Question

The standard deviation of the data:
5, 7, 9, 11, 13, 16, 17, 18, 19, 35
lies between:​

Answer 1

Answer:

The standard deviation of this data is 8.49

so it lies between = 8.2 and 8.6

Answer 2

The standard deviation of the data 5, 7, 9, 11, 13, 16, 17, 18, 19, 35 lies between 7.8 and 8.2

Correct question : The standard deviation of the data 5, 7, 9, 11, 13, 16, 17, 18, 19, 35 lies between a. 7.8 and 8.2 b. 7.4 and 7.8 c. 7 and 7.4 d. 8.2 and 8.6

Given :

The data 5, 7, 9, 11, 13, 16, 17, 18, 19, 35

To find :

The standard deviation of the data 5, 7, 9, 11, 13, 16, 17, 18, 19, 35 lies between

a. 7.8 and 8.2

b. 7.4 and 7.8

c. 7 and 7.4

d. 8.2 and 8.6

Solution :

Step 1 of 3 :

Write down the given data set

Here the given data set is 5, 7, 9, 11, 13, 16, 17, 18, 19, 35

Step 2 of 3 :

Calculate mean of the data set

Mean of the data set

$\displaystyle \sf = \bar{x}$

$\displaystyle \sf = \frac{Sum \: of \: the \: data }{Number \: of \: data }$

$\displaystyle \sf = \frac{ 5 + 7 + 9 + 11 + 13 + 16 + 17 + 18 + 19 + 35}{10}$

$\displaystyle \sf = \frac{150}{10}$

$\displaystyle \sf = 15$

Step 3 of 3 :

Calculate standard deviation of the data

The required standard deviation

$\displaystyle \sf = \sqrt{ \frac{ {( x_i - \bar{x} )}^{2} }{n} }$

$\displaystyle \sf = \sqrt{ \frac{ {(5 - 15)}^{2} +{(7 - 15)}^{2} +{(9 - 15)}^{2} +{(11 - 15)}^{2} + {(13 - 15)}^{2} + {(16 - 15)}^{2} +{(17 - 15)}^{2} +{(19 - 15)}^{2} +{(35 - 15)}^{2} }{10} }$

$\displaystyle \sf = \sqrt{ \frac{ {( - 10)}^{2} +{( - 8)}^{2} +{( - 6)}^{2} +{( - 4)}^{2} + {( - 2)}^{2} + {(1)}^{2} +{(2)}^{2} +{(4)}^{2} +{(20)}^{2} }{10} }$

$\displaystyle \sf = \sqrt{ \frac{100 + 64 + 36 +16 + 4 + 1 + 4 + 9 + 16 + 400 }{10} }$

$\displaystyle \sf = \sqrt{ \frac{650}{10} }$

$\displaystyle \sf = \ \sqrt{65}$

$\displaystyle \sf \approx 8.06$

So standard deviation of the data 5, 7, 9, 11, 13, 16, 17, 18, 19, 35 lies between 7.8 and 8.2

Hence the correct option is a. 7.8 and 8.2

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