Find the median of first 10 even numbers

In simple words, statistics implies the process of gathering, sorting, examine, interpret and then present the data in an understandable manner so as to enable one to form an opinion of it and take necessary action, if necessary. Examples:

A teacher collecting students’ marks, organizing them in ascending or descending manner, and calculating the average class marks, or finding the number of students who failed, informing them so that they start working hard.
Government officials collecting data for the census, and comparing it with previous records to see whether population growth is in control or not.
Analyzing the number of followers of a particular religion of a country.

Statistical Tools

The most popular tools of statistics are as follows:

Arithmetic Mean: Also known as average, the arithmetic mean for a given set of data is calculated by adding up the numbers in the data and dividing the sum so obtained with the number of observations.
Median: Such a value as separates the higher and lower values of a given set of statistical data is called the median.
Mode: Such s value as occurs most frequently in a given series of statistical data is called the mode.
Standard Deviation: Such a value as indicates the extent to which certain values of a statistical series tend to vary or disperse from its mean or median is called standard deviation.
Range: Such a value depicts the difference between the highest and lowest values in a series.
Correlation: Such a statistical tool as helps study the relationship between two variables is called correlation.

Median

In the context of statistics and probability, the median is the positional average that lies in the middle of a statistical series and separates the higher and lower values when the said data has been arranged in an ascending or descending order. Unlike arithmetic mean, which is influenced by all the values in a population, median does not get affected at all. The median is sometimes used in place of the arithmetic mean when one has doubts regarding the extreme values in the statistical series influencing the value of the average. Another important thing to be kept in mind while calculating the median is that the concerned series must be sorted either in an ascending or descending manner.

Calculation of Median

The value of median depends upon the number of items given the statistical series. For example, if the number of items is odd, then we just have to pick up the middle number out of all the terms, and declare it as the median. It would separate all the numbers above and below it equally. This won’t be the case if the number of items is odd in a given series. Here, the two terms in the middle must be picked up, summed up, and be divided by 2 in order to calculate the value of the median.

Example 1: Median of Odd Amount of Numbers.

Solution:

Let there be a data set: {7, 24, 12, 44, 35, 20, 2}.

It needs to be sorted into ascending order first: {2, 7, 12, 20, 24, 35, 44}.

As we can observe, the number of terms in the given set of data is odd, and that the observation which divides the whole set into two equal parts is called the median.

Here, 20 divides the sorted data set in two parts containing 3 numbers each, numbers lesser than 20 above it and those bigger that it, below it.

Hence, the median of the given data set is 20.

Example 2: Even Amount of Numbers

Let there be a data set: {7, 24, 12, 44, 56, 35, 20, 2}.

It needs to be sorted into ascending order first: {2, 7, 12, 20, 24, 35, 44, 56}.

As we can observe, the number of terms in the given set of data is even, and the two observations that lie in the middle are 12 and 20, since they divide the rest of the set with three numbers each.

Now, Median = (12+20) / 2

= 32 / 2

= 16

Hence, the median of the given data set is 16.

Merits of Median

The calculation of the median does not involve a lot of mathematical or statistical knowledge. It can be easily calculated by people who are not even well versed in the intricacies of mathematics.
Median, by itself, is a well- defined measure of the central tendency.
Unlike arithmetic mean, the median can be easily represented on a graph, making it much more easier to understand.
Median can also be used for the study or analysis of qualitative attributes, unlike arithmetic mean, which takes into account only the quantitative aspects.
Median can also be used for the computation of mean deviation(either from mean or median).
Median does not get affected by highest or lower values in the data set.

Demerits of Median

Arranging the statistical data in ascending or descending order when the number of items is large, is a tedious process.
Median does, in fact, depend upon the arithmetic mean in case the number of terms in a data set is even, and thus yields inappropriate result, since mean is swayed by quantities.
Median cannot be trusted to be the best measure in case the data set is in fractions or percentages.
Since it is not dependent on all items, it cannot be deemed as a proper representative.