# Interactive Statistics

- Page ID
- 8323

- 2.1: Random Number Generator
- The student enters the lower and upper bounds and the computer generates a random integer between them.

- 2.2: Completing a Frequency, Relative, and Cumulative Relative Frequency Table Activity
- This is an activity where a partially completed table is presented and the student must fill in the rest of the table.

- 2.3: The Box Plot Creation Game
- This is a game where the student needs to first select what five components are part of the five number summary. Then the student draws the corresponding box plot.

- 2.4: Online Calculator of the Mean and Median
- The student enters in data and the computer calculates the mean and the median.

- 2.5: Online Mean, Median, and Mode Calculator From a Frequency Table
- The student enters in the lower and upper bounds and the frequencies and the compute calculates the mean, median and mode.

- 2.6: Standard Deviation Calculator
- This is an online calculator where the student enters the data and the standard deviation is calculated.

- 2.7: Guess the Standard Deviation Game
- This is a game where a random histogram is given and the student has to guess the standard deviation.

- 2.8: Mean and Standard Deviation for Grouped Frequency Tables Calculator
- The student enters the midpoints and the frequencies of a frequency table and the mean and standard deviation are computed.

- 2.9: Z-Score Calculator
- The student enters in all but one of: observed value, mean, standard deviation, z-score. Then the calculator finds the value left blank

- 2.10: Expected Value and Standard Deviation Calculator
- This is a calculator that computes the expected value and standard deviation from a probability distribution table.

- 2.11: Be the Player Or the Casino Expected Value Game
- This is a game where the player is given the rules to a randomly selected hypothetical casino game. The student computes the expected value and based on the result chooses to be either the casino or the player. Then 1000 games are played and the student wins or loses tat amount of money (in theory).

- 2.12: Binomial Distribution Calculator
- The student enters in the lower and upper bounds for the number of successes, the number of trials, and the probability of success for a binomial experiment and the calculator computes the probability.

- 2.13: Normal Probability Calculator
- The student enters in all but one of the low, high, mean, standard deviation, and probability. The computer then finds the entry that was left blank

- 2.14: Calculator For the Sampling Distribution for Means
- The student enters the low, high, mean, standard deviation, and sample size and the computer calculates the probability. The student can leave either the low or the high blank and enter in the probability and the low or the high will be calculated.

- 2.15: Discover the Central Limit Theorem Activity
- This is a discovery activity where the student enters in a distribution: skewed left, skewed right, uniform, normal, or a hand drawn distribution. The student then enters the sample size and the computer simulates taking many samples and draws the histogram and shows the mean and standard deviation of the sampling distribution.

- 2.16: Sampling Distribution Calculator for Sums
- The student enters the lower bound, upper bound, mean, standard deviation, and sample size. The computer then finds the probability. The student can also leave out either the lower bound or upper bound and enter the probability and the computer will calculate the missing bound.

- 2.17: Observe the Relationship Between the Binomial and Normal Distributions
- The student uses a slider to change the sample size and the probability of success and the binomial distribution along with the normal distribution are displayed.

- 2.18: Confidence Interval Calculator for a Mean With Statistics (Sigma Unknown)
- The student enters in the sample size, sample mean, sample standard deviation, and confidence level. The computer then calculates the confidence interval.

- 2.19: Visually Compare the Student's t Distribution to the Normal Distribution
- The student uses a slider to change the sample size and the Student's t distribution and the normal distribution are graphed.

- 2.20: Sample Size for a Mean Calculator
- The student enters in the population standard deviation, the error, and the confidence level and the computer calculates the needed sample size.

- 2.21: Confidence Interval for a Mean (With Data) Calculator
- The student enters in their data, the population standard deviation and confidence level. Then the computer calculates the sample mean and the confidence interval.

- 2.22: Interactively Observe the Effect of Changing the Confidence Level and the Sample Size
- The student uses a slider to change the sample size and the confidence level and then many confidence intervals for a population mean are produced from many samples. This helps visualize the confidence interval and how it relates to the sample size and the confidence level.

- 2.23: Confidence Interval for a Mean (With Statistics) Calculator
- The student enters in the sample size, the sample mean, the confidence level and the population standard deviation. The computer then calculates the lower and upper bounds for the confidence interval.

