Correct Answer – Option 2 : Standard Deviation

Dispersion is the extent to which values in a distribution differ from the average of the distribution. To quantify the extent of the variation, there are certain measures namely:

• Measures of Dispersion From Average:
  • ​The mean deviation (MD) of a series is the arithmetic average of the deviation of various items from a measure of central tendency (mean, median and mode).
  • Standard Deviation (S. D.): One of the most stable measure of variability, it is the most important and commonly used measure of dispersion. It measures the absolute dispersion or variability of a distribution. Standard deviation is the positive square root of the mean of the squared deviations of observations from their mean. It is denoted by S.D. or σ_x.
• Measures Based Upon Spread of Values:
  • Range: It is the simplest measure of variability both from the point of view of calculation and understanding. It is the difference between the largest and the smallest observations in the data. For example, the range of scores 2, 5, 6, 4, 12, 10, 9 and 8 is 12-2 = 10.
  • Interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. It divides a rank-ordered data set into four equal parts. Q1 is the mid-value in the first half of the rank-ordered data, Q2 is the score that has exactly two quarters (median). Q3 is the mid-value in the second half of the rank-ordered data. 
    For example, consider the number 3, 4, 6, 9, 11, 12, 14, 15.
    Q1 is the middle value in the first half of the data set.
    The middle value is the average of the two middle values; that is, Q1 = \(4+6\over 2\) = 5.
    Q3 is the middle value in the second half of the data set.
    i. e. Q3 = \(12+14\over 2\) = 13
    Semi Quartile Range = \(Q3 – Q1\over 2\) = \(13 – 5 \over 2\) = 4