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MaRussiya [10]
2 years ago
5

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 sta

ndard deviation of the data a)12 b)7 c)2 d)5
Mathematics
2 answers:
natulia [17]2 years ago
8 0
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.
BARSIC [14]2 years ago
8 0

Answer:b

Step-by-step explanation:

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