Question

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

4.9, 4.9, 9.9, 9.9, 14.9

a. 3.74
b. 4.18
c. 8.9
d. 14

Answer 1

`\sigma =3.74`

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 = (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{((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.

Answer 2

Standard deviation is calculated by the square root of the variance. Now, how do we solve the variance? The variance is the average of the squared differences from the Mean. Calculating the variance, we can obtain a standard deviation of 3.74. Therefore, the correct answer is option A.