Projectile Sampling Distributions: Bin width default should be 0.5

[matthew-blackman]

@catherinecarter and Kelly Findley advocated for the default bin width of the Projectile Sampling Distributions sim should be 0.5. There are several benefits to this that @catherinecarter and Kelly F raised. @catherinecarter can you describe the pedagogical reasoning in this issue?

[catherinecarter]

Sure thing. Essentially the logic is:

• The point of sampling is to estimate values about a population we don't know, like the population's mean (µ) and SD (𝛔), called parameters
• In real life, there is usually only one sample taken from the population due to time and money constraints
• Because you're only taking one sample, the hope is that your sample's mean and SD (called statistics) closely match the population's parameters
• Due to sampling variability and probability, you know that your sample's statistics are likely to be close the parameters, even though you know they aren't exactly correct
• Probability and the Central Limit Theorem tell us that our statistics will be close, especially for larger sample sizes

Having the default bin width set to be 0.5 m rather than 1 m helps us see more of the sampling variability, an important concept in sampling. The concept of a theoretical sampling distribution is very challenging for students.

Being able to see more detail in the sample means (i.e. visually seeing the means varying) helps bridge the idea of a sampling distribution being concretely started and a theoretical smooth sampling distribution. The transition from concrete to abstract helps students abstractly visualize how a theoretical sampling distribution makes sense.

[matthew-blackman]

Please close after verifying.

[KatieWoe]

Looks good