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STALIN [3.7K]
3 years ago
13

On a 10-item test, three students in Professor Hsin's advanced chemistry seminar received scores of 2, 5, and 8, respectively. F

or this distribution of test scores, the standard deviation is equal to the square root of A) 4. B) 5. C) 6. D) 9
Mathematics
2 answers:
Inessa [10]3 years ago
4 0

Answer:

For this distribution of test scores, the standard deviation is equal to the square root of 9

D) 9

Step-by-step explanation:

We need to know the standard deviation formula:

S=\sqrt{\frac{sum(x-Am)^2}{n-1} } (1)

Where:

S: Standard deviation

sum: Summation

x: Sample values

Am: Arithmetic mean

n:   Number of terms, in this case 3

Now, we need to know the arithmetic mean of the sample values: 2, 5 and 8

Am=\frac{2+5+8}{3} = 5

To know the standard deviation we need to have the summation of each term minus the arithmetic mean squared.

(x-Am)^2 of each term:

(2-5)^2=9\\(5-5)^2=0\\(8-5)^2=9

Now, we can find the standard deviation:

S=\sqrt{\frac{9+0+9}{3-1} } \\S=\sqrt{\frac{18}{2} } \\S=\sqrt{9}

The standard deviation is equal to the square root of 9

docker41 [41]3 years ago
3 0

Answer:

D) 9

Step-by-step explanation:

Standard Deviation is Calculated by formula:  

Standard deviation(\sigma) = Standard deviation(\sigma) = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}} }

where, \bar{x} is mean of the distribution.

First: Calculating Mean of 2, 5 and 8:

\text{Mean}(\bar x)=\frac{2+5+8}{3} = 5

Then Standard deviation is:

Standard deviation(\sigma) = \sqrt{\frac{1}{3-1}\sum_{i=1}^{n}{(x_{i}-5)^{2}} }

⇒ \sigma = \sqrt{\frac{1}{2}[{(2-5)^{2}}+{(5-5)^{2}}+{(8-5)^{2}} } =\sqrt 9

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\quad \huge \quad \quad \boxed{ \tt \:Answer }

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\large \tt Solution  \: :

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