You are here:

Advanced Math/standardizing a series

Advertisement

Expert: - 11/19/2008


Question
Good Morning,
I have three sets of scores, each with different means and standard deviations. Each set of scores is a measure of the demand for employees within each of 17 industries. I would like to standardize each set so I can add the values from each industry together to develop one scale of demand.

From what I remember, I am thinking I need to compute all to a Z score. Minus each number from the series mean then divide by the series standard deviation. Then I can add the (3) Z scores for each industry to make one scale. Is this correct?

Example: Series 1: .01875, .010388, .030, ... (mean=.045, stdev=.030)
series 2: .295,.453,.57, ... (mean=1.20, stdev=.496)
series 3: .02,.116,.074, ... (mean=.085, stdev=.052)

Z Scores series 1: -.875,-1.15,-.499,...
Z Scores series 2: -1.82,-1.51,-1.26,...
Z Scores series 3: -1.24,.58,-.215,...

If each column is an industry, now I can add the scores (-.875+-1.82+-1.24), (-1.15+-1.51+.58),etc. and I will have one scale?

Answer

Sample for three devia
Is this correct? Yes.
I will have one scale? Yes.

At least that is on the means, anyway.  The variances are added as well, and the variance is the standard deviation squared.

When adding together samples, it is not quite so easy to add together variances or even standard deviation.

The entire variance has to be computed again.  There is also the between sample variance which is found by treating series 1, 2, and 3 as 3 distinct values and computing the variance of these.

    Questioner's Rating
    Rating(1-10)Knowledgeability = 10Clarity of Response = 10Politeness = 10
    CommentThank you very much. This was the only expert that knew the answer.


  • Add to this Answer
  • Ask a Question

Scott A Wilson

Expertise

I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can even tell you it takes me over 2,000 steps to go a mile, but is that relevant?

Experience

Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree almost 25 years ago. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people nearby, friends with math questions, and several people every day on the PC, and you're probably make one more.

©2012 About.com, a part of The New York Times Company. All rights reserved.