what is median in math

what is median in math

what is median in math  In the theory of probability and statistics, a median is a number. This number has the property that it divides the set of observed. The values into two equal halves so that half the value is below and half is above.

 

If there is a finite number of elements, the median is easy to find. Values should be placed on the list, from the lowest to the highest. If there is an odd number of values, the median is the one at position {\ display style (n + 1) / 2} {\ display style (n + 1) / 2}. For example, if there are 13 values, they can be divided into two groups of 6, with a median between, in position 7.

 

With an even number of values, because there is no one that divides all numbers into two, the median is defined as the average of two central elements. With 14 observations it would be the average of elements 7 and 8, which is their sum divided by 2.

what is median in math

 

 

The median list

Alternatively, the median list of an even number is sometimes defined as one of the two middle elements; the choice is either (a) always the smallest, (b) always the largest, or (c) randomly chosen between the two. This alternative definition has two important advantages. It guarantees that the median is always an element of the list (eg, the list of integers will never have a fractional median).

 

 

The guarantees that the median exists for data of ordinal value. The options (a) or (b) is taken, the median of the sample will be biased. Which is an undesirable property of the statistical estimate. Definition (c) does not have this disadvantage, but it is more difficult to do. It also has the disadvantage that the same list of values does not have a well-defined, deterministic median.

 

 

 

The distribution curve with the mode, median and average. The median is the center.
Median and average

The median and average differ in several ways. The average is in many cases a better measure. The many statistical tests can use the mean and standard deviation of two observations to compare them. The same comparison cannot be done with medians.

what is median in math

 

 

 

 

The median is more useful when the value variance is not important. We only need a central measure of value. The average of this set of numbers changes, but the median does not.

 

For example, a researcher can calculate the median survival of kidney transplant patients when half of the patients participate in his study died. The calculation of the average survival requires continuing the study and following all patients until their death.

 

 

 

what is median in math Example

Suppose you want to know how many jelly beans have the most people in the room. Let’s say there are five people in the room:

Person 1 (7 jellies), Person 2 (8 jellies), Person 3 (9 jellies), Person 4 (10 jellies), Person 5 (11 jellies)
To calculate the average, add the total number of jellies (45) and divide by the number of people (5): the average is 9 jelly beans per person.

 

 

To calculate the median, align the amount of jelly beans (7, 8, 9, 10, 11) and select the median number: the median is also 9 gels.
The results change significantly when you have a larger range of numbers. Imagine another group of five people:

Person 1 (8 jellies), Person 2 (8 jellies), Person 3 (9 jellies), Person 4 (10 jellies), Person 5 (50 jellies)
To calculate the average, add the total number of jellies (85) and divide by the number of people (5): the average is now 17 jelly beans per person.

 

 

To calculate the median, align the amount of jelly beans (8, 8, 9, 10, 50) and select the median number: the median still contains 9 jellies.
In the latter case, the average gives a poor understanding of how many jelly beans have the majority of people (10 or less). The median gives a better idea of the amount of jelly beans that most people have. However, if you would like to divide the amount of jelly evenly, you would use this measure. The median is basically the average number.

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