Course schedule: continue 3.2 + 3.3

• We finished 3.2, but we’ll do a couple practice problems.

• Section 3.3: Grouped data

Find the sample variance for the data:1,3,8

A. 0B. 3C. 13D. 169

Suppose the sample mean and sd of a very large dataset were: . Assuming a bell-shaped distribution, what percent of the sample is greater than 60?A. 2.5%B. 16%C. 32%D. 68%

Section 3.3: “Measures of Central Tendency and Dispersion from Grouped Data”

We will only focus on means in this section, in particular weighted means of section 3.3.2.

So don’t worry about standard deviations and group means for section 3.3.

Suppose a course grade is weighted accordingly: midterm=20%, homework =30%, and final exam=50%. What is a student’s course grade if the student gets a 60 on the midterm, 90 on homework, and 80 on the final?A. 77.5%B. 76.7%C. 79%D. 82%

Weighted mean

𝑥𝑤=∑𝑤𝑖𝑥 𝑖

∑𝑤𝑖

More about weights ()

• For course grade problem, use 0.2 to represent 20%, etc.

• 100%=1, =1• Could have used 20 instead of 0.2, but would

have had =100 in the denominator

Suppose last semester a student’s grades were:Math (4 units): AHistory (3 units): A-Chemistry( 5 units): CYoga (1 unit): PassWhat was the student’s semester GPA?(Hint: A=4.0, A-=3.7, C=2.0, Pass=ignored)

Recall: A(4units), A-(3units), C(5units), Pass(1unit)GPA=?A. 2.85B. 2.93C. 3.09D. 3.23

Suppose a course grade is calculated as follows:Midterm=30%, Homework=30%, Final=40%.If you had an 80% on the midterm and 90% on homework, what is the minimum grade you can get on the final to get at least a 70% in the course?A. 40B. 47.5C. 55D. 68

Suppose a course grade is calculated as follows:Midterm=30%, Homework=30%, Final=40%.If you had an 80% on the midterm and 90% on homework, what is the minimum grade you can get on the final to get at least a 90% in the course?A. 92.5B. 97.5C. 100D. Over 100%

Your “average” is a weighted mean.

• For example: Calculate the mean of 2,3,7.• Now repeat, but use w=1 for each value.• Now repeat, but use w=2 for each value.• What you’ve always called an “mean” is

actually a weighted mean where all values are equally weighted.

One more problem…

Suppose you had 90 units and your GPA=3.0 at the start of the fall. In the fall semester you had 15 units, got sick and only earned a semester GPA of 2.0. What is your new GPA?(A) 2.50 (B) 2.86 (C) 3.33 (D) 60

For later in the semester…

• Probabilities for the possible outcomes will be our weights.

• Often the weights will add to one, thus no division needed.