subject: Statistics Median Learning [print this page] Introduction to learning median in statistics:
Statistics median approach is the different method of calculating the mean value of the given set of numbers. Statistics median is most probably used in distributions of skewed forms. This statistics median calculation of data is very simple for understanding and processing. So they are used in the summary of statistics and also in the summarizing process of statistical data. It provides the robust value than the mean value.
Merits Of Median
Median of a distribution is the value of the data which divides the distribution into two equal parts. It is the value of the data such that the number of observations above it is equal to the number of observations below it.
The raw data is first arranged in ascending order of their magnitudes, then the middle, most value in the arrangement is called median.
Median is the only average which is used while dealing with qualitative data which cannot be measured quantitatively but still can be arranged in ascending or descending order of magnitude.
For ex: median is used to find the average honesty, average beauty, average intelligence.
Median is also used for determining typical value in problems concerning wages, distribution of wealth.
The median can be calculated graphically.
Median is not affected by the end values (outliers).
The sum of the absolute deviations taken from the median is less than the sum of the deviations taken from any other observation in the data
Theoretical Properties: in Learning Statistics Median
An optimality property:
The absolute deviations common is minimized by the median worth, which is the central point in the given set in the statistics median method.
E(|X c|) is the median of the probability distribution in random variable X.
c is not defined in an unique manner in the above equation, where it is the median. The statisticians say the median formally when there is center value if not they say in an informal manner.
An inequality relating means and medians:
The variations among median and mode are considered in continuous probability distributions. Therefore the variations will be less than or equal to one standard deviation.
The Sample Median: Learning Median in Staitistics
For an odd number of values:
Ex: Find the sample median for the following set of observations: 1, 6, 3, 9, 5.
Start by sorting the values: 1, 3, 5, 6, 9
The median value is five (5).
Explanation:
First get the known position of numbers and arrange them in an ascending order. If the totals given numbers are in odd collection then the middle number will be the median value.
For an even number of values:
Ex: Find the sample median for the following set of observations: 1, 3, 2, 3, 9, 7.
Start by sorting the values: 1, 2, 3, 3, 7, 9
The median value is calculated from average of the two middle most terms, that is
(3 + 3)/2 = 3. Therefore, the median value is 3.
Explanation:
Get the known set of numbers and arrange them in an ascending order. Since the given set of numbers is even ordered the middle two terms are considered and their mean value is calculated for the value of median.
Exercise Problems on Learning Median in Statistics:
1) Find the sample median for the given set of observations:
