Objective:

• Understand what statistics are and how they should be approached.

A good introduction of the prolific dominance of statistics in our world.

https://www.youtube.com/watch?v=Tp53kvPL9W4

Anything that is powerful when used properly is, unfortunately, also equally problematic and potentially destructive when used poorly.  This video illustrates that. 

https://www.youtube.com/watch?v=p4m9E4f6vwU

Objective:

• Recognize and differentiate between the terms:

  • Census

  • Parameter

  • Population

  • Representative Sample

  • Sample

The concepts of "population" and "sample" are foundational to statistics.  These concepts are layed out in the following video. 

https://www.youtube.com/watch?v=NlcDpqnqBKY

Objectives:

Recognize and differentiate between the terms:

• • Differential statistics

  • Inferential statistics

The job of the statistician can be divided into two parts - accurate and insightful descriptions of what can be seen, and educated prediction of what cannot be seen.  Such is illustrated in the following video. https://www.youtube.com/watch?v=eOj5dwV4hbU

Objectives:

• Recognize and differentiate between the terms:

  • Qualitative Data

  • Discrete Quantitative Data

  • Continuous Quantitative Data

This video describes the difference between quantitative and qualitative data as well as the two kinds of quantitative data. 

https://www.youtube.com/watch?v=5rUVYWfZOb8

Objectives:

• Recognize and differentiate between the terms:

  • Cluster Sampling

  • Convenience Sampling

  • Random Assignment

  • Random Sampling

  • Simple Random Sampling

  • Stratified Sampling

  • Systematic Sampling

These videos describe the procedures associated with simple random sampling (SRS), stratified sampling, cluster sampling, and systematic sampling.  (Note: "convenience sampling" is simply a sampling process that does not involve any of the rigor or planning described in any of the following techniques.  It simply involves a "quick and dirty" process of quickly acquiring a set of samples that are easy to acquire, but may not necessarily comprise a representative sample.) 

https://www.youtube.com/watch?v=yx5KZi5QArQ

https://www.youtube.com/watch?v=sYRUYJYOpG0

https://www.youtube.com/watch?v=QOxXy-I6ogs

https://www.youtube.com/watch?v=QFoisfSZs8I

Objectives:

• Recognize and differentiate between the terms:

  • Sampling with Replacement

  • Sampling without Replacement

This video summarizes the difference between sampling with and without replacement.  We will explore the probability aspects of the video more in later chapters. 

https://www.youtube.com/watch?v=dQ9r2S7NWLs

Objectives:

• Recognize and differentiate between the terms:

  • Sampling Error

  • Non-Sampling Error

  • Sampling Bias

The following two videos describe sampling and non-sampling error, respectively.  Sampling bias is described mostly in the second video. 

https://www.youtube.com/watch?v=y3A0lUkpAko

https://www.youtube.com/watch?v=5a_cf21f6N4

Objectives:

• Recognize and differentiate between the terms:

  • Variable

  • Level of Measurement

  • Nominal Data

  • Ordinal Data

  • Interval Data

  • Ratio Data

This video describes the different levels of measurement found in different kinds of data.  Pay particular attention to the differing ways in which you can analyze or graph the different kinds of data. 

https://www.youtube.com/watch?v=LPHYPXBK_ks

Objectives:

• Recognize and differentiate between the terms:

  • Frequency Distribution

  • Frequency

  • Relative Frequency

  • Cumulative Frequency

  • Cumulative Relative Frequency

  • Class Width

  • Class Limits (Lower, Upper)

  • Class Boundaries

• Create and interpret frequency tables of data and grouped data

These videos describe in detail the process of creating a grouped frequency distribution, including how to calculate class width, class limits, and class boundaries. 

https://www.youtube.com/watch?v=tcU_hApd-j0

https://www.youtube.com/watch?v=k2U1TDfSB9U

https://www.youtube.com/watch?v=pOBOtSHW0bc

Objectives:

• Recognize and differentiate between the terms:

  • Observational Study

  • Experimental Study

The following video describes the difference between observational and experimental studies. 

https://www.youtube.com/watch?v=Nh3ByyM2rzE

Objectives:

• Recognize and differentiate between the terms:
  
  

