median

(noun)

the numerical value separating the higher half of a data sample, a population, or a probability distribution, from the lower half

Related Terms

Examples of median in the following topics:

  • 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

  • Median

    • The median is the middle value in distribution when the values are arranged in ascending or descending order.
    • There are three main measures of central tendency: the mode, the median and the mean .
    • The median divides the distribution in half (there are 50% of observations on either side of the median value).
    • In a distribution with an odd number of observations, the median value is the middle value.
    • Comparison of mean, median and mode of two log-normal distributions with different skewness.

  • Skewness and the Mean, Median, and Mode

    • The mean, the median, and the mode are each 7 for these data.
    • In a perfectly symmetrical distribution, the mean and the median are the same.
    • The mean is 6.3, the median is 6.5, and the mode is 7.
    • The mean and the median both reflect the skewing but the mean more so.
    • The mean is 7.7, the median is 7.5, and the mode is 7.

  • Statistical Literacy

    • They reported the mean household income and the median age of theatergoers.
    • What might have guided their choice of the mean or median?
    • Therefore the mean is probably higher than the median, which results in higher income and lower age than if the median household income and mean age had been presented.

  • Robust statistics

    • (a) Which is more affected by extreme observations, the mean or median?
    • The median and IQR are called robust estimates because extreme observations have little effect on their values.
    • The median and IQR do not change much under the three scenarios in Table 1.27.
    • The median and IQR are only sensitive to numbers near Q1, the median, and Q3.
    • 1.35: Buyers of a "regular car" should be concerned about the median price.

  • Which Average: Mean, Mode, or Median?

    • The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one (e.g., the median of $\{3, 5, 9, \}$ is 5).
    • The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one (e.g., the median of $\{3,5, 9\}$ is 5).
    • The mean is 2.5, as is the median.
    • In this case, the arithmetic mean is 6.2 and the median is 4.
    • Unlike mean and median, the concept of mode also makes sense for "nominal data" (i.e., not consisting of numerical values in the case of mean, or even of ordered values in the case of median).

  • Interquartile Range

    • Divide the data into four quartiles by finding the median of all the numbers below the median of the full set, and then find the median of all the numbers above the median of the full set.
    • This will give you the position of your median:
    • Median is 1+3 = 4/2 = 2nd position, which is 21.
    • This median separates the third and fourth quartiles.
    • This median separates the first and second quartiles.

  • Sign Test

    • This test concerns the median $\tilde { \mu }$ of a continuous population.
    • The idea is that the probability of getting a value below the median or a value above the median is $\frac{1}{2}$.
    • Therefore, we conclude that the median age of the population is not less than $24$ years of age.
    • Actually in this particular class, the median age was $24$, so we arrive at the correct conclusion.
    • The sign test involves denoting values above the median of a continuous population with a plus sign and the ones falling below the median with a minus sign in order to test the hypothesis that there is no difference in medians.

  • Comparing Measures of Central Tendency

    • Understand how the difference between the mean and median is affected by skew
    • For these data, the mean of 91.58 is higher than the median of 90.
    • Typically the trimean and trimmed mean will fall between the median and the mean, although in this case, the trimmed mean is slightly lower than the median.
    • In the media, the median is usually reported to summarize the center of skewed distributions.
    • You will hear about median salaries and median prices of houses sold, etc.

  • Box plots, quartiles, and the median

    • Figure 1.25 shows 50% of the data falling below the median (dashes) and other 50% falling above the median (open circles).
    • If the data are ordered from smallest to largest, the median is the observation right in the middle.
    • What percent of the data fall between Q1 and the median?
    • What percent is between the median and Q3?
    • 1.30: Since Q1 and Q3 capture the middle 50% of the data and the median splits the data in the middle, 25% of the data fall between Q1 and the median, and another 25% falls between the median and Q3.