Statistics

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Statistics is another branch of math which was developed to interpret large volumes of data.

A Single Measure is Not Sufficient

Let us take a familiar scenario of comparing the academic performance of 2 sections of the same grade in a particular test. Typically, the number of students in each of the sections would different and the scores of the students would be different.

If we think about it, there is no single figure which would help us decide this issue. But statistics provides us with several parameters which can give some idea of the performance. It is like having several photographs of a hill from various directions to get a &ldquo;wholistic&rdquo; picture of the hill in our mind. Let us see some of these.

Average OR Arithmetic Mean

The average of a class is simply the sum of all the scores divided by the number of students. This is the most used parameter in comparisons of data. The class whose average is higher has performed better.

Average is also called the Arithmetic Mean. There are other kinds of mean also. Using the average as a measure assumes that the marks are uniformly spread among the students.



Median

We use the measure of median when the marks are not uniformly spread. For example, in a class of 30, 28 may have scored 70 or less and 2 students may have scored in the 90s. Because of the unusual performance of these 2 students, the average of the class would be higher and hence convey a wrong idea of the class performance.

To get the median score, we arrange all the scores in an ascending order and locate the score which falls exactly in the middle.

Mode

Mode is the score which the maximum number of students score.

Spread

Another quick measure is the difference between the maximum &amp; minimum marks in a class. If the spread is smaller then there is less variation in the scores of the students. You could say the class which has a smaller spread has a better performance.

Frequency Distribution

If we present the data of a class in terms of a frequency table, an expert can say which of the various measures described above would give the best measure of the performance.

A frequency table, as we have seen earlier, presents the various scores or score intervals on the horizontal scale and shows on the vertical axis, the number of students who scored in that range.

Mean & Average

In Arithmetic, both Mean & Average have the same meaning & same value.

But Mean is a broader concept as compared to Average. For a series of values we could also find the "Geometric Mean".

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