Impact of transforming (scaling and shifting) random variables | AP Statistics | Khan Academy

Linear transformations (addition and multiplication of a constant) and their impacts on center (mean) and spread (standard deviation) of a distribution.

AP Statistics on Khan Academy: Meet one of our writers for AP¨_ Statistics, Jeff. A former high school teacher for 10 years in Kalamazoo, Michigan, Jeff taught Algebra 1, Geometry, Algebra 2, Introductory Statistics, and AP¨_ Statistics. Today he's hard at work creating new exercises and articles for AP¨_ Statistics.

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[tarab]

My stats teacher is the worst at explaining things- this was perfect, thank you

[Optimal_Production]

Thanks so much for this video, amazing work. - coming from a IB DP Math Application student!

[sebastiangutierrez]

Hi thanks for the video. I have a question related to Var of Y


Isn't it k^2 * VarX ? In your video you say that VarY = k * VarX but I think you are missing the k squared.


If X is normal, and you have Y = aX + b then:
Mean(Y) = a* Mean(X) + b
Var(Y) = a^2 * Var(X)


Thanks in advance

[jeffgalef]

Showing the shifted curve on the same chart is confusing. The new curve no longer has the x-variable along the abscissa; it now has the y-variable. It should be on its own chart.

[katerynajastrebowa]

Hi, thanks for the video! I have one doubt though, when we add K to Y(x), we get Y = X + K and I think that K should lift the bell curve up, not to move it to the right as presented at 2:24, or am I crazy?

[justwiicked]

Why am I here im still on the qudratic formula thingy😂

[nickfleming]

Is A = X + X not the same thing as B = 2*X ?
the standard deviation of A = ( sigma(X)^2 + sigma(X)^2 )^(1/2)
but the standard deviation of B = 2 * sigma(X)
Why are these different?