Respuesta :
Answer:
The standard deviation is zero.
Explanation:
The standard deviation is a number that is used to measure how much the data values in a particular data set are spread out from the mean value.
It is basically the square root of the variance ( it is a measurement of the spread between data values in a data set).
It can be any non-negative rational number.
It can never be negative.
Further explanation:
The formula to find the population standard deviation :-
- [tex]\sigma=\sqrt{\dfrac{\sum_{i=1}^n (x_i-\overline{x})^2}{n}][/tex] , where n is the population size.
The formula to find the sample standard deviation :-
- [tex]\sigma=\sqrt{\dfrac{\sum_{i=1}^N (x_i-\overline{x})^2}{N-1}[/tex] , where N is the sample size.
For example : We have a sample as : x= 1, 2, 1, 3, 4 , 2, 2, 2, 3
Then, sample mean = [tex]\overline{x}=\dfrac{\sum_{i=1}^n x_i}{n}[/tex]
[tex]\overline{x}=\dfrac{20}{9}\approx2.22[/tex]
Now,
Data values difference from the mean Square the difference from mean
[tex]x_i[/tex] [tex]x_i-\overline{x}[/tex] [tex](x_i-\overline{x})^2[/tex]
1 -1.22 1.4884
2 -0.22 0.0484
1 -1.22 1.4884
3 0.78 0.6084
4 1.78 3.1684
2 -0.22 0.0484
2 -0.22 0.0484
2 -0.22 0.0484
3 0.78 0.6084
[tex]\sum_{i=1}^9 (x_i-\overline{x})^2=7.5556 [/tex]
Sample standard deviation: [tex]\s=sqrt{\dfrac{\sum_{i=1}^N (x_i-\overline{x})^2}{N-1}}[/tex]
[tex]=\sqrt{\dfrac{\7.5556 }{8}}=0.971828174113 \approx0.9718[/tex]
So, the sample standard deviation is 0.9718.
If all the data values are identical then the mean value will also be the same, thus the distance of all the data values from the mean values must be zero.
It means , the standard deviation would also be zero . (According to the formula of the standard deviation.)
Learn more:
- https://brainly.com/question/475676 [Answered by Blahwhatever ]
- https://brainly.com/question/12477452 [ Answered by MsEHolt ]
Key words :
Data set , Mean , Spread of data , Variance , Population , sample.
