weighted average

(noun)

an arithmetic mean of values biased according to agreed weightings

Related Terms

Examples of weighted average in the following topics:

  • Expected Values of Discrete Random Variables

    • The expected value of a random variable is the weighted average of all possible values that this random variable can take on.
    • In probability theory, the expected value (or expectation, mathematical expectation, EV, mean, or first moment) of a random variable is the weighted average of all possible values that this random variable can take on.
    • The weights used in computing this average are probabilities in the case of a discrete random variable.
    • If all outcomes $x_i$ are equally likely (that is, $p_1 = p_2 = \dots = p_i$), then the weighted average turns into the simple average.
    • If the outcomes $x_i$ are not equally probable, then the simple average must be replaced with the weighted average, which takes into account the fact that some outcomes are more likely than the others.

  • The Correction Factor

    • The expected value is a weighted average of all possible values in a data set.
    • More formally, the expected value is a weighted average of all possible values.
    • The weights used in computing this average are the probabilities in the case of a discrete random variable (that is, a random variable that can only take on a finite number of values, such as a roll of a pair of dice), or the values of a probability density function in the case of a continuous random variable (that is, a random variable that can assume a theoretically infinite number of values, such as the height of a person).
    • Thus, for a continuous random variable the expected value is the limit of the weighted sum, i.e. the integral.
    • More informally, it can be interpreted as the long-run average of the results of many independent repetitions of an experiment (e.g. a dice roll).

  • Interpreting Significant Results

    • If the sample mean for the obese patients is significantly lower than the sample mean for the average-weight patients, then one should conclude that the population mean for the obese patients is lower than the sample mean for the average-weight patients.
    • If the former of these is rejected, then the conclusion is that the population mean for obese patients is lower than that for average-weight patients.
    • If the latter is rejected, then the conclusion is that the population mean for obese patients is higher than that for average-weight patients.

  • Hypothesis tests based on a difference in means

    • We would like to know, is convincing evidence that newborns from mothers who smoke have a different average birth weight than newborns from mothers who don't smoke?
    • Set up appropriate hypotheses to evaluate whether there is a relationship between a mother smoking and average birth weight.
    • The null hypothesis represents the case of no difference between the groups.H0: There is no difference in average birth weight for newborns from mothers who did and did not smoke.
    • In statistical notation: µn−s = 0, where µn represents non-smoking mothers and µs represents mothers who smoked.HA: There is some difference in average newborn weights from mothers who did and did not smoke (µn −s 0).
    • Does the conclusion to Example 5.10 mean that smoking and average birth weight are unrelated?

  • Review

    • The first six exercises refer to the following study: In a survey of 100 stocks on NASDAQ, the average Statistic percent increase for the past year was 9% for NASDAQ stocks.
    • Their two-week weight gain is below.
    • (Note: a loss is shown by a negative weight gain. )

  • Introduction to multiple regression exercises

    • The summary table below shows the results of a linear regression model for predicting the average birth weight of babies, measured in ounces, based on the smoking status of the mother.
    • (c) Is there a statistically significant relationship between the average birth weight and smoking?
    • The summary table below shows the results of a linear regression model for predicting the average birth weight of babies, measured in ounces, from parity.
    • (c) Is there a statistically significant relationship between the average birth weight and parity?
    • The summary table below shows the results of a regression model for predicting the average birth weight of babies based on all of the variables included in the data set.

  • Difference of two means exercises

    • Randomized treatment assignment was performed, and at the beginning of the study, the average difference in weights between the two groups was about 0.
    • (b) Based on this confidence interval, do the data provide convincing evidence that the Paleo diet is more effective for weight loss than the pamphlet (control)?
    • The average weight gain of younger moms is 30.56 pounds, with a standard deviation of 14.35 pounds, and the average weight gain of mature moms is 28.79 pounds, with a standard deviation of 13.48 pounds.
    • Calculate a 95% confidence interval for the difference between the average weight gain of younger and mature moms.
    • Distribution of weight gained during pregnancy for younger moms (top) and mature moms (bottom).

  • The t distribution for the difference of two means exercises

    • In Exercise 5.26, we discussed diamond prices (standardized by weight) for diamonds with weights 0.99 carats and 1 carat.
    • (b) Do these data provide strong evidence that the average weights of chickens that were fed linseed and horsebean are different?
    • Casein is a common weight gain supplement for humans.
    • Using data provided in Exercise 5.29, test the hypothesis that the average weight of chickens that were fed casein is different than the average weight of chickens that were fed soybean.
    • If your hypothesis test yields a statistically significant result, discuss whether or not the higher average weight of chickens can be attributed to the casein diet.

  • Characteristics of Estimators

    • Although this scale has the potential to be very accurate, it is calibrated incorrectly and, on average, overstates your weight by one pound.
    • However, the average of a large number of measurements would be your actual weight.
    • Scale 1 is biased since, on average, its measurements are one pound higher than your actual weight.
    • Scale 2, by contrast, gives unbiased estimates of your weight.
    • A statistic is biased if the long-term average value of the statistic is not the parameter it is estimating.

  • Mean: The Average

    • An average is a measure of the "middle" or "typical" value of a data set.
    • If the numbers are not the same, the average is calculated by combining the numbers from the list in a specific way and computing a single number as being the average of the list.
    • The use of a geometric mean "normalizes" the ranges being averaged, so that no range dominates the weighting, and a given percentage change in any of the properties has the same effect on the geometric mean.
    • If these ratios are averaged using an arithmetic mean (a common error), high data points are given greater weights than low data points.
    • The harmonic mean, on the other hand, gives equal weight to each data point.