  • Experimental Unit

  • Treatments

  • Control Group

  • Placebo

  • Completely Randomized Design

  • Blocking Design

  • Matched Pairs Design

  • Double-Blind Experiment

  • Explanatory Variable (Independent Variable)

  • Response Variable (Dependent Variable)

  • Lurking Variable

  • Confounding Variable

The next two videos describe important considerations for when beginning a scientific study. 

https://www.youtube.com/watch?v=10ikXret7Lk

https://www.youtube.com/watch?v=GMqrOdCx4Yg

A good explanation of explanatory and response variables 

https://www.youtube.com/watch?v=V_13eXh7ctY

A similarly good explanation of lurking and confounding variables. 

https://www.youtube.com/watch?v=nMrEq_kf3ME

Objectives:

• Create and interpret bar and line graphs

A good video on the creation and interpretation of bar graphs. 

https://www.youtube.com/watch?v=PoH1Y2DW2Es

The same for line graphs. 

https://www.youtube.com/watch?v=xn9zHCWAXEM

Objectives:

• Create and interpret stem-and-leaf plots

A good video on the creation and interpretation of stem-and-leaf plots. 

https://www.youtube.com/watch?v=zBPRAx0UIOc

Objectives:

• Define and understand the following terms:

  • Frequency Polygon

  • Histogram

  • Midpoint

  • Ogive

• Display data graphically and interpret graphs: histograms, frequency polygons and ogives

Good description of the procedure for creating a histogram. 

https://www.youtube.com/watch?v=rXl52dP7fEI

Good description of how to create a frequency polygon. 

https://www.youtube.com/watch?v=mNVaj8zGul8

Good description of how to create an ogive. 

https://www.youtube.com/watch?v=rl18PzVOPmQ

Objectives:

• Define and understand the following terms:
  
  

  • First Quartile

  • Median

  • Percentile

  • Quartiles

  • Third Quartile

• Recognize, describe, and calculate the measures of location of data: quartiles and percentiles.

This video discusses the meaning of percentiles and quartiles. 

https://www.youtube.com/watch?v=mDJvDRvvDXo

Objectives:

• Calculate the IQR

• Define an outlier

• Calculate a rating for identifying outliers

Statisticians oftentimes play a role in assessing and improving the quality of a dataset.  Part of this process involves finding outliers.  This video describes what an outlier is, and how to determine if a data value is a likely outlier. 

https://www.youtube.com/watch?v=9aDHbRb4Bf8

Objectives:

• Construct and interpret a Five-Number Summary

• Create and interpret box plots

Good description of how to create a box and whisker plot, another name for a box plot. 

https://www.youtube.com/watch?v=fJZv9YeQ-qQ

Objectives:

• Calculate sample and population means

• Use the rounding rule or calculation of means

• Calculate medians

• Calculate modes and modal classes

• Identify a distribution as unimodal, bimodal, or multimodal

• Calculate midranges

• Calculate weighted means

• Calculate the mean, median, and mode of linearly transformed data

Good video on finding the mean, median, and mode. 

https://www.youtube.com/watch?v=k3aKKasOmIw

This video shows how to find the mean of grouped data. 

https://www.youtube.com/watch?v=z_CBPRrEJUw

Good video for calculating midranges. 

https://www.youtube.com/watch?v=tYYaXebF_JU

Good video for determining if a distribution is unimodal, bimodal, or multimodal. 

https://www.youtube.com/watch?v=7kw9dlAJmA8

Good video for calculating weighted means. 

https://www.youtube.com/watch?v=8mhVQU-ZX8I

Objectives:

• Identify distributions as symmetric, positively (right) skewed, or negatively (left) skewed

• Describe how the relative order of the mean, median, and mode is affected by the skewness or symmetry of the distribution

Good discussion of the skewness of a distribution, how such skewness is visible in many different graphical contexts, and the relationship of this skewness to the relative placement of the mean and median. 

https://www.youtube.com/watch?v=pfujiA5Mk_U

Objectives:

• Calculate the range of a dataset

• Calculate the variance and standard deviation of a population

• Calculate the variance and standard deviation of a sample

• Make use of the alternate methodology for calculating the variance and standard deviation of a sample

• Use the rounding rule for calculating standard deviations

Good video on calculating the range of a data set. 

https://www.youtube.com/watch?v=DsFCi-u1G_8

The next two videos give a good description of how to calculate the variance and standard deviation for both a sample and a population. 

https://www.youtube.com/watch?v=s7WTQ0H0Acc

https://www.youtube.com/watch?v=y_wdorJ7cXE

This video is a good follow-up to the previous two videos, addressing some common questions.  It also gets into "degrees of freedom", which we will be discussing later in the course. 

https://www.youtube.com/watch?v=wpY9o_OyxoQ

This video gives an alternate formula for calculating the sample mean -- only the sample mean! 

