Correct option is B
The correct answer is (B) Mean deviation
Explanation:
• Mean deviation (or Average Deviation) is a measure of dispersion that calculates the arithmetic average of the absolute deviations of the data points from a central value (usually the mean or median).
• In its calculation, the signs (+ or -) of the deviations are ignored; only the magnitude (absolute value) is considered.
• Formula: $MD = \frac{\sum |X - \bar{X}|}{N}$ where $X$ is the value, $\bar{X}$ is the mean, and $N$ is the number of observations.
• It gives a better picture of the spread of data than just the range, as it considers every observation in the data set.
Information Booster:
• Mean deviation is least when calculated from the median.
• It is simpler to understand than standard deviation but is not as useful for higher statistical analysis because it ignores algebraic signs.
• The coefficient of mean deviation is a relative measure used for comparing two distributions.
Additional Knowledge:
• Quartile deviation (Option A): Also known as the Semi-Interquartile Range, it is half the difference between the third and first quartiles: $(Q_3 - Q_1) / 2$.
• Standard deviation (Option C): The square root of the arithmetic mean of the squares of the deviations from the mean. It is the most widely used measure of dispersion.
• Relative dispersion (Option D): This is a general term for measures that are independent of units, such as the Coefficient of Variation.
when the population standard deviation is known, the appropriate test is: