We continue study of standard deviation. We first review the formula for ungrouped data and grouped data.

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: Page 1, Page 2, Page 3, Page 4

Workbook Page 2, #7, 8, 9, 10, 12, 14, 16.

Answers to last week’s homework:

Answers

We study standard deviation. In statistics, we have learned using mean to find the average, and we have learned to use range and interquartile range to see the spread of the data. But both range and interquartile range are 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

For a set of grouped data in the form of a frequency table, we have

Mean AvgX = sum of fx / sum of f

where x is the class mark of each class and f is the frequency of the corresponding class.

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

[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:

Page 1  and Page 2: #1, #2, #3, #4, #5, #6.

Answers to last week’s homework:

Answers

We have our first class today.

First thing first, each student should prepare two notebooks, one for taking the notes in the classroom, and one for doing the homework.

For this year, while we learn new material, we will also spend time reviewing what we have learned in the past. The review sessions will be mixed with the new lessons.

Today we review the topics of Algebraic Manipulation And Formulae. You can find the corresponding material in your Workbook on Page 72.

For homework, please download the following 4 pages and do the following: #3, #4, #5, #6, #7, #9, #11, #13, #14, #15, #18, #19, #20.

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