(Note: You do NOT need to memorize this derivation process - only the final formula.) 

https://www.youtube.com/watch?v=dymCh1EusjU

Objectives:

• Calculate the sample variance and sample standard deviation for grouped data

This video describes how to calculate the variance and standard deviation of grouped (sample) data. 

https://www.youtube.com/watch?v=vL3fcfujB5w

Objectives:

• Calculate the coefficient of variation

• Estimate the sample standard deviation using the "Range Rule-of-Thumb"

This video gives a quick description of how to calculate the coefficient of variation. 

https://www.youtube.com/watch?v=b_dafTU6opk

A quick description of how to use the range rule of thumb to estimate the standard deviation. 

https://www.youtube.com/watch?v=G0p05yokDvU

This (optional) additional video gives an alternate perspective on the range rule of thumb. 

https://www.youtube.com/watch?v=dqR3gWIdrck

Objectives:

• Use Chebyshev's Theorem to estimate the minimum proportion of data within a given number of standard deviations

• Use Chebyshev's Theorem to estimate the minimum of standard deviations encompassing a given proportion of the data

• Recite the percentage of total area of a Normally-shaped distribution within one, two, and three standard deviations from the mean

This video gives examples of the use of Chebyshev's inequality. 

https://www.youtube.com/watch?v=RZj2stql-L4

Objectives:

• Recalculate the variance and standard deviation of linearly transformed data

This video describes the changes in the mean and standard deviation when a given set of data is either multiplied by a constant value or added by a constant value. 

https://www.youtube.com/watch?v=fx3TtExi9e8

One thing the video misses is that, when the data set is multiplied by a constant value, since the new standard deviation is multiplied by the same constant:

 `sigma_Y=k sigma_X` 

then the variance will be increased by the same constant SQUARED:

 `sigma_Y^2=k^2 sigma_X^2`  

Objectives:

• Define, identify, and determine the following terms in the context of various given problems:

  • Probability experiment

  • Outcome

  • Sample space

  • Event

  • Classical probability

  • Empirical probability

  • Subjective probability

  • Equally likely events

  • Probability

Good video on the fundamental vocabulary of probability. 

https://www.youtube.com/watch?v=LoslgAfS6KA

Objectives:

• Create a Tree Diagram

Good explanation of tree diagrams and their usage. 

https://www.youtube.com/watch?v=nusdB5jgcIk

Objectives:

• Calculate classical probabilities

• Understand and apply basic probability rules

Good video describing problems in classical probability. 

https://www.youtube.com/watch?v=Yjp6z3Kr234

Objectives:

• Calculate the probability of complementary events

Good discussion of complementary events and their probabilities. 

https://www.youtube.com/watch?v=z9pxyiOiaM0

Objectives:

• Calculate empirical probabilities

• Law of Large Numbers

Good demonstration of how to calculate empirical probabilities. 

https://www.youtube.com/watch?v=gskebdiMOcw

Good discussion of the law of large numbers and how it connects classical probability with empirical probability. 

https://www.youtube.com/watch?v=MntX3zWNWec

Objectives:

• Define, identify, and determine the following terms in the context of various given problems:

  • Independent events

  • Mutually exclusive / Disjoint events

• Calculate probabilities using the Addition Rule

• Calculate probabilities using the Multiplication Rule

Good description of the definition of mutually exclusive and independent events.  It also presents the formula for conditional probability. 

https://www.youtube.com/watch?v=aVqmWW3xmdU

Good description of how to calculate probabilities of independent events. 

https://www.youtube.com/watch?v=7QlZjoLmg3I

Objectives:

• Define, identify, and determine the following terms in the context of various given problems:
  
