central tendency

Examples of central tendency in the following topics:

• Comparing Measures of Central Tendency

  • How do the various measures of central tendency compare with each other?
  • Measures of central tendency are shown in Table 1.
  • Table 2 shows the measures of central tendency for these data.
  • No single measure of central tendency is sufficient for data such as these.
  • Measures of central tendency for baseball salaries (in thousands of dollars)

• Median

  • A measure of central tendency (also referred to as measures of center or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution.
  • There are three main measures of central tendency: the mode, the median and the mean .
  • Each of these measures describes a different indication of the typical or central value in the distribution.
  • The median is less affected by outliers and skewed data than the mean, and is usually the preferred measure of central tendency when the distribution is not symmetrical.
  • Identify the median in a data set and distinguish it's properties from other measures of central tendency.

• Averages of Qualitative and Ranked Data

  • The central tendency for qualitative data can be described via the median or the mode, but not the mean.
  • The mode, i.e. the most common item, is allowed as the measure of central tendency for the nominal type.
  • The median, i.e. middle-ranked, item is allowed as the measure of central tendency; however, the mean (or average) as the measure of central tendency is not allowed.
  • An opinion survey is an example of a non-dichotomous data set on the ordinal scale for which the central tendency can be described by the median or the mode.
  • Categorize levels of measurement and identify the appropriate measures of central tendency.

• Exercises

  • (S) Test the difference in central tendency between the two conditions using a rank-randomization test (with the normal approximation) with a one-tailed test.
  • (SL) Test the difference in central tendency between the four conditions using a rank-randomization test (with the normal approximation).

• Measures of Central Tendency

  • In the previous section we saw that there are several ways to define central tendency.
  • This section defines the three most common measures of central tendency: the mean, the median, and the mode.
  • The relationships among these measures of central tendency and the definitions given in the previous section will probably not be obvious to you.
  • The arithmetic mean is the most common measure of central tendency.
  • The median is also a frequently used measure of central tendency.

• Mean: The Average

  • The term central tendency relates to the way in which quantitative data tend to cluster around some value.
  • The term central tendency relates to the way in which quantitative data tend to cluster around some value.
  • A measure of central tendency is any of a variety of ways of specifying this "central value".
  • Central tendency is contrasted with statistical dispersion (spread), and together these are the most used properties of distributions.
  • Statistics that measure central tendency can be used in descriptive statistics as a summary statistic for a data set, or as estimators of location parameters of a statistical model.

• The Average and the Histogram

  • The shape of a histogram can assist with identifying other descriptive statistics, such as which measure of central tendency is appropriate to use.
  • The shape of the distribution can assist with identifying other descriptive statistics, such as which measure of central tendency is appropriate to use.
  • Skewness is the tendency for the values to be more frequent around the high or low ends of the $x$-axis.
  • Demonstrate the effect that the shape of a distribution has on measures of central tendency.

• What is Central Tendency?

  • What is "central tendency," and why do we want to know the central tendency of a group of scores?
  • In the succeeding sections we will give statistical measures for these concepts of central tendency.
  • All three are called measures of central tendency.
  • One definition of central tendency is the point at which the distribution is in balance.
  • We are now in a position to define a second measure of central tendency, this time in terms of absolute deviations.

• Additional Measures of Central Tendency

  • Although the mean, median, and mode are by far the most commonly used measures of central tendency, they are by no means the only measures.
  • This section defines three additional measures of central tendency: the trimean, the geometric mean, and the trimmed mean.
  • These measures will be discussed again in the section "Comparing Measures of Central Tendency."

• Mode

  • A measure of central tendency (also referred to as measures of center or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle or center of its distribution.
  • There are three main measures of central tendency: the mode, the median and the mean .