Join the IDNLearn.com community and start finding the answers you need today. Find the answers you need quickly and accurately with help from our knowledgeable and experienced experts.

Find the standard deviation, [tex]\(\sigma\)[/tex], of the data.

Data: 198, 190, 245, 211, 193, 193
Mean ([tex]\(\bar{x}\)[/tex]): 205
Variance ([tex]\(\sigma^2\)[/tex]): 366.3

[tex]\(\sigma = ?\)[/tex]


Sagot :

To calculate the standard deviation, [tex]\(\sigma\)[/tex], of the given data, we need to follow these steps:

1. Understand the given values:
- The mean of the data, [tex]\(\bar{x}\)[/tex], is 205.
- The variance, [tex]\(\sigma^2\)[/tex], is 366.3.

2. Recall the relationship between variance and standard deviation:
Variance ([tex]\(\sigma^2\)[/tex]) is the square of the standard deviation ([tex]\(\sigma\)[/tex]). Therefore, to find the standard deviation, we need to take the square root of the variance.

3. Compute the standard deviation:
Given the variance ([tex]\(\sigma^2\)[/tex]) is 366.3, the standard deviation ([tex]\(\sigma\)[/tex]) is given by the square root of the variance.

[tex]\[ \sigma = \sqrt{\sigma^2} = \sqrt{366.3} \][/tex]

4. Find the numerical value:
Taking the square root of 366.3, we get:

[tex]\[ \sigma \approx 19.138965489283898 \][/tex]

Hence, the standard deviation, [tex]\(\sigma\)[/tex], of the data is approximately [tex]\(19.139\)[/tex] (rounding to three decimal places).