  

  • Dependent events

  • Conditional probability

• Calculate conditional probabilities

• Make calculations involving conditional probabilities

Good description of how to calculate probabilities of dependent events. 

https://www.youtube.com/watch?v=LS-_ihDKr2M

Objectives:

• Create and interpret a contingency table

• Calculate probabilities from a contingency table

Good discussion of all the ways that a contingency table can be read for calculating probabilities. 

https://www.youtube.com/watch?v=qLXjqNrLKuM

Objectives:

• Create and interpret a tree diagram

• Create and interpret a Venn diagram

This first video on tree diagrams focuses on its use with independent events. 

https://www.youtube.com/watch?v=mkDzmI7YOx0

This second video does the same for dependent events. 

https://www.youtube.com/watch?v=NOOMC_rc-8Q

Good discussion of how to use a Venn diagram to organize events such that probabilities can be easily calculated. 

https://www.youtube.com/watch?v=UsPyZybCI5Y

Objectives:

• Utilize the Fundamental Counting Rule to calculate the total number of possibilities

• Utilize factorial notation

• Define permutations and combinations, and understand the difference between them, both qualitatively and quantitatively

• Calculate permutations of `r` objects taken from `n` objects and placed in a specific order

• Calculate combinations of `r` objects taken from `n` objects

• Calculate permutations of `r` objects, where some objects are identical

• Calculate probabilities using counting rules

This video presents a solid derivation of the formula for permutations. 

https://www.youtube.com/watch?v=DROZVHObeko

Good description of permutations and combinations and the difference between them. 

https://www.youtube.com/watch?v=ssoTzwA_Aug

Good discussion of how to find the number of permutations of items, some of which are identical. 

https://www.youtube.com/watch?v=3VBdsNCSBXM

Objectives:

• Define the following terms:

  • Random variable

  • Discrete probability distribution

• Construct a discrete probability distribution

Great introduction to random variables, both continuous and discrete, along with a reinforcement of the probability notation we use. 

https://www.youtube.com/watch?v=lHCpYeFvTs0

Objectives:

• Calculate the expectation (mean) of a discrete probability distribution

• Calculate the variance and standard deviation of a discrete probability distribution

Good discussion of how to calculate means (expected values), variances, and standard deviations of a probability distribution. 

https://www.youtube.com/watch?v=OvTEhNL96v0

Objectives:

• Define the characteristics of a binomial experiment

• Use the binomial distribution to calculate probabilities

• Calculate the mean, variance, and standard deviation of the binomial distribution

This video gives a good description of a binomial experiment (here referred to as a "binomial setting"). 

https://www.youtube.com/watch?v=nRuQAtajJYk

Good description of how to use the binomial distribution to calculate probabilities. 

https://www.youtube.com/watch?v=qIzC1-9PwQo

This video may be a bit challenging, but gives a more in-depth discussion of the binomial distribution. 

https://www.youtube.com/watch?v=8idr1WZ1A7Q

This video focuses on finding the mean, variance, and standard deviation for a binomial distribution. 

https://www.youtube.com/watch?v=YhQ-jOLY3MY

Objectives:

• Calculate probabilities from continuous probability distributions

Good introduction to continuous probability distributions, also called "probability density functions", or PDF's. 

https://www.youtube.com/watch?v=j8XLYFzTJzE

Objectives:

• Students will use uniform probability density functions to:

  • write the functions

  • calculate means, variances, and standard deviations,

  • calculate probabilities

  • calculate conditional probabilities, and

  • calculate percentiles

This video gives a good introduction to uniform probability distributions. 

https://www.youtube.com/watch?v=UC-CBUSQXAo

This video focuses a bit more on finding probabilities, including conditional probabilities. 

https://www.youtube.com/watch?v=KfunVw-0AH0

Objectives:

• Describe the properties of a normal distribution

• Find areas under the standard normal distribution

• Find boundaries on the standard normal distribution that encompass a given area

Good video introducing the properties of the normal distribution. 

https://www.youtube.com/watch?v=gBCwOPHrUFc

Good introduction to describing areas under the normal distribution curve. 

https://www.youtube.com/watch?v=T7-eeg6rhjY

Objectives:

• Create z values for individual data points

• Find areas under any Normal curve

• Find data values given probabilities

• Determine normality of a distribution

Good discussion of how to find probabilities using a generalized normal distribution.

