الإحصاء والاحتمالات | Statistics & probability —…
مِسبار · مقرر جامعي مجاني
Statistics & probability
تعلم الإحصاء والاحتمالات (Statistics & probability) مجانًا عبر 16 وحدات و324 فيديو تعليميًا، بإجمالي نحو 38 ساعة، ضمن مكتبة مِسبار الجامعية.
Learn statistics and probability—everything you'd want to know about descriptive and inferential statistics.
- 16 وحدات.
- 324 فيديو.
- نحو 38 ساعة مشاهدة.
- المستوى: college.
ابدأ مشاهدة المقرر داخل مكتبة مِسبار
التخصصات المرتبطة بالمقرر
- الهندسة الصناعية (Industrial Engineering)
- علوم الحاسوب (Computer Science)
- الذكاء الاصطناعي (Artificial Intelligence)
- علم البيانات (Data Science)
- الاقتصاد (Economics)
- المالية (Finance)
- إدارة الأعمال (Business Administration)
- المحاسبة (Accounting)
- التسويق (Marketing)
- سلاسل الإمداد (Supply Chain Management)
- الطب (Medicine)
- الصيدلة (Pharmacy)
- التمريض (Nursing)
- الصحة العامة (Public Health)
- التغذية (Nutrition)
- المختبرات الطبية (Medical Laboratory Sciences)
- الرياضيات (Mathematics)
- الإحصاء (Statistics)
- الأحياء (Biology)
- العلوم السياسية (Political Science)
- العلاقات الدولية (International Relations)
- الإعلام (Media Studies)
- التخطيط العمراني (Urban Planning)
- تعليم الرياضيات (Mathematics Education)
- تعليم الدراسات الاجتماعية (Social Studies Education)
وحدات ودروس المقرر
1. Analyzing categorical data
14 فيديو تعليمي.
موضوعات ودروس الوحدة
- 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 frequency tables and Venn diagrams
- Two-way relative frequency tables
- Interpreting two-way tables
- Categorical data example
- Analyzing trends in categorical data
- Marginal and conditional distributions
2. Displaying and comparing quantitative data
14 فيديو تعليمي.
موضوعات ودروس الوحدة
- Representing data
- Frequency tables & dot plots
- Creating a histogram
- Histograms
- Interpreting a histogram
- Stem-and-leaf plots
- Reading stem and leaf plots
- Shapes of distributions
- Clusters, gaps, peaks & outliers
- Comparing distributions with dot plots (example problem)
- Comparing dot plots, histograms, and box plots
- Example: Comparing distributions
- Reading line graphs
- Misleading line graphs
3. Summarizing quantitative data
29 فيديو تعليمي.
موضوعات ودروس الوحدة
- Statistics intro: Mean, median, & mode
- Mean, median, & mode example
- 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)
- 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
- Sample variance
- Sample standard deviation and bias
- 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
- 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
- Range and mid-range
- Mean absolute deviation (MAD)
- Mean absolute deviation example
4. Modeling data distributions
20 فيديو تعليمي.
موضوعات ودروس الوحدة
- Calculating percentile
- Analyzing a cumulative relative frequency graph
- Normal distribution problem: z-scores (from ck12.org)
- Comparing with z-scores
- How parameters change as data is shifted and scaled
- Density Curves
- Median, mean and skew from density curves
- Density curve worked example
- Worked example finding area under density curves
- Qualitative sense of normal distributions
- Normal distribution problems: Empirical rule
- Standard normal distribution and the empirical rule (from ck12.org)
- More empirical rule and z-score practice (from ck12.org)
- 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
- Deep definition of the normal distribution
- Normal distribution excel exercise
5. Exploring bivariate numerical data
30 فيديو تعليمي.
موضوعات ودروس الوحدة
- Constructing a scatter plot
- Example of direction in scatterplots
- Scatter plot: smokers
- Bivariate relationship linearity, strength and direction
- Example: Correlation coefficient intuition
- Calculating correlation coefficient r
- Fitting a line to data
- Estimating the line of best fit exercise
- Estimating with linear regression (linear models)
- Line of best fit: smoking in 1945
- Introduction to residuals and least squares regression
- Calculating residual example
- Calculating the equation of a regression line
- Interpreting slope of regression line
- Interpreting y-intercept in regression model
- Interpreting a trend line
- Residual plots
- R-squared or coefficient of determination
- Standard deviation of residuals or Root-mean-square error (RMSD)
- Interpreting computer regression data
- Impact of removing outliers on regression lines
- Squared error of regression line
- Proof (part 1) minimizing squared error to regression line
- Proof (part 2) minimizing squared error to regression line
- Proof (part 3) minimizing squared error to regression line
- Proof (part 4) minimizing squared error to regression line
- Regression line example
- Second regression example
- Calculating R-squared
- Covariance and the regression line
6. Study design
17 فيديو تعليمي.
