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.

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

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

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

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

Mutual Fund performance calculations

A mutual fund’s performance is calculated by change in its net asset value (NAV). It would help compare performance of different schemes.

Let’s consider a simple example and explore it to cover performance calculations of basic schemes. Example: A mutual fund scheme issued Rs 10 face value units to an investor at a NAV of Rs 20 on 1st Jan 2007 and the NAV at the end of Dec 07 is Rs 25. The performance of the fund for this period is calculated by the below formula.

Performance of the fund = (Current NAV – NAV at the time of Investment) * 100 / NAV at the time of Investment
Performance of the fund = (30 – 25)* 100/25 = 20%

This is the simplest case. Usually the funds also issue dividends. Let’s say the fund issued a dividend of 30% of face value. So the dividend amount per unit is Rs 3. Say the NAV at the time of dividend distribution is Rs 27. Read more

December 25, 2009 | Filed Under Fundamental Analysis | 1 Comment