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Sagot :
The mean of a dataset is the average of the dataset.
- The mean is 1.5
- The standard deviation is 1.58
- The median remains unchanged, the mean increases, and the standard deviation decreases when 5 is increased to a larger value
The given parameters are:
[tex]\mathbf{x = 0, 0, 0, 1, 1, 1, 2, 2, 3, 5}[/tex]
(a) Mean and Standard deviation
The mean of the dataset is calculated using:
[tex]\mathbf{\bar x = \frac{\sum x}{n}}[/tex]
So, we have:
[tex]\mathbf{\bar x = \frac{0+ 0+ 0+ 1+ 1+ 1+ 2+ 2+ 3+ 5}{10}}[/tex]
[tex]\mathbf{\bar x = \frac{15}{10}}[/tex]
[tex]\mathbf{\bar x = 1.5}[/tex]
Hence, the mean is 1.5
The standard deviation is calculated using:
[tex]\mathbf{\sigma_x = \sqrt{\frac{\sum(x - \bar x)^2}{n - 1}}}}[/tex]
So, we have:
[tex]\mathbf{\sigma_x = \sqrt{\frac{(0 - 1.5)^2 + (0- 1.5)^2 + (0- 1.5)^2 + (1- 1.5)^2 + (1- 1.5)^2 + (1- 1.5)^2 + (2- 1.5)^2 + (2- 1.5)^2 + (3- 1.5)^2 + (5- 1.5)^2}{10 - 1}}}[/tex]
[tex]\mathbf{\sigma_x = \sqrt{\frac{22.5}{9}}}[/tex]
[tex]\mathbf{\sigma_x = \sqrt{2.5}}[/tex]
[tex]\mathbf{\sigma_x = 1.58}[/tex]
Hence, the standard deviation is 1.58
(b) When 5 is increased to a larger value
When 5 is increased:
- The median remains unchanged
- The mean increases
- The standard deviation decreases
Read more about median, mean, and standard deviation at:
https://brainly.com/question/12598273
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