviations" here implies the absolute values of the deviations \(|x_i - \bar{x}|\), because the sum of the simple deviations \(\sum(x_i - \bar{x})\) is always zero. Given the options, this is the intended correct answer. The formula is: MD = \(\frac{\sum |x_i - \bar{x}|}{N}\).
- (D) Dividing the sum of squares of all the deviations from mean... by the number of observations... This is the definition of the population variance (\(\sigma^2\)).

Step 3: Final Answer:
Option (C) provides the correct description for calculating the mean deviation.