# 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
= (x

_{n/2}+ x_{n/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 x

_{6}is 5.
Whereas
for grouped data as arranged in a frequency table, the median is:

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.

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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