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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).