Describing data - Arithmetic mean and standard deviation

8 important questions on Describing data - Arithmetic mean and standard deviation

What is the relationship between the variance and the standard deviation?

The sd is calculated form the variance, as the square root of the variance.

Most observations of the sample are far away from the mean, is the sd large or small?

Large sd

Why would the variance be used, when the sd is a more intuitive measure?

The variance has mathematical proportions that can be useful
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Why is the average of the spread of a distribution not he the same as average of deviations?

The average of the deviations is always zero, because the negative deviations cancel the positive deviations.

Why should the deviations be squared to find the variance?

Because the negative deviations cancel the positive deviations. When squared all the deviations become positive.

How can the relationship between the sd and the frequency distribution be decribed in terms of percentage of observations that lies within x standard deviations?

When the frequency distribution is bell-shaped:
  • 95% of the observations lies within 2 sd. 
  • 67& of the observations lies within 1 sd.

What does the coefficient of variation (CV) calculate? How?

In order to calculate relative variations among individuals
The sd as a percentage of the mean

What type comparison of data can CV be used for?

When the data comprises of variabled that are measured in different units (such as age and weight)

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