Standard Deviation homework

In summary: So the mean gets shifted by b and stretched by a. In summary, the linear transformation of y= -2x+1 will result in the <y> value being shifted by 1 and stretched by -2, the standard deviation y being multiplied by 4, the median y being shifted by 1 and stretched by -2, the Q1y being shifted by 1 and stretched by -2, the Q2y being shifted by 1 and stretched by -2, the Ymin being shifted by 1 and stretched by -2, and the Ymax being shifted by 1 and stretched by -2. This transformation can easily be applied to all the given values to obtain the corresponding transformed values.
  • #1
Ezekiel20
2
0
Help please??

To anybody that can offer a hand.


<x>=5, Standard Deviation = 2, median Mx=4.5, Quartile1=4, Quartile 2=6, xmin=0, xmax=9.

After a linear tranform: y= -2x+1. What are <y>, Standard deviation y, median y, Q1y, Q2y, Ymin, Ymax.

I was given this equation for homework and I am totally lost.
 
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  • #2
Except for the standard deviation, all the items you want can be botained by simply applying the linear transformation to an x quantity to get the corresponding y quantity. For example <y>=-2<x>+1. To get the standard deviation, you multiply by the absolute value of the multiplicative constant, therefore y standard deviation is 4.
 
  • #3


Originally posted by Ezekiel20
To anybody that can offer a hand.


<x>=5, Standard Deviation = 2, median Mx=4.5, Quartile1=4, Quartile 2=6, xmin=0, xmax=9.

After a linear tranform: y= -2x+1. What are <y>, Standard deviation y, median y, Q1y, Q2y, Ymin, Ymax.

I was given this equation for homework and I am totally lost.

you know how you've got all the formulae for workingout those quantities? we,, instead of putting an x in the, try putting ax+b and seeing what the answer is and how it relates to the untransformed quantity:

mean: [tex]E:=\sum_nx_i/N[/tex] where N is the number of measurements (or whatever) transform by ax+b [tex]\sum_n(ax_i+b)/N=a\sum_nx_i/N +\sum_nb/N = b+ a\sum_nx_i/N = b+aE[/tex]
 

1. What is standard deviation?

Standard deviation is a measure of how spread out a set of data is from its mean (average) value. It tells us how much the data values vary from the average.

2. How is standard deviation calculated?

To calculate the standard deviation, you must first find the mean of the data. Then, for each data point, subtract the mean and square the result. Next, find the average of these squared differences. Finally, take the square root of this average to get the standard deviation.

3. What does a high or low standard deviation mean?

A high standard deviation indicates that the data values are spread out from the mean, meaning there is a lot of variation in the data. A low standard deviation means that the data values are close to the mean, indicating less variation in the data.

4. How is standard deviation used in data analysis?

Standard deviation is commonly used to measure the spread of data in a data set. It can also help identify outliers or unusual data points. In addition, it is used to calculate confidence intervals and in statistical tests to determine the significance of results.

5. Can standard deviation be negative?

No, standard deviation cannot be negative. This is because it is calculated by taking the square root of the average of squared differences, which will always result in a positive value.

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