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Julli [10]
3 years ago
6

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.
Mathematics
1 answer:
Tems11 [23]3 years ago
8 0

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

<u>Data Set 1</u>

<u />\mu =\dfrac{1+2+3+3+6}{5}= \dfrac{15}{5}=3<u />

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

\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

<u>Data Set 2</u>

<u />\mu =\dfrac{2+2+3+3+4+4}{6}= \dfrac{18}{6}=3<u />

<u />\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<u />

<u />

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.

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