mean

(noun)

one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution

Related Terms

Examples of mean in the following topics:

  • Mean of All Sample Means (μ x)

    • The mean of the distribution of differences between sample means is equal to the difference between population means.
    • which says that the mean of the distribution of differences between sample means is equal to the difference between population means.
    • If numerous samples were taken from each age group and the mean difference computed each time, the mean of these numerous differences between sample means would be 34 - 25 = 9.
    • The mean height of Species 1 is 32, while the mean height of Species 2 is 22.
    • Discover that the mean of the distribution of differences between sample means is equal to the difference between population means

  • Which Standard Deviation (SE)?

    • For example, the sample mean is the usual estimator of a population mean.
    • The standard error of the mean (i.e., of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population.
    • However, the mean and standard deviation are descriptive statistics, whereas the mean and standard error describes bounds on a random sampling process.
    • Put simply, standard error is an estimate of how close to the population mean your sample mean is likely to be, whereas standard deviation is the degree to which individuals within the sample differ from the sample mean.
    • The red population has mean 100 and SD 10; the blue population has mean 100 and SD 50.

  • The Sample Average

    • The sample average (also called the sample mean) is often referred to as the arithmetic mean of a sample, or simply, $\bar{x}$ (pronounced "x bar").
    • The mean of a population is denoted $\mu$, known as the population mean.
    • The sample mean makes a good estimator of the population mean, as its expected value is equal to the population mean.
    • For example, the population mean height is equal to the sum of the heights of every individual divided by the total number of individuals.The sample mean may differ from the population mean, especially for small samples.
    • The arithmetic mean is the "standard" average, often simply called the "mean".

  • Sampling Distribution of Difference Between Means

    • State the mean and variance of the sampling distribution of the difference between means
    • As you might expect, the mean of the sampling distribution of the difference between means is:
    • which says that the mean of the distribution of differences between sample means is equal to the difference between population means.
    • The mean height of Species 1 is 32 while the mean height of Species 2 is 22.
    • Nonetheless it is not inconceivable that the girls' mean could be higher than the boys' mean.

  • Median and Mean

    • State whether it is the mean or median that minimizes the mean absolute
    • State whether it is the mean or median that minimizes the mean squared deviation
    • The mean and median are both 5.
    • Absolute and squared deviations from the median of 4 and the mean of 6.8
    • The distribution balances at the mean of 6.8 and not at the median of 4.0

  • Mean: The Average

    • The arithmetic mean, often simply called the mean, of two numbers, such as 2 and 8, is obtained by finding a value $A$ such that $2+8 = A + A$.
    • The three most common averages are the Pythagorean means – the arithmetic mean, the geometric mean, and the harmonic mean.
    • When we think of means, or averages, we are typically thinking of the arithmetic mean.
    • The arithmetic mean is defined via the expression:
    • For example, the harmonic mean of 1, 2, and 4 is:

  • Using Two Samples

    • To compare two means or two proportions, one works with two groups.
    • You will compare two means or two proportions to each other.
    • To compare two means or two proportions, one works with two groups.
    • Recall that as more sample means are taken, the closer the mean of these means will be to the population mean.
    • In this section, we explore hypothesis testing of two independent population means (and proportions) and also tests for paired samples of population means.

  • Sampling Distribution of the Mean

    • State the mean and variance of the sampling distribution of the mean
    • The mean of the sampling distribution of the mean is the mean of the population from which the scores were sampled.
    • Therefore, if a population has a mean μ, then the mean of the sampling distribution of the mean is also μ.
    • The symbol μM is used to refer to the mean of the sampling distribution of the mean.
    • Therefore, the formula for the mean of the sampling distribution of the mean can be written as:

  • Working Backwards to Find the Error Bound or Sample Mean

    • Working Backwards to find the Error Bound or the Sample Mean
    • From the upper value for the interval, subtract the sample mean
    • We may know that the sample mean is 68.
    • If we know that the sample mean is 68: EBM = 68.82 − 68 = 0.82
    • If we don't know the sample mean: EBM = (68.82 − 67.18)/2 = 0.82

  • The Law of Large Numbers and the Mean

    • The Law of Large Numbers says that if you take samples of larger and larger size from any population, then the mean $\bar{x}$ of the sample is very likely to get closer and closer to µ.
    • NOTE : The formula for the mean is located in the Summary of Formulas (Section 2.10) section course.