Respuesta :
The coding of the statistic is used to make it easier to work with the large sunshine data set
- The mean of the sunshine is 3.05[tex]\overline 6[/tex]
- The standard deviation is approximately 18.184
Reason:
The given parameters are;
The sample size, n = 3.
∑x = 947
Sample corrected sum of squares, Sₓₓ = 33,065.37
The mean and standard deviation = Required
Solution:
[tex]Mean, \ \overline x = \dfrac{\sum x_i}{n}[/tex]
The mean of the daily total sunshine is therefore;
[tex]Mean, \ \overline x = \dfrac{947}{30} \approx 31.5 \overline 6[/tex]
[tex]s = \dfrac{x}{10 } - \dfrac{1}{10}[/tex]
- [tex]E(s) = \dfrac{Ex}{10 } - \dfrac{1}{10}[/tex]
[tex]E(s) = \dfrac{31.5 \overline 6}{10 } - \dfrac{1}{10} = 3.05 \overline 6[/tex]
- The mean ≈ 3.05[tex]\overline 6[/tex]
Alternatively
,[tex]The \ mean \ of \ the \ daily \ total \ sunshine, \, s = \dfrac{31.5 \overline 6 - 1}{10 } = 3.05\overline 6[/tex]
The mean of the daily total sunshine, [tex]\overline s[/tex] ≈3.05[tex]\overline 6[/tex]
- [tex]Var(s) = Var \left(\dfrac{x}{10 } - \dfrac{1}{10} \right)[/tex]
[tex]Var(s) = \left(\dfrac{1}{10}\right)^2 \times Var \left(x \right)[/tex]
Therefore;
[tex]Var(s) = \left(\dfrac{1}{10}\right)^2 \times 33,065.37 = 330,6537[/tex]
Therefore;
- [tex]s = \sqrt{330.6537} \approx 18.184[/tex]
The standard deviation, [tex]s_s[/tex] ≈ 18.184
Learn more about coding of statistic data here:
https://brainly.com/question/14837870
