Applet Correlation Applet Concept Illustrated Descriptor Applet Activity Random numbers This applet investigates how a sample of random numbers is distributed, and how to use randomly generated numbers to select a random sample from a numbered list of values. This applet generates random numbers from a range of integers specified by the user. The random sample of numbers can be generated with or without replacement. 1.3 Mean versus median The mean and the median of a data set respond differently to changes in the data. This applet investigates how skewedness and outliers affect measures of central tendency. This applet allows the user to visualize the relationship between the mean and median of a data set. The user may easily add and delete data points. The applet automatically updates the mean and median for each change in the data. 2.3 Standard deviation Standard deviation measures the spread of a data set. This applet investigates how the shape and spread of a distribution affect the standard deviation. This applet allows the user to visualize the relationship between the mean and standard deviation of a data set. The user may easily add and delete data points. The applet automatically updates the mean and standard deviation for each change in the data. 2.4 Simulating the stock market An “up” day is a day in which the stock market shows a net gain. This applet investigates how the proportion of “up” days will tend to approach the theoretical probability of an “up” day over time. This applet simulates fluctuation in the stock market, where on any given day going up is equally likely as going down. The user specifies the number of days and the applet reports whether the stock market goes up or down each day and creates a bar graph for the outcomes. It also calculates and plots the proportion of days that the stock market goes up during the simulation. 3.1 Simulating the probability of rolling a 3 or 4 This applet investigates how the proportion of times a 3 or 4 is rolled will tend to approach the theoretical probability of rolling a 3 or 4 over time. This applet simulates rolling a fair die. The user specifies the number of rolls and the applet reports the outcome of each roll and creates a bar graph for the outcomes. It also calculates and plots the proportion of times a 3 or 4 is rolled during the simulation. 3.3 Binomial distribution This applet investigates how estimates of binomial probabilities obtained using the outcomes of N samples of a binomial distribution tend to improve with larger values of N. This applet simulates values from a binomial distribution. The user specifies the parameters for the binomial distribution (n and p) and the number of values to be simulated (N). The applet plots N values from the specified binomial distribution in a bar graph and reports the frequency of each outcome. 4.2 Sampling distributions The mean and standard deviation of the distribution of sample means are unbiased estimators of the mean and standard deviation of the population distribution. This applet compares the means and standard deviations of the distributions and assesses the effect of sample size. This applet simulates repeatedly choosing samples of a fixed size n from a population. The user specifies the shape of the population distribution, the two sample statistics to be analyzed, the sample size n, and the number N of samples. The applet plots the value of each specified sample statistic for each sample, and shows the mean, median, and standard deviation of these values for all the samples. 5.4 (continued on next page)
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