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slavikrds [6]
3 years ago
5

Compute the standard deviation of the data set. Round to the nearest hundredth, if needed.

Mathematics
2 answers:
Nookie1986 [14]3 years ago
7 0

Answer:

\sigma =3.74

Step-by-step explanation:

Given : 4.9, 4.9, 9.9, 9.9, 14.9

To Find: Standard deviation

Solution:

Total number of observations = 5

Mean = \frac{\text{Sum of all observations}}{\text{Total no. of observations}}

Mean = \frac{4.9+4.9+9.9+9.9+14.9}{5}

Mean = 8.9

Thus \bar{x}=8.9

Now, Formula of standard deviation =\sigma = \sqrt{\frac{\sum(x_i-{x})^2}{n}}

So, \sigma = \sqrt{\frac{(4.9-8.9)^2+(4.9-8.9)^2+(9.9-8.9)^2+(9.9-8.9)^2+(14.9-8.9)^2}{5}}

\sigma =3.74

Thus Option A is correct.

Hence the standard deviation of the data set is 3.74.

Mkey [24]3 years ago
3 0
Standard deviation is calculated by the square root of the variance. Now, how do we solve the variance? The variance is the <span>average of the </span>squared differences from the Mean. Calculating the variance, we can obtain a standard deviation of <span>3.74. Therefore, the correct answer is option A.</span>
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