Question

Imagine that we divided the class into groups of 5, everyone did one speed test on their own device, and we calculated variance and SD for each group. Then we calculated variance and SD for the entire class (n = about 45). How would variance and SD for the entire class differ from variance and SD for the smaller groups?

Answer 1

As we Calculate Variance and Standard Deviation of each Group and we have 5 Groups and about n = 45 students

Means in One group there are 9 students (45/5=9)

So no. of students in a group (9) is smaller than in Entire Class(45)

So as we know As the no. of samples increases Variance and Standard deviation both Decreases

And hence Variance and SD are Less for Entire class than for smaller groups

Hence Variance and SD for the entire class differ from variance and SD for the smaller groups