2040 Mon Jun 17 1:26 PM AutoSave C Week 2 Assignment Abiga... - Saved w Pag Home Insert Draw Design Layout >> Comments Editing Summarize v Remove Dup Convert to R Pastel %A la P Ą Font Paragraph Styles Dictate Sensitivity Add-ins Editor fx Sum C 48 49 51 50 10 20 30 40 45 50 50 45 40 30 20 10, 8. Suppose you have a distribution that consists of the observations {1, 2, 4, 5}. a. What happens to the mean if you increase every observation by 5? Explain why this makes sense with a picture. Increasing every observation in the distribution {1, 2, 4, 5} by 5 results in a new distribution {6, 7, 9, 10} where the mean increases from 3 to 8. This change in mean makes sense because increasing each observation shifts the entire distribution upwards on the number line, resulting in a higher average value (mean) of the dataset. b. What happens to the sample standard deviation s if you increase every observation by 5? Explain why this makes sense with a picture. Increasing every observation in the dataset by 5 units does not affect the sample standard deviation standard deviation. This is because standard deviation measures the relative spread of data points around the mean, and adding a constant to each observation does not alter their relative distances from the mean. Therefore, standard deviation remains the same before and after the increase, reflecting the unchanged dispersion of the dataset despite the uniform addition to all data points. c. What happens to the mean if you instead double each observation? When you double each observation in a dataset the mean of the dataset is also doubled. This is because Share
2040 Mon Jun 17 1:26 PM AutoSave C Week 2 Assignment Abiga... - Saved w Pag Home Insert Draw Design Layout >> Comments Editing Summarize v Remove Dup Convert to R Pastel %A la P Ą Font Paragraph Styles Dictate Sensitivity Add-ins Editor fx Sum C 48 49 51 50 10 20 30 40 45 50 50 45 40 30 20 10, 8. Suppose you have a distribution that consists of the observations {1, 2, 4, 5}. a. What happens to the mean if you increase every observation by 5? Explain why this makes sense with a picture. Increasing every observation in the distribution {1, 2, 4, 5} by 5 results in a new distribution {6, 7, 9, 10} where the mean increases from 3 to 8. This change in mean makes sense because increasing each observation shifts the entire distribution upwards on the number line, resulting in a higher average value (mean) of the dataset. b. What happens to the sample standard deviation s if you increase every observation by 5? Explain why this makes sense with a picture. Increasing every observation in the dataset by 5 units does not affect the sample standard deviation standard deviation. This is because standard deviation measures the relative spread of data points around the mean, and adding a constant to each observation does not alter their relative distances from the mean. Therefore, standard deviation remains the same before and after the increase, reflecting the unchanged dispersion of the dataset despite the uniform addition to all data points. c. What happens to the mean if you instead double each observation? When you double each observation in a dataset the mean of the dataset is also doubled. This is because Share
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Graphs for a and b
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Summarize v
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Convert to R
Pastel
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la
P
Ą
Font
Paragraph
Styles
Dictate
Sensitivity
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51
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10,
8. Suppose you have a distribution that consists of the observations {1, 2, 4, 5}.
a. What happens to the mean if you increase every observation by 5? Explain why this makes
sense with a picture.
Increasing every observation in the distribution {1, 2, 4, 5} by 5 results in a new distribution {6, 7, 9,
10} where the mean increases from 3 to 8. This change in mean makes sense because increasing each
observation shifts the entire distribution upwards on the number line, resulting in a higher average value
(mean) of the dataset.
b. What happens to the sample standard deviation s if you increase every observation by 5?
Explain why this makes sense with a picture.
Increasing every observation in the dataset by 5 units does not affect the sample standard deviation
standard deviation. This is because standard deviation measures the relative spread of data points around
the mean, and adding a constant to each observation does not alter their relative distances from the mean.
Therefore, standard deviation remains the same before and after the increase, reflecting the unchanged
dispersion of the dataset despite the uniform addition to all data points.
c. What happens to the mean if you instead double each observation?
When you double each observation in a dataset the mean of the dataset is also doubled. This is because
Share
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