(Note: This video uses the TI84 calculator.  You will be using your spreadsheets!) 

https://www.youtube.com/watch?v=uoQ_g9O7Ij4

We can also find thresholds given a probability for the generalized normal distribution. 

https://www.youtube.com/watch?v=gHgrIQGkXOQ

This video provides some additional practice. 

https://www.youtube.com/watch?v=vrS1EpH3Yoo

Objectives:

• Define the following:

  • Sampling error

  • Central Limit Theorem

  • Sampling distribution of sample means

  • Standard error of the mean

• Calculate the mean and standard deviation for a distribution of sample means

• Utilize the Finite Population Correction for calculating the standard error of the mean

Good introduction to the concept of sampling distributions. 

https://www.youtube.com/watch?v=PZRiJdOyLaw

This video extends the concept to sampling means. 

https://www.youtube.com/watch?v=q50GpTdFYyI

This describes the Central Limit Theorem. 

https://www.youtube.com/watch?v=Pujol1yC1_A

This video describes the implementation of the Finite Population Correction Factor. 

https://www.youtube.com/watch?v=lnQzVP1vcJQ

Objectives:

• Describe when a binomial distribution can be approximated by a normal distribution

• Employ a normal approximation to the binomial using a continuity correction

How does the Central Limit Theorem direct us to handle samples of proportion data?  Find out below: 

https://www.youtube.com/watch?v=fuGwbG9_W1c

The binomial distribution is discrete.  The normal distribution is continuous.  Thus, when we use the normal distribution to approximate the binomial, we have to employ a "continuity correction factor", explained in this video. 

https://www.youtube.com/watch?v=YC2ruKn02pE

This section provides additional practice for the concepts introduced in sections 7.1A and 7.1B.

Objectives:

• Define the following:

  • Point estimate

  • Interval estimate

  • Confidence level

  • Confidence interval

  • Margin of error

• Understand the assumptions for finding a confidence interval for a single population mean when the population standard deviation is known

• Calculate a confidence interval for a single population mean given a confidence level when the population standard deviation is known

• Calculate the same confidence interval with a finite population correction

• Calculate a required sample size given a margin of error and confidence level when the population standard deviation is known

• Calculate the same required sample size using a finite population correction

Good explanation of how to calculate a confidence interval when the population standard deviation is known.  (Note, in British-style English the letter "z" is pronounced "zed".) 

https://www.youtube.com/watch?v=ENnlSlvQHO0

This is a reminder video (shown before) describing the finite population correction factor (FPC) and its usage. 

https://www.youtube.com/watch?v=lnQzVP1vcJQ

Good discussion of the calculation of sample size. 

https://www.youtube.com/watch?v=Z2dKK1xicgs

Objectives:

• Understand the assumptions for finding a confidence interval for a single population mean when the population standard deviation is unknown

• Calculate a confidence interval for a single population mean given a confidence level when the population standard deviation is unknown

• Calculate the same confidence interval with a finite population correction

This is an introduction to the T distribution, used when the population standard deviation is unknown. 

https://www.youtube.com/watch?v=NACUg0PdjIc

This is a good discussion of how to create a confidence interval on a single population mean when the population standard deviation is unknown. 

https://www.youtube.com/watch?v=vrod7OScpC4

Objectives:

• Understand the assumptions for finding a confidence interval for a single population proportion

• Calculate a confidence interval for a single population proportion

• Calculate the same confidence interval with a finite population correction

• Calculate a required sample size given a margin of error and confidence level for a population proportion

• Calculate the same required sample size using a finite population correction

This video describes how to create a confidence interval on a population proportion. 

https://www.youtube.com/watch?v=3ReWri_jh3M

Objectives:

• Define and identify in various situations:

• Statistical hypothesis

• Null hypothesis

• Alternative hypothesis

• Define and identify in various situations:

  • Type I error

  • Type II error

  • Level of significance

  • Power

This video gives a good first glance of hypothesis testing, focuses on the language of hypothesis generation. 

https://www.youtube.com/watch?v=YoeFpQw44Uw

There are two possible errors when performing a hypothesis test, commonly referred to as Type I and Type II.  Both are described in this next video. 

