# Math and Statistics

Learn essential math and statistics concepts that underpin key concepts in business and finance.

### Mathematical essentials for the finance world

• What is the relative standard error?

In statistics, a relative standard error (RSE) is equal to the standard error of a survey estimate divided by the survey estimate and then multiplied by 100. The number is multiplied by 100 so it can be expressed as a percentage. The RSE does not necessarily represent any new information beyond the standard error, but it might be a superior method of presenting statistical confidence. Standard error measures how much a survey estimate is likely to deviate from the actual population. By contrast, relative standard error (RSE) is the standard error expressed as a fraction of the estimate and is usually displayed as a percentage.

• How do odds work in casino and sports betting?

If you are planning to enter the betting world, it is important to be able to understand and interpret all types of odds well. You need to be familiar with the conversions between the different formats of odds, the conversion of odds into implied probabilities, and the differences between the true chances of an outcome, as well as the odds on display. The three main types of betting odds are fractional (British) odds, decimal (European) odds, and moneyline (American) odds. These types are alternate ways of presenting the same thing and hold no difference in terms of payouts.

• What do I apply the geometric mean?

In statistics, the geometric mean is calculated by raising the product of a series of numbers to the inverse of the total length of the series. The geometric mean is most useful when numbers in the series are not independent of each other or if numbers tend to make large fluctuations. Applications of the geometric mean are most common in business and finance, where it is frequently used when dealing with percentages to calculate growth rates and returns on a portfolio of securities. It is also used in certain financial and stock market indexes.

• When is it better to use systematic over simple random sampling?

Systematic sampling is easier to execute than simple random sampling, and it can produce skewed results if the data set exhibits patterns. It is also more easily manipulated. Meanwhile, systematic sampling chooses a data point per each predetermined interval. On the contrary, simple random sampling is best used for smaller data sets and can produce more representative results. In simple random sampling, each data point has an equal probability of being chosen.

• What’s the difference between positive and inverse correlation?

A positive correlation is evident when two variables move in the same direction. When the strength of the correlation is measured, a positive correlation will be a positive number.

An inverse correlation is evident when two variables move in the opposite direction and will be a negative number and then strength of the correlation is measured. Investors who want to hedge against risk often seek out stocks in sectors that have a negative price correlation with their other investments. Correlation can be accidental. Investors look for rational reasons why one sector moves in tandem with another sector or in the opposite direction. That makes it more likely that the correlation will occur consistently.

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