2.2 Measures of the Location of the Data
where i = the ranking or position of a data value,
k = the kth percentile,
n = total number of data.
Expression for finding the percentile of a data value: (100)
where x = the number of values counting from the bottom of the data list up to but not including the data value for which you want to find the percentile,
y = the number of data values equal to the data value for which you want to find the percentile,
n = total number of data
2.3 Measures of the Center of the Data
Where f = interval frequencies and m = interval midpoints.
The arithmetic mean for a sample (denoted by ) is
The arithmetic mean for a population (denoted by μ) is
2.5 Geometric Mean
The Geometric Mean:
2.6 Skewness and the Mean, Median, and Mode
Formula for skewness:
Formula for Coefficient of Variation:
2.7 Measures of the Spread of the Data
Formulas for Sample Standard Deviation or or For the sample standard deviation, the denominator is n - 1, that is the sample size - 1.
Formulas for Population Standard Deviation or or For the population standard deviation, the denominator is N, the number of items in the population.