This assignments purpose is to investigate how translation and enlargement of data affects statistical parametersI

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3 Transforming Data Type I

This assignment’s purpose is to investigate how translation and enlargement of data affects statistical parameters.

The following data I entered in a TI-84 using STAT: EDIT: ENTER 

This table shows the height in centimeters of 60 students.

  1. To find the mean (The sum of all observed values divided by the total number of values.) and the Standard deviation (The most used of all measures of dispersion. Simply defined as the square root of the variance.), I used my TI-84 (STAT: CALC: 1-Var Stats: ENTER: List: 2ND: 2: ENTER: Calculate: ENTER), which is shown the picture below

The mean of the student’s hieght is 152.9166667 and the standard deviation is 17.08731661.

  1.  a) To find the mean and the standard deviation, if I added 5 cm to each height I would first have to add 5 cm to each height which is shown in the table below:

 

Then, repeating the steps I used on the first question using my TI-84 (STAT: CALC: 1-Var Stats: ENTER: List: 2ND: 2: ENTER: Calculate: ENTER) which gives me the following data:

The mean and standard deviation of adding 5 cm to each height gives you 157.9166667 as the mean, and 17.08731661 as the standard deviation.

b) To find the mean and the standard deviation if subtracting 12 cm from each height, I would first have to subtract 12 cm from each height which is shown in the table below:

 

Then I would repeat the steps I used on the first question using my TI-84 (STAT: CALC: 1-Var Stats: ENTER: List: 2ND: 2: ENTER: Calculate: ENTER), which gives me the following data

The mean and standard deviation of subtracting 12 cm in each height gives you 140.9166667 as the mean and 17.08731661 as the standard deviation.

If finding the mean is the sum of all observed values divided by the total number of values, it would affect it because you are adding and subtracting numbers from every value, therefore the mean increased and decreased by the same constant.

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If finding the standard deviation is defined as the square root of the variance, adding and subtracting numbers in the data will not affect the variance, because the distance between values does not change.

  1.  a) To find the mean and the standard deviation if I multiplied each height by 5.

I would first have to multiply 5 to each height which is shown in the table below:

 

Then repeating steps I used on the first question using my TI-84 (STAT: CALC: 1-Var Stats: ENTER: List: 2ND: 2: ENTER: Calculate: ENTER). The following data ...

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