The median is the middle value when the data is arranged in order of size.
Find the median of the followin set of data: 2, 3, 5, 3, 4, 3, 6
Step 1. Rewrite the numbers in ascending order: 2, 3, 3, 3, 4, 5, 6.
Step 2. There are 7 values in the data set. The median is the fourth value.
The median is 3.
Find the median for the following set of values:
0 2 3 5 1 4 5 3
Step 1. Rank the data in ascending order as follows:
0 2 3 3 4 4 5 5
Step 2. Because the number of values in this set is even (eight), the median is the midpoint between the fourth and the fifth values, 3 and 4.
The median for grouped data is slightly more difficult to compute. We know that the median occurs in the particular class interval for which the cumulative frequency is . On observing the less-than type, say, cumulative frequencies, we can obtain the class interval that contains te median. In fact, the cumulative frequency for this interval is just more than or equal to .
The value of the median for grouped data can be approximately obtained by the following formula: (Proof):
where l and u respectively denote the lower and upper class-boundaries of the class in which the median lies and Fl and Fu represent the corresponding cumulative frequencies.
where and c respectively represent the frequency and the width of the class-interval containing the median.
Find the median of following grouped data:
Let us construct a cumulative frequency table of less than type for the above data to find the particular class interval where the median occurs.
After than we calculate =25, with its help we determine the class whose cumulative frequency is nearly equal to =25. This class is known as median class. Then, the median is calculated by
the following formula: