Upload
toni-menninger
View
32
Download
2
Embed Size (px)
Citation preview
http://www.slideshare.net/amenning/documents
Handout: Descriptive Statistics - Numerical Methods → Fundamental concepts: Population parameter; Point estimate; Sample statistic; Sampling error
Concept Definition Symbol Excel equivalent
or formula
Number of observations
Population size / sample size / number of entries in a data set
n COUNT()
Data set A data set / population / sample of observations or measurements
x1, x2, …, xn A range of cells, e.g. (A2:A52)
Minimum Smallest measurement MIN()
Maximum Largest measurement MAX()
Summation/ Aggregate
All measurements added up ∑ 𝒙𝒊
𝒏
𝒊=𝟏 SUM()
Population mean The sum (aggregate) divided by the number of measurements; the average
μ (‘mew’) AVERAGE()
Sample mean The sum (aggregate) divided by the number of measurements; the average
x̄ (x-bar) AVERAGE()
Median The middlemost measurement Md MEDIAN()
Mode The measurement that occurs most frequently Mo MODE()
Range Difference between Maximum and Minimum MAX()-MIN()
Population Variance Average of the squared deviations from the mean σ2 (sigma square)
(also VAR) VAR.P()
Sample Variance Sum of squared deviations from the mean, divided by (n-1)
s2
(also VAR) VAR.S()
Population Standard Deviation
Square root of the population variance σ (sigma) (also SD)
STDEV.P()
Sample Standard Deviation
Square root of the sample variance s (also SD) STDEV.S()
Coefficient of Variation
A measure of the variation of a sample or population relative to its mean
SD/mean
z-score Deviation of a data value from the mean, measured in standard deviations
z=(x-mean)/SD
Tolerance Interval An interval of several SDs around the population mean that contains a specified percentage of a population (according to the Empirical Rule)
Standard Error of the Sample Mean
A measure of the accuracy with which the sample mean estimates the population mean.
SE=SD/√n
Confidence
Interval
An interval of about 2 standard errors around the sample mean, which with a high confidence contains the population mean
Percentile The pth percentile is a value such that p percent of measurements fall at or below that value.
PERCENTILE.EXC()
Quartiles The 25
th, 50
th (i. e. median) and 75
th percentile of
a data set; the three points that divide the data set into four equal groups
Q1, Q2=Md, Q3
Interquartile range Difference between the third and first quartile IQR Q3- Q1
5-number summary Summary of a dataset as: Minimum, First quartile, Median, Third quartile, Maximum
Quartile, Quintile, Decile
A data set ordered from smallest to largest can be thought of as divided into 4, 5 or 10 equal-sized subsets. The terms quartile, quintile or decile may refer either to these subsets (sociology, economics) or to the values that divide them (descriptive statistics, cf. Quartiles).