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STATISTICS (Types of Statistics
Statistics is a general, broad term, so…
STATISTICS
Types of Statistics
Statistics is a general, broad term, so it's natural that under that umbrella there exist a number of different models.
Mean
A mean is the mathematical average of a group of two or more numerals. The mean for a specified set of numbers can be computed in multiple ways, including the arithmetic mean, which shows how well a specific commodity performs over time, and the geometric mean, which shows the performance results of an investor’s portfolio invested in that same commodity over the same period.
Variance
Variance is a measurement of the span of numbers in a data set. The variance measures the distance each number in the set is from the mean. Variance can help determine the risk an investor might accept when buying an investment.
Kurtosis
Kurtosis measures whether the data are light-tailed (less outlier-prone) or heavy-tailed (more outlier-prone) than the normal distribution. Data sets with high kurtosis have heavy tails, or outliers, which implies greater investment risk in the form of occasional wild returns. Data sets with low kurtosis have light tails, or lack of outliers, which implies lesser investment risk.
Skewness
Skewness describes the degree a set of data varies from the standard distribution in a set of statistical data. Most data sets, including commodity returns and stock prices, have either positive skew, a curve skewed toward the left of the data average, or negative skew, a curve skewed toward the right of the data average.
Regression Analysis
Regression analysis determines the extent to which specific factors such as interest rates, the price of a product or service, or particular industries or sectors influence the price fluctuations of an asset. This is depicted in the form of a straight line called linear regression.
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Statistics Formula
Population Mean
The term population mean, which is the average score of the population on a given variable, is represented by:
μ = ( Σ Xi ) / N
The symbol ‘μ’ represents the population mean. The symbol ‘Σ Xi’ represents the sum of all scores present in the population (say, in this case) X1 X2 X3 and so on. The symbol ‘N’ represents the total number of individuals or cases in the population.
Population Standard Deviation
The population standard deviation is a measure of the spread (variability) of the scores on a given variable and is represented by:
σ = sqrt[ Σ ( Xi – μ )2 / N ]
The symbol ‘σ’ represents the population standard deviation. The term ‘sqrt’ used in this statistical formula denotes square root. The term ‘Σ ( Xi – μ )2’ used in the statistical formula represents the sum of the squared deviations of the scores from their population mean.
Population Variance
The population variance is the square of the population standard deviation and is represented by:
σ2 = Σ ( Xi – μ )2 / N
The symbol ‘σ2’ represents the population variance.
Sample Mean
The sample mean is the average score of a sample on a given variable and is represented by:
x_bar = ( Σ xi ) / n
The term “x_bar” represents the sample mean. The symbol ‘Σ xi’ used in this formula represents the represents the sum of all scores present in the sample (say, in this case) x1 x2 x3 and so on. The symbol ‘n,’ represents the total number of individuals or observations in the sample.
Sample Standard Deviation
The statistic called sample standard deviation, is a measure of the spread (variability) of the scores in the sample on a given variable and is represented by:
s = sqrt [ Σ ( xi – x_bar )2 / ( n – 1 ) ]
The term ‘Σ ( xi – x_bar )2’ represents the sum of the squared deviations of the scores from the sample mean.
Sample Variance
The sample variance is the square of the sample standard deviation and is represented by:
s2 = Σ ( xi – x_bar )2 / ( n – 1 )
The symbol ‘s2’ represents the sample variance.
Pooled Sample Standard Deviation
The pooled sample standard deviation is a weighted estimate of spread (variability) across multiple samples. It is represented by:
sp = sqrt [ (n1 – 1) s12 + (n2 – 1) s22 ] / (n1 + n2 – 2) ]
The term ‘sp’ represents the pooled sample standard deviation. The term ‘n1’ represents the size of the first sample, and the term ‘n2’ represents the size of the second sample that is being pooled with the first sample. The term ‘s12’ represents the variance of the first sample, and ‘s22’ represents the variance of the second sample.
Statistics is a form of mathematical analysis that uses quantified models, representations and synopses for a given set of experimental data or real-life studies. Statistics studies methodologies to gather, review, analyze and draw conclusions from data