normalize

(verb)

(in mathematics) to divide a vector by its magnitude to produce a unit vector

Related Terms

Examples of normalize in the following topics:

  • Student Learning Outcomes

  • Probability Histograms and the Normal Curve

    • The occurrence of the normal distribution in practical problems can be loosely classified into three categories: exactly normal distributions, approximately normal distributions, and distributions modeled as normal.
    • How can we tell if data in a probability histogram are normal, or at least approximately normal?
    • A normal probability plot is a graphical technique for normality testing--assessing whether or not a data set is approximately normally distributed.
    • This is a sample of size 50 from a normal distribution, plotted as a normal probability plot.
    • The plot looks fairly straight, indicating normality.

  • The normality condition

    • We use a special case of the Central Limit Theorem to ensure the distribution of the sample means will be nearly normal, regardless of sample size, provided the data come from a nearly normal distribution.
    • The sampling distribution of the mean is nearly normal when the sample observations are independent and come from a nearly normal distribution.
    • It is inherently difficult to verify normality in small data sets.
    • We should exercise caution when verifying the normality condition for small samples.
    • You may relax the normality condition as the sample size goes up.

  • Introduction

    • The normal, a continuous distribution, is the most important of all the distributions.
    • Some of your instructors may use the normal distribution to help determine your grade.
    • Most IQ scores are normally distributed.
    • Often real estate prices fit a normal distribution.
    • In this chapter, you will study the normal distribution, the standard normal, and applications associated with them.

  • The Standard Normal Distribution

    • The standard normal distribution is a normal distribution of standardized values called z-scores.
    • For example, if the mean of a normal distribution is 5 and the standard deviation is 2, the value 11 is 3 standard deviations above (or to the right of) the mean.
    • The mean for the standard normal distribution is 0 and the standard deviation is 1.
    • The value x comes from a normal distribution with mean µ and standard deviation σ.

  • Introduction to evaluating the normal approximation

    • Many processes can be well approximated by the normal distribution.
    • While using a normal model can be extremely convenient and helpful, it is important to remember normality is always an approximation.
    • Testing the appropriateness of the normal assumption is a key step in many data analyses.
    • The observations are rounded to the nearest whole inch, explaining why the points appear to jump in increments in the normal probability plot.

  • Tangent Vectors and Normal Vectors

    • An object is normal to another object if it is perpendicular to the point of reference.
    • Not only can vectors be ‘normal' to objects, but planes can also be normal.
    • Tangent vectors are almost exactly like normal vectors, except they are tangent instead of normal to the other vector or object.
    • This plane is normal to the point on the sphere to which it is tangent.
    • Each point on the sphere will have a unique normal plane.

  • Change of Scale

    • In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary.
    • In order to consider a normal distribution or normal approximation, a standard scale or standard units is necessary.
    • In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution.
    • Normalization can also refer to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets.
    • Explain the significance of normalization of ratings and calculate this normalization

  • Areas Under Normal Distributions

    • State the proportion of a normal distribution within 1 standard deviation of the mean
    • Use the normal calculator to calculate an area for a given X"
    • Use the normal calculator to calculate X for a given area
    • Areas under portions of a normal distribution can be computed by using calculus.
    • Areas under the normal distribution can be calculated with this online calculator: http://onlinestatbook.com/2/calculators/normal.html.

  • Introduction to normal distribution

    • Indeed it is so common, that people often know it as the normal curve or normal distribution, shown in Figure 3.1.
    • Variables such as SAT scores and heights of US adult males closely follow the normal distribution.
    • Many variables are nearly normal, but none are exactly normal.
    • Thus the normal distribution, while not perfect for any single problem, is very useful for a variety of problems.