Question

MARKETING RESEARCH

“Measures of Variability” for any distribution. Please discuss the following two measures: (1) Variance; and (2) Standard Deviation. Please include in your response how each is calculated (please discuss this conceptually, you need not provide the mathematical equations) and the relationship between the two (how are they related, and why do we use the Standard Deviation in analyses instead of the Variance?).

Answer 1

Variance is denoted by s2 for a sample.

x = recorded data point

x bar = mean of recorded data point

n = number of records of data points of the sample

Variance is the average of squared distances from the mean, calculated to measure spread from the mean. Covariance of variable with itself is Variance.

Standard deviation is denoted by for a sample

x = recorded data point

x bar = mean of recorded data point

n = number of records of data points of the sample

Therefor Standard deviation is square root of Variance.

If I take the height of my family members, I can calculate the following

Data points	(x-x bar) squared
165	77.44
158	3.24
167	116.64
162	33.64
129	739.84
Σ ( x-x bar) squared	970.8
n=	5
x bar=	156.2
variance	242.7	cm2
Std. Deviation	15.57883179	cm

We use standard deviation over variance because the unit of measurement of data and the standard deviation is the same. and hence it is easy for comprehension.

PS. When calculating standard deviation and variance for the whole population, replace (n-1) in the denominator of the formula by just n. Rest all calculations are the same.