Respuesta :
Using the concepts of mean and standard deviation, and the central limit theorem, it is found that:
a. The mean is of: 3.3
b. The standard deviation is of: 1.23.
c. They would have a mean of 3.3 and a standard deviation of 0.55.
What are the mean and the standard deviation of a data-set?
- The mean of a data-set is given by the sum of all values in the data-set, divided by the number of values.
- The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values.
For this problem, the mean is given by:
M = (2 + 3 + 2 + 3 + 3 + 4 + 2 + 4 + 3 + 2 + 2 + 7 + 3 + 4 + 5 + 3 + 3 + 3 + 3 + 5)/20 = 3.3
The standard deviation is:
[tex]S = \sqrt{\frac{(2 - 3.3)^2 + (3 - 3.3)^2 + \cdots + (3 - 3.3)^2 + (5 - 3.3)^2}{20}} = 1.23[/tex]
What does the Central Limit Theorem states?
It states that for distribution of sample means of size n:
- The mean remains constant.
- The standard deviation is of S/sqrt(n).
Hence, since 1.23/sqrt(5) = 0.55, the sample means would have a mean of 3.3 and a standard deviation of 0.55.
More can be learned about the standard deviation of a data-set at https://brainly.com/question/24754716
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