Percentile – Calculating Percentile

This is widely used in calculating the positions of students participated in entrance exams, though the calculations vary slightly.

The p^th percentile of a data set is a value such that at least p % of the items in
the dataset have a value equal to or less than the value of the data item. It also means that
(100 - p) % of the items have a value more than the value of the data item.

Calculating Percentile
Percentile can be calculated using the following approach:

Arrange the data in ascending order.
The position of the p^th percentile item, i = (p/100) * n where n is the total numbers in the data sample.
If i is not an integer, round up. The p^th percentile is the value in the i^th position.
If i is an integer, the p^th percentile is the average of the values in positions ‘i’ and ‘i +1’.

Calculating 90th Percentile

Consider the below sample of data.

5,6,2,3,4,4,4,5,8,9

Arrange the data in ascending order

2,3,4,4,4,5,5,6,8,9

i = (p/100) * n = (90/100) x 10 = 9

Averaging the 9th and 10th data value you get 90th percentile = (8 +9)/2 = 8.5

March 14, 2010 | Filed Under Basic Mathematics | Leave a Comment

Median and Mode

Median: The median of a data set is the value in the middle when the data items are arranged in ascending or descending order. If there are an odd number of items, the median is the value of the middle item. If there is an even number of items, the median is the average of the values for the middle two items.

Consider the below sample of data.

5,6,2,3,4,4,4,5,8,9

Arrange the data in ascending order

2,3,4,4,4,5,5,6,8,9

Median = (4 + 5 )/2 = 4.5

Mode
Definition: The mode of a data set is the value that occurs with greatest frequency or is the value that is repeated most often in the data set.

In the above example 4 is repeated thrice. So 4 is the Mode of the sample data.

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Arithmetic Mean

Mean: The mean of a data set is the average of all the data values. Mean is one of the most widely used measures of central tendency for various data distributions.

If the data are from a sample, the mean is denoted by

x =    ∑xi
       ___
        n

For example arithmetic mean of sample 2,3,4,4,4,4,5,6 is 32/8 = 4

If the data are from a population, the mean is denoted by Calculating mean

µ =   ∑xi
      ____
       N

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Basic Mathematics for Finance

The below mathematical summary statistics are widely used in the finance world for calculating different ratios etc.

Central tendency: This is middle point of a data set or distribution. The below are the measures of central tendency.

Mean

Median

Mode

Percentile

Quartile

Mean, Median and Mode are most commonly used.

Dispersion: This is the spread of data in a data set or distribution. It is also a measure of

how much the data is scattered. The below are the important measures of dispersion.

Range

Variance

Standard Deviation

Coefficient of variation

March 14, 2010 | Filed Under Basic Mathematics | Leave a Comment

Investing in Infrastructure bonds FY 2010 – 2011

As you know during FY 2010 – 2011 if you invest in long term infrastructure bonds you will get tax benefit. The limit of investment for tax benefit is Rs 20,000.

This Rs 20,000 is apart from the regular investments under section 8 0 ( c ). So after looking at this don’t make a quick decision to invest in these bonds to avail tax benefit. Consider your taxable income, other investment avenues, inflation etc before investing in it.

I have come across a good article and here giving the link for the readers. Please go through it and make decision whether to invest in these bonds or not.

Investing in long term infrastructure bonds

March 11, 2010 | Filed Under Income Tax | Leave a Comment