• Let’s consider two R Built-in Data Sets: women and chickens
• The 1^st data frame contains only 15 observations, the 2^nd contains 578 observations.
• How will the plots differ? How does sample size effect our ability to draw conclusions?

• First lets plot our tiny data set:

• Now lets plot our larger data set, and consider how they differ:

• In this case, the difference in sample sizes is not as immediately obvious!

• Because the weights of living things are continuous, we should use the formula for Continuous Mean:

\(\mu=\int xf(x) dx\)

• Recall the formula for Standard Deviation:

\(\sigma=\sqrt{V(X)}=\sqrt{\sum_{i} P_{i}(x_{i} - \mu)^2}=\sqrt{\frac{\sum_{i} (x_{i} - \mu)^2}{n}} \\ \sigma=\sqrt{V(X)}=\sqrt{\int (x-\mu)^{2}f(x) dx}\)

• Below is the code that calculates Standard Deviation for our two data sets:

stand_dev_women = sd(women$weight, na.rm =TRUE) 
stand_dev_women

[1] 15.49869

stand_dev_chickens = sd(ChickWeight$weight, na.rm =TRUE)
stand_dev_chickens

[1] 71.07196

• In general, a data set must have at least 30 observations to be meaningful.
• In general, accuracy will increase as sample size increases.
• In general, standard deviation will decrease as sample size increases.