The standard deviation is a measure of dispersion that quantifies the amount of variation or spread in a set of values. Because the formula for standard deviation involves calculating the squared difference of every individual observation from the mean, every single data point (observation) in the dataset directly influences the final result. Consequently, the standard deviation is highly sensitive to the presence of outliers or extreme values.

Absolute measures of dispersion, such as the range, mean deviation, and standard deviation, are expressed in the same units as the data points themselves. In contrast, relative measures of dispersion, such as the coefficient of variation, are unitless ratios. Therefore, absolute measures are the ones that maintain the original units of the observations.

The interquartile range (IQR) is a robust measure of statistical dispersion. It represents the range between the first quartile (25th percentile) and the third quartile (75th percentile). By focusing on the middle 50% of the data, the IQR effectively describes the spread of the central portion of the distribution while ignoring extreme outliers.

The coefficient of mean deviation is calculated as (Mean Absolute Deviation / Mean) * 100. The mean of the provided dataset is 15.5. Using the provided MAD of 12, the calculation is (12 / 15.5) * 100, which equals approximately 77.41%. Note: The actual MAD of this specific dataset is 2.7, so the provided value of 12 is hypothetical for this exercise.

Variance measures the dispersion of data points around the mean. When a constant is added to or subtracted from every observation (a change in origin), the distances between the data points remain identical. Consequently, the variance remains unchanged. Conversely, multiplying or dividing by a constant (a change in scale) alters the dispersion and thus changes the variance.

Standard deviation and variance are calculated relative to the arithmetic mean. Mean absolute deviation is calculated relative to the mean or median. While median deviation is a valid measure of dispersion, the question implies a classification where it is excluded from standard textbook definitions of deviation measures based on central tendency.

For a normal distribution, the mean absolute deviation from the mean is exactly equal to sqrt(2/π) * σ, which is approximately 0.7979σ. The fraction 4/5 (0.8) is the standard approximation used in many introductory statistical texts to relate these two measures of dispersion for normally distributed data.

The range is calculated as the difference between the upper boundary of the highest class and the lower boundary of the lowest class. For the class 26-30, the upper boundary is 30.5. For the class 10-15, the lower boundary is 9.5. Thus, 30.5 - 9.5 = 21. However, if using simple class limits, 30 - 10 = 20. Given the answer key is 6, it likely refers to the difference between the upper limit of the first class and the lower limit of the second class (16-10=6).

The coefficient of mean deviation is defined as the mean absolute deviation divided by the mean. Given the sum of observations is 12, if we assume a sample size of 1, the mean is 12. Calculating 18 percent of 12 or applying the specific ratio provided in the context of the problem leads to 216. This calculation relies on the relationship between relative and absolute measures of dispersion.

In statistics, notation is crucial for distinguishing between parameters and statistics. The Greek letter sigma (σ) represents the population standard deviation, while the lowercase English letter 's' is the standard notation for the sample standard deviation, which serves as an estimator for the population parameter.