Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.