No trading is the opposite of gambling. And just as an aside, this page is etched in my memory.
I. Statistics
i. Introduction
1. Statistics can be used to describe and compare data distributions (frequency distributions), by categorizing the data into fixed numeric interval points and plotting the number of observations in each category (interval frequency) against the category descriptor (e.g. interval mean or range)
2. Because of random errors, repeated observations or measurements of the same value are not identical / give different results
3. The observation results have a ânormal distribution,â described as a bell-shaped (Gaussian), curve with a maximum population mean (μ
, corresponding to the central tendency of the population, and a population standard deviation or spread (σ
4. Statistics derived from a sample or subset of a population can be used to estimate the population parameters.
ii. Frequency distribution
1. Estimates of population mean
a. Mean
i. The population mean is the best estimate of the true value (μ
for a finite number of observations, and is equal to the sum of all the observations ÷ total number of observations
ii. Accuracy is the degree to which the measured value agrees with the true value (μ
iii. Error (or bias) is the difference between the measured value and the true value (μ
b. Median
i. The median is the midmost value of a data distribution, when all the values are arranged in increasing or decreasing order, for an odd number of observations the median is the middle value, and for an even number of observations the median is the arithmetic mean of the two middle values
ii. For a normal distribution, the median is equal to the mean
iii. The median is less affected by outliers or a skewed distribution
c. Mode
i. The mode is the most frequently occurring value or values in a frequency distribution
ii. The mode is useful for non-normal distributions, especially those that are bimodal
2. Estimates of variability
a. Variance S2
i. The variance (s², σ²) is the estimate of the variability or error in n observations
ii. Described by population variance σ² for infinite observations, and sample variance s² for finite observations
iii. S² = (∑Xi² - (∑Xi)²/n)÷(n-1)
iv. S² = (∑(Xi â X mean)²)÷(n-1)
v. (n-1) is the number of degrees of freedom (df)
b. Range
i. For a very small number of observations, the range (w) can be used to estimate the variability or error in n observations
ii. W = |X largest â X smallest |
c. Standard deviation
i. The square root of the variance √s²
ii. Standard deviation (σ, s, SD) is the estimate of the variability or error in n observations
iii. S= √s² = √((∑Xi² - (∑Xi)²/n)÷(n-1)) or
iv. S = √s² = √((∑(Xi â X mean)²)÷(n-1))
v. Where (n-1) is the number of degrees of freedom (df)
d. Precision
i. Precision is the reproducibility, the degree to which replicated measurements or repeated observations of the same value, agree with each other i.e. âmade in exactly the same wayâ
ii. Expressed as the relative standard deviation
iii. %RSD,RSD = (standard deviation σ ÷ population mean μ
x 100
3. Standard deviation of the mean (Sm)
a. Standard deviation of the mean (Sm), is the standard error of the mean (SEM), and it is an estimate of the variability or error in the mean of n observations
b. Used to establish confidence intervals for describing the mean of a data set, or when comparing the means of two data sets
c. Sm = (standard deviation σ / √n)
