Formulas            Standard Normal Table            t-Distribution Table

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Descriptive Statistics:

Constructing Relative Frequency Distribution
Note: Construct Frequency Table, Relative Frequency Table, and Degrees for Pie Chart

Bar Chart or Colum Chart
Note: Draw Bar Chart or Colum Chart

Line Chart or Time-Series Graph
Note: Draw Line Chart or Time-Series Graph

Pie Chart
Note: Draw Pie Chart

Histogram
Note: Draw Histogram

Box Plot
Note: Draw Boxplot

Mean, Variance, Standard Deviation, Five-number Summary, Outliers (Free-Form Version)
Note: Calculate x̄, s, s2, Q1, Q2, Q3, μ, σ, and σ2 for ungrouped data

Mean, Variance, Standard Deviation, Five-number Summary, Outliers (Excel-Grid Version)
Note: Calculate x̄, s, s2, Q1, Q2, Q3, μ, σ, and σ2 for ungrouped data

Mean, Variance, and Standard Deviation of Grouped Data
Note: Calculate x̄, s, s2, μ, σ, and σ2 for grouped data

Mean, Variance, and Standard Deviation of the differences of Two Sets of Data
Note: Calculating = Mean of differences of two sets of data ;
and sd = standard deviation of the differences

Empirical Rule and Bell-Shaped Distribution (Computational Program)

Empirical Rule and Bell-Shaped Distribution (Simulation Program)

Chebyshev's Inequality (Computational Program)

Chebyshev's Inequality (Simulation Program)

Five-number Summary and Boxplot
Note: Calculate Mininum, Q1, Q2, Q3, Maximum and draw boxplot.

Finding kth Percentile

Correlation and Scatter Diagram:
Correlation Coefficient and Regression Line (new version)

Correlation Coefficient and Regression Line

Probability, Permutation, Combination:

Probability

Probability of Compound Events

Probability of Independent Events

Conditional Probability

Permutations and Combinations of n Distinct Objects Taken x at a Time
Find nCr and nPr

Discrete and Binomial Distribution:

Discrete Random Variable: Mean, Variance, and Standard Deviation
Note: Program calculates mean, variance, and standard deviation

Binomial Distribution
Note: Program calculates P(X = c), P(X < c), P(X > c), P(X ≤ c), P(X ≥ c), P(a ≤ X ≤ c)

Normal Distribution:

Find Left-Tailed Area Given Score

Find Right-Tailed Area Given Score

Find Area Between Two Scores

Find Score Given Left-Tailed Area

Find Score Given Right-Tailed Area

Find Scores Gven Left-Tailed Area and Right-Tailed Area

Simulation of Two Normal Distributions

Assessing Normality (new version)

Assessing Normality

Normal Distribution vs. Binomial Distribution:

Binomial Distribution vs. Normal Distribution

Simulation of Binomial Distribution vs. Normal Distribution

The Normal Approximation to the Binomial Probability Distribution (new version)

The Normal Approximation to the Binomial Probability Distribution(old version)

Sampling Distribution:
Sampling Distribution of the Sample Mean ( x̅ ) (computational version)
Note: Given sample size (n), use normal distribution to find P(X̅ < c), P(X̅ ≤ c), P(X̅ > c), or P(X̅ ≥ c)

Sampling Distribution of the Sample Proportion ( p̂ ) (computational version)
Note: Given sample size (n), use normal distribution to find P(p̂ < c), P(p̂ ≤ c), P(p̂ > c), or P(p̂ ≥ c)

Sampling Distribution of the Sample Mean ( x̅ ) (simulation version)

Sampling Distribution of the Sample Proportion ( p̂ ) (simulation version)

t-Distribution:

Simulation of t-Distribution vs. Standard Normal Distribution

Simulation of t-Distribution vs. Standard Normal Distribution (Animated Version)

Find Left-Tailed Area Given t-score

Find Right-Tailed Area Given t-score

Find Area Between Two t-scores

Find t-score Given Left-Tailed Area

Find t-score Given Right-Tailed Area

Find t-scores Given Left-Tailed Area and Right-Tailed Area

Finding zα/2 and tα/2:
Finding zα/2
Note: Find zα/2 and critical values when level of confidence is given. Normal Distribution is used.

Finding tα/2
Note: Find tα/2 and critical values when level of confidence and degrees of freedom (DF) or sample size (n) are given.
t-Distribution is used.

Construction of Confidence Interval:
Confidence Interval for One Population Mean (μ) with Known Population Standard Deviation (σ)
Note: Find confidence interval for population mean (μ) when population standard deviation (σ) is known.

Confidence Interval for One Population Mean (μ) with Unknown Population Standard Deviation (σ)
Note: Find confidence interval for population mean (μ) when population standard deviation (σ) is unknown.

Confidence Interval for One Population Proportion (p)
Note: Find confidence interval for population proportion (p).

Confidence Interval: Two Population Means (Assumptions: Independent Samples; σ1 ≠ σ2)
Note: Find Confidence Interval for μ1 - μ2

Confidence Interval: Two Population Means (Assumptions: Independent Samples; σ1 = σ2)
Note: Find Confidence Interval for μ1 - μ2

Confidence Interval: Two Population Means (Dependent Samples)(Matched-Pair)
Note: Find Confidence Interval for the mean difference () of two dependent populations.

Confidence Interval: Two Population Proportions
Note: Find Confidence Interval for p1 - p2

Margin of Error and Sample Size:
Find sample size (n) needed to estimate population mean (μ) for a specified margin of error (E)

Find sample size (n) needed to estimate population proportion (p) for a specified margin of error (E)

Hypothesis Testing for population mean (μ)
P-Value Approach:
Note: Program calculates p-value and test statistic.
Hypothesis Testing for One Population Mean (μ)

Classical or Traditional Approach; or Critical-Value Approach:
Note: Program calculates test statistic and critical value(s).
Hypothesis Testing for One Population Mean (μ)

Hypothesis Testing for population proportion (p)
P-Value Approach and Finding p-value:
Note: Program calculates p-value and test statistic.
Hypothesis Testing for One Population Proportion (p)

Classical or Traditional Approach; or Critical-Value Approach:
Note: Program calculates test statistic and critical value(s).
Hypothesis Testing for One Population Proportion (p)

Hypothesis Testing for Difference of Two INDEPENDENT Population Means (μ1 - μ2)
Classical or Traditional Approach; or Critical-Value Approach:
Hypothesis Testing for Difference of Two INDEPENDENT Population Means (μ1 and μ2)

P-Value Approach:
Hypothesis Testing for Difference of Two INDEPENDENT Population Means (μ1 - μ2)

Hypothesis Testing for Difference of Two DEPENDENT Population Means (μ1 - μ2)
Classical or Traditional Approach; or Critical-Value Approach:
Hypothesis Testing for Difference of Two DEPENDENT Population Means (μ1 - μ2) (Matched-Pair)

P-Value Approach:
Hypothesis Testing for Difference of Two DEPENDENT Population Means (μ1 and μ2)(Matched-Pair)

Hypothesis Testing for Difference of Two Indpendent Proportions (p1 - p2)
Classical or Traditional Approach; or Critical-Value Approach
Hypothesis Testing for Difference of Two Indpendent Proportions (p1 - p2)

P-Value Approach
Hypothesis Testing for Difference of Two Indpendent Proportions (p1 - p2)

ANOVA (Analysis of Variance):
Finds F-Distribution score

ANOVA (One-Way Analysis of Variance), Sheffé Test, Tukey Test

ANOVA (Two-Way Analysis of Variance)