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maw [93]
3 years ago
12

If the standard deviation of a data set was originally 5, and if each value in the data set was multiplied by 3.6, what would be

the standard deviation of the resulting data?
Mathematics
2 answers:
oee [108]3 years ago
7 0
You would take 5 and multiply it by 3.6 which gives you 18. I believe that is how you would do that problem. Hope it helped.
melamori03 [73]3 years ago
4 0

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

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