Question

Find the standard deviation.

Short answer

Standard deviation is$1.8.$

Step-by-step solution

Given Information

Finding standard deviation from using the given table :

Explanation

The square root of the average of squares of deviations of data taken from the mean is the standard deviation. That is the $2^{\text{nd}}$column

The values are multiplied by their respective probability. The mean of this column's sum is $5.4$Each observation is deducted from the mean, which is $5.4$, in the next column. The probabilities are squared and multiplied by his value. This provides you with localid="1649402669500" $(x-\mu {)}^2*P(x)$

These values are summed up in next step. Sum will

$S=1.156+0.588+0.144+1.352=3.240$

Standard deviation can be calculated by taking a square. As a result, standard deviation is:

localid="1649402678059" $=\sqrt{3.240}=1.8$