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thif the standard deviation of data set was originally 5 and if each value ine data set was multiplied by 2.4 what would the standard deviation of the data a)12 b)7 c)2 d)5

2 Answers

2 votes

Answer:b

Explanation:

User Ganapathy C
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Let
\{x_1,x_2,\ldots,x_n\} be the data set. The variance of the data is


s^2=\displaystyle\sum_(i=1)^n((x_i-\bar x)^2)/(n-1)

where
\bar x is the mean of the data. You have


\bar x=\displaystyle\sum_(i=1)^n\frac{x_i}n

so if each data point was multiplied by 2.4, you have a "new" mean of


{\bar x}^*=\displaystyle\sum_(i=1)^n\frac{2.4x_i}n=2.4\sum_(i=1)^n\frac{x_i}n=2.4\bar x

So in the variance formula, you have


{s^2}^*=\displaystyle\sum_(i=1)^n((2.4x_i-2.4\bar x)^2)/(n-1)=2.4^2\sum_(i=1)^n((x_i-\bar x)^2)/(n-1)=5.76s^2

so the standard deviation of the new data set would be


s^*=\sqrt{{s^2}^*}=√(5.76s^2)=2.4s

The original standard deviation was
s=5 so the new one would be
s^*=2.4*5=12.
User Rogiller
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