It is that value which is greater than half the values in magnitude and is greater to half the values. In other words, it divides the distribution into two equal halves.
In case of ungrouped data , when the number of observations is odd , median will be N/2th observation when the observations are arranged in ascending order .
When the number of observations is even , median will be the average of N/2th and (N/2) + 1 th observation.
QUARTILES
As the median divides the data into half so that half the percentage of the data lies below the extracted median and half lies above it, the quartile breaks down the data into quarters so that 25% of the measurements are less than the lower quartile, 50% are less than the median, and 75% are less than the upper quartile.
There are three quartile values—a lower quartile, median, and upper quartile—to divide the data set into four ranges, each containing 25% of the data points. The lower quartile, or first quartile, is denoted as Q1 and is the middle number that falls between the smallest value of the dataset and the median. The second quartile, Q2, is also the median. The upper or third quartile, denoted as Q3, is the central point that lies between the median and the highest number of the distribution.
Now, we can map out the four groups formed from the quartiles. The first group of values contains the smallest number up to Q1; the second group includes Q1 to the median; the third set is the median to Q3; the fourth category comprises Q3 to the highest data point of the entire set.
Each interval contains 25% of the total observations. Generally, the data is arranged from smallest to largest:
- 1.First interval: The set of data points between the minimum value and the first quartile.
- 2.Second interval: The set of data points between the lower quartile and the median.
- 3.Third interval: The set of data between the median and the upper quartile.
- 4.Fourth interval: The set of data points between the upper quartile and the maximum value of the data set.
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