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

Answer:

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

Step-by-step explanation:

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

Data Set 1

$\mu =\dfrac{1+2+3+3+6}{5}= \dfrac{15}{5}=3$

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

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

Data Set 2

$\mu =\dfrac{2+2+3+3+4+4}{6}= \dfrac{18}{6}=3$

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

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.