https://www.youtube.com/watch?v=bc_sL0wuZYw

The process of hypothesis testing combines the uncertainty of probability distributions with the hard logic of mathematics.  This video gives a good description of the logic behind hypothesis testing. 

https://www.youtube.com/watch?v=ATdCPJ_4qNQ

Writing statistical hypotheses involves a lot of mathematical symbols, and so may present a problem when creating electronic documents.  This video describes how to overcome this. 

https://www.youtube.com/watch?v=Mm_eR1FWesc

Objectives:

• Define and identify in various situations:

  • Statistical test

  • Test value / Test statistic

  • One-tailed test

  • Two-tailed test

  • Right-tailed test

  • Left-tailed test

• Define and identify in various situations:

  • Critical/Rejection Region

  • Non-critical / Non-rejection Region

  • Critical Value

• Find critical values

There are three types of hypothesis tests - left-tailed, right-tailed, and two-tailed.  This video describes the difference between the three and when to use each. 

https://www.youtube.com/watch?v=-x1HYOnGWF4

Hypothesis testing requires some assumptions.  This video discusses those assumptions. 

https://www.youtube.com/watch?v=1Idv_Lts_Zg

The final step in hypothesis testing involves making a decision and providing a conclusion, explained in this video. 

https://www.youtube.com/watch?v=WC442Q_nRYI

Objectives:

• Perform a hypothesis test for a single mean using the Normal distribution

• Perform a hypothesis test for a single mean using the Student t distribution

• Calculate a p-value for a hypothesis test

• Perform a hypothesis test for a single proportion

This video gives a solid overview of the process of hypothesis testing using the approach involving critical values and rejection regions. 

https://www.youtube.com/watch?v=g6YKTa5OXhI

This video gives the same process, but employing the p-value approach to hypothesis testing. 

https://www.youtube.com/watch?v=A6WpHcCJfqc

Regardless of which approach to hypothesis testing you are using, you should have a firm grasp of the essential reasoning of hypothesis testing.  This video focuses on that. 

https://www.youtube.com/watch?v=UtgBVK333p4

This video gives an example of hypothesis testing on a single mean (using a t-test). 

https://www.youtube.com/watch?v=Vz6SMasgFT8

This video gives an example of hypothesis testing on a single proportion (using a z-test). 

https://www.youtube.com/watch?v=tTH5dYFAgag

Objectives:

• Perform a hypothesis test for the means of two populations with unknown standard deviations

This video goes through the process of performing a hypothesis test comparing two independent means. 

https://www.youtube.com/watch?v=dARY4Kg5Ftg

Objectives:

• Perform a hypothesis test for two population proportions

This video goes through the process of performing a hypothesis test comparing two proportions. 

https://www.youtube.com/watch?v=7g_1bI7VPf4

Objectives:

• Perform a hypothesis test for differences between matched or paired samples

This video gives a good explanation of performing a hypothesis test on paired samples, along with how to create an associated confidence interval.

https://www.youtube.com/watch?v=JiQR0lHLe74

This section is a review of concepts described in sections 2.3 and 2.4 in the following course:

https://www.determinedparents.com/home/algebra-ii

Objectives:

• Perform a linear regression

• Calculate the correlation coefficient

• State the assumptions for calculating the correlation coefficient

• Calculate the coefficient of determination

This video takes the viewer through the process of creating a scatter plot. 

https://www.youtube.com/watch?v=NcgRa0uotXs

This video goes through linear regression. 

https://www.youtube.com/watch?v=Qg1kSA_rGD4

This video describes the calculation of the correlation coefficient as well as the coefficient of determination between two datasets. 

https://www.youtube.com/watch?v=81TT8NvP2BY

Objectives:

• State the assumptions for performing a hypothesis test on the correlation coefficient

• Perform a hypothesis test on the correlation coefficient

Not all linear regression results should be taken seriously when it comes to predicting new data.  Only when the correlation coefficient is significant should the regression be used for prediction.  This two part video series goes through performing a hypothesis test on the significance of the correlation coefficient. 

https://www.youtube.com/watch?v=THjS0CbGDJY

https://www.youtube.com/watch?v=-U9Qfhv2LFA