Question

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

Answer 1

Answer:b

Explanation:

Answer 2

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`.