Question

The best measure of central tendency and dispersion are respectively

• A. Mean, Mode
• B. Median, Variance
• C. Mean, Standard deviation
• D. Median, Quartile

Hint:

Remember that the standard deviation is simply the square root of the variance. This brings the unit of spread back to the original unit of the data, which is a major reason why it is preferred over variance for interpretation.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The question asks for the "best" or most commonly used measures for two statistical properties:

• Central Tendency: A measure that represents the center or typical value of a dataset (e.g., mean, median, mode).

• Dispersion: A measure that describes the spread or variability of the data points (e.g., range, variance, standard deviation).
The "best" measure often refers to the one that uses all the data points in its calculation and is widely used in further statistical analysis.

Step 2: Detailed Explanation:
Measure of Central Tendency:

• Mean: The arithmetic average. It is considered the most reliable measure of central tendency because it takes every single value in the dataset into account. However, it is sensitive to outliers.

• Median: The middle value. It is less affected by outliers and skewed data.

• Mode: The most frequent value. It is useful for categorical data but can be ambiguous if a dataset has multiple modes or no mode.
Generally, the Mean is considered the best measure for symmetric distributions without extreme outliers because of its mathematical properties and its use in many statistical tests.
Measure of Dispersion:

• Mode and Quartile: Mode is a measure of central tendency, not dispersion. Quartiles describe position but not overall spread as a single number. Interquartile Range (IQR) is a measure of dispersion.

• Variance: It is the average of the squared differences from the Mean. It uses all data points but its units are squared (e.g., cm² if data is in cm), which can be hard to interpret.

• Standard Deviation: It is the square root of the variance. This is often considered the "best" measure of dispersion because:
• It is calculated using every data point.

• It is in the same units as the original data, making it directly comparable and interpretable with the mean.

• It is the most common measure of spread used in statistics (e.g., in Z-scores, normal distributions, confidence intervals).
Conclusion:
The Mean is the most comprehensive measure of central tendency, and the Standard Deviation is the most comprehensive and interpretable measure of dispersion that is directly related to the mean. Therefore, the pair (Mean, Standard deviation) is considered the best combination.

Step 3: Final Answer:
The best measure of central tendency and dispersion are Mean and Standard deviation, respectively.