Measures of Central Tendency and Dispersion

Key Questions

  • How are the measures of central tendency and measures of dispersion complementary?

    Answer:

    Please see below.

    Explanation:

    Measures of central tendency are mean, mode and median. Even we have three types of mean, such as arithmatic mean, geometric mean and harmonic mean.

    They tell us the central value around which the data is distributed. For example consider the data set 6, 8, 2, 4, 12, 5, 8, 10, 3, 4. In this sum of numbers is 62 and as they are ten in number, mean is 62/10=6.2

    Note that smallest number is 2 and largest number is 12. Now, even if we had set of numbers as 5,6,7,5,8 and as sum of numbers is 31 and they are five, mean is still 31/5=6.2. But 5,6,7,5,8 are far more narrowly spread and hence nature of data is not very well brought out by just mean.

    Similarly, we can have two data sets with same median or mode, but their spread may be different, as mode is just the more frequent among data points and median is the value of central data point, when the samme is arranged in increasing or decreasing order.

    Measures of dispersion tell us better about the kind of spread. In a way, mean deviation or standard deviation tell us more about the way data is spread.

    For example, data set 30,40,50,60,70 and data set 10,30,50,70,90 have same mean, mode and median but while mean deviation of first data set is 12, that of second data set is 24, indicating that second data set is too wide spread.

    What about two data sets 30,40,50,60,70 and 130,140,150,160,170? Their mean deviation is same i.e. 12, but are they not widely different as mean of first data set is 50, while that of second data set is 150.

    It is obvious that measures of central tendency and measures of dispersion are both important and complementary.

    Shwetank Mauria · 1 · Feb 13 2018
  • What is the standard deviation?

    The standard deviation gives us an idea on how clustered together or how scattered our data is from the average.

    If the standard deviation is small, we can say that the majority of our data are near the average.

    If the standard deviation is large, we can say that our data are quite scattered.

    seph · 2 · Oct 27 2014
  • What are the Measures of Central Tendency and Dispersion?

    The measures of central tendency are the mean, mode, and median

    The mean is the average of the given data.

    The mode is the element among the data that occurs most frequently

    The median is middle element when the data is sorted

    seph · 2 · Dec 18 2014

Questions

Radicals and Geometry Connections