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  1. A data set has a variance of 42.

What is the standard deviation of the data set?


Round to the nearest tenth.




Question 5.5. What is the standard deviation of the data set? Round your answer to the nearest tenth.


6 4 9 5 5 4 5


(Points : 1)

1.6

1.7

5.4

5.0

Verified Answer :

Q4 . Standard deviation is square root of variance so, the standard deviation of the given data set is , \(\sqrt { 42 }\) which is equal to 6.48074069841

Q5.5 

To find the standard variation first find the mean of the set.

6+4+9+5+5+4+5 = 38 

\(\frac { 38 }{ 7 } =5.42\)

Then we will subtract the mean from each number in the set, then will square that. Then we will add those all. 

Solution is in the pic. Sorry if this was not explanatory enough.

Ask me if you wanna know more.






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Answer:

Step-by-step explanation:

(A) It is given that a data set has a variance of 42, then the standard deviation is given as:

\(SD=\sqrt{variance}\)

⇒\(SD=\sqrt{42}\)

⇒\(SD=6.48\)

Thus, the standard deviation of the given data set is 6.48.

(B) The given data set is:

6 4 9 5 5 4 5

Mean of the given data set is:

\(Mean=\frac{6+4+9+5+5+4+5}{7}\)

\(Mean=\frac{38}{7}\)

\(Mean=5.42\)

Data set                                                            \((x-\overline{x})^2\)

6                                                                                0.33

4                                                                                2.01

9                                                                               12.81

5                                                                               0.17      

5                                                                               0.17    

4                                                                                2.01

5                                                                               0.17    

The variance is given as:

\(V=\frac{0.33+2.01+12.81+0.17+0.17+2.01+0.17}{7}\)

\(V=2.52\)

Thus, the standard deviation is given as:

\(SD=\sqrt{variance}\)

⇒\(SD=\sqrt{2.52}\)

⇒\(SD=1.6\)          

Hence, option A is correct.                  

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