Calculate coefficient of standard deviation?

Question

Answer

Calculation of Coefficient of Standard Deviation

The coefficient of standard deviation is a measure of relative variability or dispersion of a probability distribution or a frequency distribution. It is also known as the coefficient of variation. It is used to compare the spread of two or more data sets that have different units of measurement. The formula to calculate the coefficient of standard deviation is:

coefficient of standard deviation = (standard deviation / mean) x 100 %

Explanation of the Formula

The formula for the coefficient of standard deviation involves dividing the standard deviation of the data set by the mean of the data set. The result is then multiplied by 100% to express it as a percentage. Essentially, the coefficient of standard deviation expresses the standard deviation as a percentage of the mean. It is a dimensionless quantity that is useful for comparing the variability of data sets that have different units of measurement. Higher values of the coefficient of standard deviation indicate greater variability or dispersion, while lower values indicate less variability or dispersion.

Example Calculation

Suppose we have a data set of the heights of students in a class:

160 cm, 170 cm, 165 cm, 175 cm, 180 cm

The mean of the data set is:

mean = (160 + 170 + 165 + 175 + 180) / 5 = 170 cm

The standard deviation of the data set is:

standard deviation = 7.91 cm

Using the formula, we can calculate the coefficient of standard deviation as:

coefficient of standard deviation = (7.91 / 170) x 100 % = 4.65 %

Therefore, the coefficient of standard deviation for this data set is 4.65%. This means that the standard deviation is 4.65% of the mean height of the students, indicating a moderate level of variability in the data set.

Answer

σ is the

standard deviation

for a population, which is the same as “s” for the sample. μ is the mean for the population, which is the same as XBar in the sample. In other words, to find the

coefficient

of variation, divide the

standard deviation

by the mean and multiply by 100.

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