- 2.24: Confidence Interval Calculator for a Population Mean (With Data, Sigma Unknown)
- The student enters in the data and confidence level. The computer then calculates the sample mean and standard deviation and the confidence interval.

- 2.25: Confidence Interval For Proportions Calculator
- The student enters in the sample size, the number of successes and the confidence level. The computer then calculates the confidence interval and the sample proportion.

- 2.26: Needed Sample Size for a Confidence Interval for a Population Proportion Calculator
- The student enters in the error, confidence level and estimate for the population proportion (if known). The computer then calculates the sample size needed.

- 2.27: Hypothesis Test for a Population Mean Given Statistics Calculator
- The student enters in the standard deviation, sample mean, sample size, hypothesized population mean, and the tail of the test. The computer then calculates the test statistic and the p-value.

- 2.28: Hypothesis Test for a Population Mean With Data Calculator
- The student enters in the data, population standard deviation (if known), tail type, and hypothesized population mean. The computer then calculates the sample mean, test statistic and p-value.

- 2.29: Hypothesis Test for a Population Proportion Calculator
- The student enters the sample size, number of successes, hypothesized proportion, and the tail type. The calculator then computes the test statistic and p-value.

- 2.30: Two Independent Samples With Data Hypothesis Test and Confidence Interval Calculator
- The student enters in the data, tail type and confidence level. The computer then calculates the test statistic, p-value and confidence interval.

- 2.32: Two Independent Samples With Statistics Calculator
- The student enters the sample sizes, sample means, sample standard deviations, tail type, and confidence level. Then the computer calculates the test statistic, p-value, and confidence interval.

- 2.33: Hypothesis Test and Confidence Interval Calculator- Difference Between Population Proportions
- The student enters the sample sizes, the number of successes for each, the tail type, and the confidence level. Then the computer presents the test statistic, the p-value, and the confidence interval for the difference between the population proportions.

- 2.34: Hypothesis Test and Confidence Interval Calculator for Two Dependent Samples
- The student enters in the data for two dependent samples and then enters the tail type and confidence level. The computer then produces the test statistic, p-value, and confidence interval for the difference between the two dependent sample means.

- 2.35: Visualize the Chi-Square Distribution
- The student moves a slider to change the degrees of freedom and the computer sketches the Chi-Square distribution curve.

- 2.36: Chi-Square Goodness of Fit Test Calculator
- The student enters in the observed and expected values. Then the computer calculates the test statistic and p-value using the chi-square goodness of fit test.

- 2.37: Chi-Square Test For Independence Calculator
- The student fills in the table of observed counts. Then the computer computes the test statistic and p-value using the chi square test for independence.

- 2.38: Chi-Square Test For Homogeneity Calculator
- The student enters in the observed values for each of the two samples. The computer then displays the test statistic and p-value for the chi-square test for homogeneity.

- 2.39: Scatter Plot Calculator
- The student enters points, one by one, and the computer displays the scatter plot.

- 2.40: Scatter Plot, Regression Line, r,and r^2 Calculator
- The student enters in points, one bu one. Then the computer displays the scatter plot, the regression line, the regression equation, r and r^2.

- 2.41: Full Regression Analysis Calculator
- The student enters data points. The computer then displays the scatter plot, the equation of the regression line, r, r^2, and the test statistic an p-value for the hypothesis test for a correlation.

- 2.42: Shoot Down Money at the Correct Correlation Game
- The game shows many dollar bills floating across the screen. A correlation goal is presented. When the player shoots down a dollar bill, it turns into a point which becomes part of the scatter plot. The goal is to have the points appear with correlation within 0.1 of the goal.

- 2.43: Visualize How Changing the Numerator and Denominator Degrees of Freedom Changes the Graph of the F-Distribution
- The student moves sliders to change the numerator and denominator degrees of freedom and the computer displays graph of the F-distribution.

- 2.44: ANOVA Calculator
- The student enters in the data sets and the computer calculates the test statistic an p-value for the ANOVA hypothesis test.

*Thumbnail: Expectation–maximization algorithm clustering of Old Faithful eruption data. The random initial model (which, due to the different scales of the axes, appears to be two very flat and wide spheres) is fit to the observed data. In the first iterations, the model changes substantially, but then converges to the two modes of the geyser. Image used with permission (CC BY-SA 3.0 Unported; Chire via Wikimedia).*