Mathematics,

Statistics and probability

Statistics is the discipline that concerns the collection, organization, analysis, interpretation and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Learn statistics and probability for free—everything you'd want to know about descriptive and inferential statistics. Full curriculum of exercises and videos. This is the property of khanacademy.org and is available for free on their website.

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Hamza · April 8, 2020

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Analyzing categorical data

Analyzing one categorical variable 8 Topics

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Identifying individuals, variables and categorical variables in a data set

Reading pictographs

Reading bar graphs

Reading bar graphs: Harry Potter

Creating a bar graph

Reading bar charts: comparing two sets of data

Reading bar charts: putting it together with central tendency

Reading pie graphs (circle graphs)

Two-way tables 5 Topics

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Two-way frequency tables and Venn diagrams

Two-way relative frequency tables

Interpreting two-way tables

Categorical data example

Analyzing trends in categorical data

Distributions in two-way tables 1 Topic

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Marginal and conditional distributions

Displaying and comparing quantitative data

Displaying quantitative data with graphs 6 Topics

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Representing data

Frequency tables & dot plots

Creating a histogram

Interpreting a histogram

Stem-and-leaf plots

Reading stem and leaf plots

Describing and comparing distributions 5 Topics

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Shapes of distributions

Clusters, gaps, peaks & outliers

Comparing distributions with dot plots (example problem)

Comparing dot plots, histograms, and box plots

Example: Comparing distributions

More on data displays 2 Topics

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Reading line graphs

Misleading line graphs

Summarizing quantitative data

Measuring center in quantitative data 2 Topics

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Statistics intro: Mean, median, & mode

Mean, median, & mode example

More on mean and median 6 Topics

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Comparing means of distributions

Means and medians of different distributions

Impact on median & mean: removing an outlier

Impact on median & mean: increasing an outlier

Missing value given the mean

Median & range puzzlers

Interquartile range (IQR) 1 Topic

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Interquartile range (IQR)

Variance and standard deviation of a population 5 Topics

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Measures of spread: range, variance & standard deviation

Variance of a population

Population standard deviation

Mean and standard deviation versus median and IQR

Statistics: Alternate variance formulas

Variance and standard deviation of a sample 2 Topics

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Sample variance

Sample standard deviation and bias

More on standard deviation 4 Topics

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Why we divide by n - 1 in variance

Simulation showing bias in sample variance

Simulation providing evidence that (n-1) gives us unbiased estimate

Review and intuition why we divide by n-1 for the unbiased sample variance

Box and whisker plots 6 Topics

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Worked example: Creating a box plot (odd number of data points)

Worked example: Creating a box plot (even number of data points)

Constructing a box plot

Reading box plots

Interpreting box plots

Judging outliers in a dataset

Other measures of spread 3 Topics

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Range and mid-range

Mean absolute deviation (MAD)

Mean absolute deviation example

Modeling data distributions

Percentiles 2 Topics

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Calculating percentile

Analyzing a cumulative relative frequency graph

Z-scores 2 Topics

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Normal distribution problem: z-scores (from ck12.org

Comparing with z-scores

Effects of linear transformations 1 Topic

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How parameters change as data is shifted and scaled

Density curves 4 Topics

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Median, mean and skew from density curves

Density curve worked example

Worked example finding area under density curves

Normal distributions and the empirical rule 4 Topics

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Qualitative sense of normal distributions (from ck12.org)

Normal distribution problems: Empirical rule (from ck12.org)

Standard normal distribution and the empirical rule (from ck12.org)

More empirical rule and z-score practice (from ck12.org)

Normal distribution calculations 5 Topics

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Standard normal table for proportion below

Standard normal table for proportion above

Standard normal table for proportion between values

Finding z-score for a percentile

Threshold for low percentile

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Hamza

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Course Includes

71 Lessons
318 Topics

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