Statistics 1
Preface
Statistics as the Science of Data
Branches of Statistics
1
Statistical data
1.1
Observational studies and experiments
1.2
Population and sample
1.3
Sources of statistical data
1.4
Quantitative and qualitative variables
1.5
Measurement scales
1.5.1
Four main scales of measurement
1.5.2
Why measurement scales matter
1.5.3
Other scales
1.6
Other data classifications
1.7
Numbers
1.7.1
Names: short and long scale
1.7.2
Decimal symbol and thousands separator
1.7.3
Scientific/engineering notation
1.7.4
Percentages
1.8
Links
1.9
Questions
1.9.1
Discussion questions
1.9.2
Test questions
One variable distribution
2
Empirical distribution
2.1
Presenting empirical distribution in tables
2.1.1
Individual series (raw data)
2.1.2
Discrete frequency distribution table
2.1.3
Grouped (interval) frequency distribution table
2.2
Visualization of qualitative variable distributions
2.2.1
Bar charts
2.2.2
Stacked bar charts
2.2.3
Pie charts
2.3
Histogram – visualisation of quantitative variable distributions
2.3.1
What is on the Y-axis?
2.3.2
Shapes of histograms
2.3.3
Number of Class Intervals
2.3.4
Kernel density estimator
2.3.5
Violin plot
2.4
Empirical cumulative distribution function
2.5
Links
2.6
Exercises
3
Central tendency and positional measures
3.1
Mean
3.1.1
Arithmetic mean
3.1.2
Weighted Arithmetic Mean
3.1.3
Harmonic mean
3.1.4
Geometric mean
3.2
Median
3.2.1
Approximating the median from a grouped frequency distribution
3.3
Mode
3.3.1
Determining the mode from an interval distribution series
3.4
Quantiles
3.4.1
Quartiles
3.4.2
Two meanings of the word quartile
3.4.3
Quintiles
3.4.4
Deciles
3.4.5
Percentiles
3.4.6
Determining Quantiles in Practice
3.5
Links
3.6
Exercises
4
Measures of dispersion
4.1
Standard deviation
4.1.1
Variance
4.1.2
Coefficient of Variation
4.1.3
Using the standard deviation
4.1.4
The standard deviation is not the mean deviation
4.2
Interquartile range
4.2.1
Interquartile deviation and positional coefficient of variation
4.2.2
Decile range
4.2.3
Range
4.3
Boxplot
4.4
Links
4.5
Questions
4.6
Exercises
5
Standardization and the normal distribution
5.1
Data standardization (z-score)
5.2
Normal distribution
5.3
Empirical Rule
5.4
Chebyshev’s Inequality
6
Distribution shape measures
6.1
Skewness
6.2
Kurtosis
6.3
Outliers
6.3.1
Identifying Outliers Using Position Measures
6.3.2
Identifying Outliers Using Z-Scores
Literature
Published with bookdown
Statistics 1
Literature
Freedman, David, Robert Pisani, and Roger Purves. 2007.
Statistics, 4th Edition
. New York: W. W. Norton & Company.