Answer:
New Standard Deviation = 18
Step-by-step explanation:
\(\text{Standard Deviation for sample is given by : }s=\sqrt{\frac{\sum_{i=1} ^{n} (x_i-\bar x)}{n-1}\)
When each value is multiplied by 3.6 then there would be no effect on n as the number of terms will be same.
But the mean will be effected.
\(\implies \bar{x}=\frac{\sum_{i=1}^{n} x_i}{n}\\\\\implies \text{New mean = }\frac {\sum_{i=1} ^{n} 3.6\times x_i}{n}\\\\\text{Also, each term }x_i\text{ is multiplied by 3.6}\\\\\implies\text{New terms = }3.6\times x_i\)
So, the New standard deviation now becomes :
\(s'=\sqrt{\frac{\sum_{i=1} ^{n} (3.6\times x_i-3.6\times \bar x)}{n-1}}\\\\\implies s'= 3.6\times \sqrt{\frac{\sum_{i=1} ^{n} (x_i-\bar x)}{n-1}}\\\\\implies s'=3.6\times s\\\\ \implies s'=3.6\times 5\\\\\implies\textbf{New Standard Deviation = }\bf 18\)
