Respuesta :
Answer:
Cannot create sample
Step-by-step explanation:
We are given the following in the question:
4, -2, -6, 19, 6
Formula:
[tex]\text{Variance} = \displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{21}{5} = 4.2[/tex]
Sum of squares of differences = 0.04 + 38.44 + 104.04 + 219.04 + 3.24 = 364.8
[tex]s^2 = \dfrac{364.8}{4}} = 91.2[/tex]
If we add an observation equal to the mean of given sample, then the mean and of new sample will not change.
New sample:
4, -2, -6, 19, 6, 4.2
[tex]Mean =\displaystyle\frac{25.2}{6} = 4.2[/tex]
Sum of squares of differences = 0.04 + 38.44 + 104.04 + 219.04 + 3.24 + 0 = 364.8
[tex]s^2 = \dfrac{364.8}{5}} = 72.96[/tex]
Thus, the variance of new sample changes.
Thus, it is not possible to create a sample.
The true statement is: "Cannot create sample".
The sample is given as:
4, −2, −6, 19, 6
Using a graphing tool, the mean and the variance are:
Mean = 4.2
Variance = 72.96
Add a sample value (x) to the distribution.
So, we have:
-6, -2, 4, 6, 19, x.
The mean is calculated as:
[tex]Mean = \frac{-6 -2+ 4+ 6+ 19 + x}{6}[/tex]
Substitute 4.2 for mean
[tex]4.2= \frac{21 + x}{6}[/tex]
Multiply through by 6
[tex]25.2= 21 + x[/tex]
Solve for x
[tex]x = 25.2- 21[/tex]
[tex]x = 4.2[/tex]
So, the new sample is: -6, -2, 4, 6, 19, 4.2
Using a graphing tool, the mean and the variance are:
Mean = 4.2
Variance = 60.80
Hence, it is not possible to add one more sample value without changing the mean or the variance
Read more about mean and variance at:
https://brainly.com/question/15858152
