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7. These values represent the expected number of paintings a person will produce over the next 10 days. 0, 0, 0, 1, 1, 1, 2, 2, 3, 5 a. What are the mean and standard deviation of the data? b. The artist is not pleased with these statistics. If the 5 is increased to a larger value, how does this impact the median, mean, and standard deviation?

Sagot :

MrRoyal

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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