موضوعات ودروس الوحدة
- Statistical questions
- Statistical and non statistical questions
- Reasonable samples
- Identifying a sample and population
- Examples of bias in surveys
- Example of undercoverage introducing bias
- Correlation and causality
- Picking fairly
- Techniques for generating a simple random sample
- Techniques for random sampling and avoiding bias
- Types of statistical studies
- Worked example identifying experiment
- Worked example identifying observational study
- Worked example identifying sample study
- Appropriate statistical study example
- Introduction to experiment design
- Matched pairs experiment design
7. Probability
41 فيديو تعليمي.
موضوعات ودروس الوحدة
- Intro to theoretical probability
- Simple probability: yellow marble
- Simple probability: non-blue marble
- Intuitive sense of probabilities
- The Monty Hall problem
- Example: All the ways you can flip a coin
- Die rolling probability
- Subsets of sample spaces
- Intersection and union of sets
- Relative complement or difference between sets
- Universal set and absolute complement
- Subset, strict subset, and superset
- Bringing the set operations together
- Experimental probability
- Theoretical and experimental probabilities
- Making predictions with probability
- Experimental versus theoretical probability simulation
- Random number list to run experiment
- Random numbers for experimental probability
- Statistical significance of experiment
- Probability with Venn diagrams
- Addition rule for probability
- Sample spaces for compound events
- Compound probability of independent events
- Probability of a compound event
- "At least one" probability with coin flipping
- Free-throw probability
- Three-pointer vs free-throw probability
- Probability without equally likely events
- Independent events example: test taking
- Die rolling probability with independent events
- Dependent probability introduction
- Dependent probability: coins
- Dependent probability example
- Independent & dependent probability
- Dependent probability
- Calculating conditional probability
- Conditional probability explained visually
- Conditional probability tree diagram example
- Conditional probability and independence
- Analyzing event probability for independence
8. Counting, permutations, and combinations
23 فيديو تعليمي.
موضوعات ودروس الوحدة
- Count outcomes using tree diagram
- Counting outcomes: flower pots
- Permutation formula
- Zero factorial or 0!
- Factorial and counting seat arrangements
- Possible three letter words
- Ways to arrange colors
- Ways to pick officers
- Intro to combinations
- Combination formula
- Handshaking combinations
- Combination example: 9 card hands
- Probability using combinations
- Probability & combinations (2 of 2)
- Example: Different ways to pick officers
- Example: Combinatorics and probability
- Getting exactly two heads (combinatorics)
- Exactly three heads in five flips
- Generalizing with binomial coefficients (bit advanced)
- Example: Lottery probability
- Conditional probability and combinations
- Mega millions jackpot probability
- Birthday probability problem
9. Random variables
47 فيديو تعليمي.
موضوعات ودروس الوحدة
- Random variables
- Discrete and continuous random variables
- Constructing a probability distribution for random variable
- Probability models example: frozen yogurt
- Valid discrete probability distribution examples
- Probability with discrete random variable example
- Mean (expected value) of a discrete random variable
- Variance and standard deviation of a discrete random variable
- Probability density functions
- Probabilities from density curves
- Impact of transforming (scaling and shifting) random variables
- Example: Transforming a discrete random variable
- Mean of sum and difference of random variables
- Variance of sum and difference of random variables
- Intuition for why independence matters for variance of sum
- Deriving the variance of the difference of random variables
- Example: Analyzing distribution of sum of two normally distributed random variables
- Example: Analyzing the difference in distributions
- Binomial variables
- Recognizing binomial variables
- 10% Rule of assuming "independence" between trials
- Binomial distribution
- Visualizing a binomial distribution
- Binomial probability example
- Generalizing k scores in n attempts
- Free throw binomial probability distribution
- Graphing basketball binomial distribution
- Binompdf and binomcdf functions
- Mean and variance of Bernoulli distribution example
- Bernoulli distribution mean and variance formulas
- Expected value of a binomial variable
- Variance of a binomial variable
- Finding the mean and standard deviation of a binomial random variable
- Geometric random variables introduction
- Probability for a geometric random variable
- Cumulative geometric probability (greater than a value)
- Cumulative geometric probability (less than a value)
- TI-84 geometpdf and geometcdf functions
- Proof of expected value of geometric random variable
- Term life insurance and death probability
- Getting data from expected value
- Expected profit from lottery ticket
- Expected value while fishing
- Comparing insurance with expected value
- Law of large numbers
- Poisson process 1
- Poisson process 2
10. Sampling distributions
12 فيديو تعليمي.
