A summary of all fundamental concepts in descriptive statistics on a single page, with Excel functions: measures of central tendency, measures of variation, percentiles, five-number summary, etc.

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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).