Statistics



Median
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 lessthan 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 classboundaries of the class in which the median lies and F_{l} and F_{u} represent the corresponding cumulative frequencies.
or
where and c respectively represent the frequency and the width of the classinterval 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:
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