Embedded Files
Play to Learn
Normal Distribution
A histogram is a graph that shows the data organized along an x-axis. Many histograms are bell shaped, like the one pictured here. The shape is seen so frequently that it is simply referred to as the 'Normal Distribution'.
In addition to the above game,, check out the interactive applet: Normal distribution and the proportion under the curve.
Empirical Rule
For a normal distribution (without outliers) the mean occurs in the exact middle of the distribution. Half the population is below the mean, and the other half is above the mean. The standard deviation is a measure of the typical amount of variability in a distribution. According to the Empirical Rule, for a normal distribution, 68% of a population occurs within one standard deviation of the mean.
If you were to draw the normal distribution, you might wonder where to indicate along the x-axis the values "One Standard Deviation" above and below the mean. Take a look at the illustration above of the Empirical Rule (68%, 95%, 99.8%). When drawing a normal distribution, about half way down the curve is approximately one standard deviation away from the mean. When you are two standard deviations out, the curve starts to flatten out, approaching but never reaching the x-axis.
Almost the entire population, roughly 95% of it, is within two standard deviations of the mean. If you follow the curve out on either side, going out to three standard deviations, then 99.8% of the population is covered.
Amazingly, with just two numbers, the mean and standard deviation, we can describe both the location of the distribution, and how widely it is spread out.
Percent, Proportion, & Percentile Ranking
When describing someone's performance or attribute, it helps to put it within a context. Doug earns a verbal score of 23 on a test. Is it good, poor, or typical of others? Here are three ways to contextualize Doug's performance. We could provide a proportion, by saying that approximately .25 of the group scored below Doug. In terms of percentages, 25% of the group performed worse than Doug. Finally, we could say that Doug scored in the 25th percentile on the verbal test. These three methods all say the same thing: Doug scored better than one fourth of the group. Now we know how Doug did compared to others in the same group of people - his performance has been contextualized.
Game Play
Game Play
Click Start to play. You will get practice with making 30 decisions.
Accessibility Options
Accessibility Options
To enable the following accessibility options, first click upon the activity itself, then using a physical keyboard attached to a desktop computer:
To enable the following accessibility options, first click upon the activity itself, then using a physical keyboard attached to a desktop computer:
During a decision trial, press the 'f' key to select the option on the left and the 'j' key to select the option on the right.
If visibility is an issue, the Voice System can be turned on for this activity by pressing the Tab key (after clicking on the activity and waiting for it to load). Pressing the left and right arrows adjusts the rate of speech. The 'Z' key will interrupt the Voice System. Pressing the period turns the voice system off. During a decision trial, the keys 'e' and 'i' may be pressed for a verbal description of the left and right choices, respectively. Unlimited decision time is allowed when the Voice System is on. Performance of the Voice System can be impacted by the browser/system/device used.
If the decision time (before the correct answer is shown) is too quick, then you may re-start the game (e.g., by refreshing the browser tab). From the game menu, click the 'Accommodations' button, and then enter the code "#17" for unlimited decision time. Click the 'Continue' button to return back to the game menu. The student's passcode can be combined with an accessibility code (e.g., '4524#17' to indicate that the student's passcode is 4524, using the accessibility code 17).
Alternatively, to switch to unlimited decision time during game play, using a physical keyboard, press the left bracket '[' key. Doing so will affect the next decision trial. Press the right bracket ']' to return back to the specified decision time.
Modify Game Play
Modify Game Play
Enjoy the game, but would like to change it up? From the game menu, click the 'Accommodations' button. In the Accommodations dialog box, enter a code to change how the game functions:
Minimum number of decision trials: Use the code 0## (replacing the two digit '##' with the number of trials desired). For example, the code 009 would result in a minimum of 9 decision trials, whereas the code 060 would result in a minimum of 60 decision trials.
Decision time: 2## (replacing the two digits '##' with the number of seconds available to make a decision). For example, the code 205 would result in an allowed decision time of up to 5 seconds. The code 212 would result in an allowed decision time of up to 12 seconds.
The code consists entirely of digits. After entering a code in the Accommodations dialog , press the 'Continue' button to return back to the game menu. You can also combine codes, such as '020204' to indicate 20 decision trials ('020') and a decision time of four seconds ('204').
Finally, the student's passcode can be combined with codes to modify game play (e.g., '4524-015205' to indicate that the student's passcode is 4524, with '015' indicating a minimum of 15 trials and '205' indicating that up to five seconds is allowed for each decision before the correct answer is shown.
To view more options for modifying game play, visit the Play to Learn modifications page.
Optional Completion Code
Optional Completion Code
Instructors can provide their students with a four digit passcode to enter at the start of the game. The student would click the 'Accommodations' button, and in the Accommodations dialog box provide the passcode, and then press the 'Continue' button to return back to the game menu.
At the end of game play, a completion code will be provided for a successfully played game (i.e., performance reached the specified threshold; e.g., 85%). The student would enter the completion code as their answer to a quiz question.
Use of the accessibility options will modify the completion code (by +/- 2). Modifying game play (e.g., changing the number of decision trials) will result in an entirely different completion code. Instructors can choose to allow accommodations by accepting a completion code that comes within +/- 2 of the expected completion code value. Those students whose quiz question is graded correctly, but where the completion code is different than the expected result, used an accommodation.
The use of Completion codes represents one way to recognize students for successful game play.
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