Answer:
11.73
Step-by-step explanation:
28
34
27
42
52
15
first we aid the term and we divide the expression and we get the anser 11.73
Answer:
[tex] \sigma \approx 11.75 [/tex]
Step-by-step explanation:
The standard deviation of a data set measures the amount of variation or dispersion in the values. The formula for calculating the standard deviation (σ) is as follows:
[tex] \sigma = \sqrt{\dfrac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N}} [/tex]
where:
Let's calculate the standard deviation for the given data set: 28, 34, 27, 42, 52, 15.
Find the mean ([tex] \bar{x} [/tex]):
[tex] \bar{x} = \dfrac{28 + 34 + 27 + 42 + 52 + 15}{6} \\\\ = \dfrac{198}{6}\\\\ = 33 [/tex]
Subtract the mean from each data point and square the result:
[tex] \begin{aligned} (28 - 33)^2 & = 25, \\\\ (34 - 33)^2 &= 1, \\\\ (27 - 33)^2 & = 36, \\\\ (42 - 33)^2 & = 81, \\\\ (52 - 33)^2 & = 361, \\\\ (15 - 33)^2 &= 324\end{aligned}[/tex]
Find the sum of these squared differences:
[tex] \sum_{i=1}^{N} (x_i - \bar{x})^2 = 25 + 1 + 36 + 81 + 361 + 324 = 828 [/tex]
Divide the sum by the number of data points ([tex] N = 6 [/tex]):
[tex] \dfrac{\sum_{i=1}^{N} (x_i - \bar{x})^2}{N} = \dfrac{828}{6} = 138 [/tex]
Take the square root of the result to get the standard deviation:
[tex] \sigma = \sqrt{138} [/tex]
[tex] \sigma \approx 11.74734012 [/tex]
[tex] \sigma \approx 11.75 \textsf{in 2 d.p.)} [/tex]
Therefore, the standard deviation of the given data set is approximately [tex] \sigma \approx 11.75 [/tex].
