Question

Which statement correctly relates the standard deviation of the two data sets below? Data set 1 Data set 2 1 2 2 2 3 3 3 3 6 4 4 Answer choices: A.) The standard deviation of Data Set 1 is less than the standard deviation of Data Set 2. B.) The standard deviation of Data Set 1 is equal to the standard deviation of Data Set 2. C.) The standard deviation of Data Set 1 is about twice the standard deviation of Data Set 2.

Answer 1

C.) The standard deviation of Data Set 1 is about twice the standard deviation of Data Set 2.

Explanation:

• Data Set 1: 1,2,3,3,6
• Data Set 2: 2,2,3,3,4,4

Data Set 1

`\mu =(1+2+3+3+6)/(5)= (15)/(5)=3`

`S$tandard Deviation, \sigma =\sqrt{(\sum (x-\mu)^2)/(N)}`

`\sigma =\sqrt{((1-3)^2+(2-3)^2+(3-3)^2+(3-3)^2+(6-3)^2)/(5)}\\=\sqrt{(4+1+0+0+9)/(5)}\\=\sqrt{(14)/(5)}\\\\=1.67`

Data Set 2

`\mu =(2+2+3+3+4+4)/(6)= (18)/(6)=3`

`\sigma =\sqrt{((2-3)^2+(2-3)^2+(3-3)^2+(3-3)^2+(4-3)^2+(4-3)^2)/(6)}\\=\sqrt{(1+1+0+0+1+1)/(6)}\\=\sqrt{(4)/(5)}\\\\=0.89`

0.89 X 2=1.78 which is close to 1.67

Therefore, the standard deviation of Data Set 1 is about twice the standard deviation of Data Set 2.