Find Median and Mode Values ​​For Group or Non-Group Data


Median

From the name, we can guess what is meant by the median. Median is the observation value that is in the middle of the data we have and has been sorted from small to large or from large to small. To find the median value of data, the observational data depends on n, whether n is odd or even. If the number of observations (n) is even then the observations referred to are the data between the ½ and ½ n + 1, while for n the odd observations in question are the ½ (n + 1).
Thus for non-grouped data, the medium is:
For n odd
            Me = x (n+1)/2 …………………………………………………………………..(1)
For n even
            Me = (xn/2 + xn/2+1)/2 …………………………………………………………..(2)

Example For Median

For example if x = 4, 5, 3, 7, 8, 5, 6, 5, 5, 9, 10.

Where n = 11 and odd. Then the median is: x which is 6. After the data is sorted it turns out that x6 is 5.
Whereas for grouped data as arranged in a frequency table, the median is:
Median
Explanation:

Me = Median
l = the lowest class limit in the median class class, i.e. at the ½ n cumulative frequency.
N = total frequency
F = total frequency before the class containing the median
f = frequency in the class containing the median
h = class width (interval in class)
From the data in the table below we can find the median:

Before finding the Median value, what must be known is the value of f (frequency in the median class). To get this value, make a cumulative frequency column like the table above.

The number of observational data obtained is 50 an even number, then the frequency in the median class is (50/2) = 25. The number 25 is used as a standard value that the cumulative frequency value that approaches the standard value is the class interval at 52 - 63. So that f = 25.
Therefore, the median of 50 insurance companies in New York is 63 (billions of dollars) and is in the 4th class.

Mode

Mode is the data that appears most often, or data that has the greatest frequency. If all data have the same frequency it means that the data does not have a mode, but if there are two that have that frequency then the data has two modes, and so on.
Mode value of grouped data can be determined based on the middle value of the interval class that has the most frequency. But the value generated from the middle value of this interval class is a rough value. A finer mode value can be obtained using the formula below.
Mode
Explanation:
L = lowest class limit on the class with the largest frequency
a = (fm -fbm), deviation of the highest frequency with the frequency of the previous class
b = (fm - fam), the deviation from the highest frequency to the next class frequency
I = class interval
For the data table below we can find the mode is
Before, find the mode value, the highest high frequency value is in class k-4 is 11. By getting the frequency value, the table mode above is
Thus, the Mode of 50 Insurance Companies in New York is 63 (Billion Dollars) and is in the 4th class.
The relationship between mean, median and mode is as follows:
Mode = 3 (Media) – 2(Mean) = (3 x 63) – (2 x 63) = 64.88

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