موضوعات ودروس الوحدة
- Introduction to sampling distributions
- Sample statistic bias worked example
- Sampling distribution of sample proportion part 1
- Sampling distribution of sample proportion part 2
- Normal conditions for sampling distributions of sample proportions
- Probability of sample proportions example
- Inferring population mean from sample mean
- Central limit theorem
- Sampling distribution of the sample mean
- Sampling distribution of the sample mean (part 2)
- Standard error of the mean
- Example: Probability of sample mean exceeding a value
11. Confidence intervals
20 فيديو تعليمي.
موضوعات ودروس الوحدة
- Confidence intervals and margin of error
- Confidence interval simulation
- Interpreting confidence level example
- Confidence interval example
- Margin of error 1
- Margin of error 2
- Conditions for valid confidence intervals for a proportion
- Conditions for confidence interval for a proportion worked examples
- Critical value (z*) for a given confidence level
- Example constructing and interpreting a confidence interval for p
- Determining sample size based on confidence and margin of error
- Introduction to t statistics
- Simulation showing value of t statistic
- Conditions for valid t intervals
- Example finding critical t value
- Example constructing a t interval for a mean
- Confidence interval for a mean with paired data
- Sample size for a given margin of error for a mean
- T-statistic confidence interval
- Small sample size confidence intervals
12. Significance tests (hypothesis testing)
29 فيديو تعليمي.
موضوعات ودروس الوحدة
- Simple hypothesis testing
- Idea behind hypothesis testing
- Examples of null and alternative hypotheses
- P-values and significance tests
- Comparing P-values to different significance levels
- Estimating a P-value from a simulation
- Introduction to Type I and Type II errors
- Type 1 errors
- Examples identifying Type I and Type II errors
- Introduction to power in significance tests
- Examples thinking about power in significance tests
- Constructing hypotheses for a significance test about a proportion
- Conditions for a z test about a proportion
- Calculating a z statistic in a test about a proportion
- Calculating a P-value given a z statistic
- Making conclusions in a test about a proportion
- Writing hypotheses for a significance test about a mean
- Conditions for a t test about a mean
- When to use z or t statistics in significance tests
- Example calculating t statistic for a test about a mean
- Using TI calculator for P-value from t statistic
- Using a table to estimate P-value from t statistic
- Comparing P-value from t statistic to significance level
- Free response example: Significance test for a mean
- Hypothesis testing and p-values
- One-tailed and two-tailed tests
- Z-statistics vs. T-statistics
- Small sample hypothesis test
- Large sample proportion hypothesis testing
13. Two-sample inference for the difference between groups
9 فيديو تعليمي.
موضوعات ودروس الوحدة
- Comparing population proportions 1
- Comparing population proportions 2
- Hypothesis test comparing population proportions
- Statistical significance of experiment
- Statistical significance on bus speeds
- Difference of sample means distribution
- Confidence interval of difference of means
- Clarification of confidence interval of difference of means
- Hypothesis test for difference of means
14. Inference for categorical data (chi-square tests)
8 فيديو تعليمي.
موضوعات ودروس الوحدة
- Chi-square distribution introduction
- Pearson's chi square test (goodness of fit)
- Chi-square statistic for hypothesis testing
- Chi-square goodness-of-fit example
- Filling out frequency table for independent events
- Contingency table chi-square test
- Introduction to the chi-square test for homogeneity
- Chi-square test for association (independence)
15. Advanced regression (inference and transforming)
9 فيديو تعليمي.
موضوعات ودروس الوحدة
- Introduction to inference about slope in linear regression
- Conditions for inference on slope
- Confidence interval for the slope of a regression line
- Calculating t statistic for slope of regression line
- Using a P-value to make conclusions in a test about slope
- Using a confidence interval to test slope
- Comparing models to fit data example
- Transforming nonlinear data
- Worked example of linear regression using transformed data
16. Analysis of variance (ANOVA)
3 فيديو تعليمي.
مقررات مرتبطة
- حساب المثلثات | Trigonometry
- ما قبل التفاضل والتكامل | Precalculus
- التفاضل والتكامل AP (AB) | AP®︎ Calculus AB
- التفاضل والتكامل AP (BC) | AP®︎ Calculus BC
- الإحصاء AP | AP®︎ Statistics
- التفاضل والتكامل متعدد المتغيرات | Multivariable calculus
المصدر والحقوق
المحتوى الأصلي المرخص: أكاديمية خان. تقوم مِسبار بالفهرسة والتنظيم حسب التخصص، وتعرض الفيديوهات المرخصة غير التجارية داخل مكتبة مجانية مستقلة.