Deviation From the Mean

Topic Content:

In a given set of numbers, the amount by which each value differs from the mean is known as the deviation from the mean. Remember that the sum of the deviations of any set of data from the mean is always 0.

Mean Deviation:

Another measure of dispersion or spread is called the mean deviation.

The Mean deviation is the mean of all the absolute values (modulus) of the deviation from the mean.

The formula to find the mean deviation is:

Mean Deviation = \(\normalsize \frac{\sum|x\:-\:\bar{x}|}{n}\)

Where \(\scriptsize x\:-\:\bar{x} \)is the deviation from the mean

x = a value in the distribution

\(\scriptsize |x\:-\:\bar{x} | \)= the modulus of \(\scriptsize x\:-\:\bar{x} \)

The lines “| |” before and after the deviation from the mean show that all the differences must be taken as positive.

Mean Deviation = \( \normalsize \frac{\sum f|x\:-\:\bar{x}|}{\sum f}\)(with frequencies)

Mean Deviation = \(\normalsize \frac{\sum f|x_m\:-\:\bar{x}|}{\sum f}\)(for grouped data x_m = mid- class)

Variance:

Variance is defined as the arithmetic mean of the squares of the deviations from the mean. It is also referred to as the mean squared deviation. Variance is usually denoted by σ² or S² .

Suppose we have n values x₁ , x₂