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

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

$s^2=\displaystyle\sum_{i=1}^n\frac{(x_i-\bar x)^2}{n-1}$

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

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

so the standard deviation of the new data set would be

$s^*=\sqrt{{s^2}^*}=\sqrt{5.76s^2}=2.4s$

The original standard deviation was $s=5$ so the new one would be $s^*=2.4\times5=12$.

Answer 2

Answer:b

Step-by-step explanation: