We continue study of standard deviation.

We apply the standard deviation to help analyze two data sets. While means can give us the picture of average, standard deviation helps us to determine how consistent the data are. For example, if we look at two sets of data representing two basketball players’ scores, the lower the standard deviation, the more consistent the player is.

Homework:

Print these pages (they are links, click to download): Page 1, Page 2, Page 3

Workbook Page 1, 2, 3: #10, 12, 14, 16.

We continue study of standard deviation. Today we study standard deviation for grouped data.

We talk about the formulae for grouped data.

Homework:

Print these pages (they are links, click to download): Page 1,  Page 2, Page 3, 

Workbook Page 1, 2, 3: #2, #3, #7, #8, #9

We study standard deviation. In statistics, we have learned using mean to find the average, and we have learned to use range to see the spread of the data. But range is not very good as the tool to represent the spread of the data.

A better way is the measure called standard deviation:

Standard Deviation SD = sqrt(sum of (Xi – AvgX)^2/N)

where N is the total number of data, AvgX is the mean of the data. Xi – AvgX is called the deviation of Xi from the mean AvgX for each i = 1, 2, …, N

[Sorry, I can’t type using the summation notation sigma, which is what we learn in the class. This will simplify the writing.]

Here is a written proof of going from the definition to a formulae often used:

sqrt(∑(Xi – AvgX)^2 / N) = ∑Xi^2 / N – (∑Xi / N)^2

I showed the proof in the classroom, but students may not get it.

Homework (pages are links, click to download):

Page 1  and Page 2: #1, #4, #5, #6.