1 of 27

Algebra Room 424 Ms. Miller

Please sign in next to your name on the sheet by the door.

I have pencils, pens, paper, if you need it.

I will be available in my room from 12:00 - 12:30 for tutoring on Tuesdays and Thursdays if you ever want extra help. (PLEASE LET ME KNOW AHEAD OF TIME)

The day’s lesson and the homework will be posted to my website by the end of each day.

www.mrsmillersmathtutoring.com

Always feel free to email me with any questions or concerns.

jmiller1@camdencc.edu

2 of 27

No Tutoring Today

Spring Fling today, AFTER CLASSES, in the Courtyard

Use your Aztec accounts!

Continue using this email during the School Year

jmiller1@camdencc.edu

Use this email if you need me for ANYTHING over the summer

absjmiller@gmail.com

3 of 27

Warm Up: You have 5 minutes to work on these problems. Then, we will go over them.

4 of 27

Workbook page 41

Solve as directed.

  1. The minimum and maximum values in a data set are 31 and 95. The mode is 67, the median is 62, and the mean is 52. Is this data symmetric, skewed right, or skewed left?
  1. Which data set would have higher variation: driving times through downtown during rush hour or driving times in the countryside at 4 A.M.?

HOMEWORK

Skewed Left

When the mode is the highest and the mean is the lowest, data is skewed left.

The Mean gets pulled TOWARD the Outlier

Driving times through downtown during rush hour.

5 of 27

Workbook page 42

Making Predictions and Identifying Trends

Trends show how situations change over time.

When you look at a graph or a table, observe whether the data set increases, decreases, or remains steady.

If you see a patterns, you have identified a trend.

6 of 27

Workbook page 42

IDENTIFYING TRENDS

Example: The graph shows the profits for Intricate Design over five years. What trends does the graph show?

Look for places where the graph increases, decreases, or remains steady.

This graph shows two trends.

Trend #1: Profits decreased sharply from Year 1 to Year 3.

Trend #2: Profits increased slightly from Year 3 to Year 5.

7 of 27

Workbook page 42

You can use graphs and tables as the basis for making predictions.

Predictions use information from past events to guess what will happen in the future.

To make a prediction, you need to determine the trends in a data set and then decide if you think the current trend will continue.

8 of 27

Workbook page 42

MAKING PREDICTIONS

Example: If Intricate Design profits are more than $190,000 in Year 6, it will open a new storefront. Based on the graph, are profits likely to be over $190,000?

Let’s look at the graph

9 of 27

10 of 27

Workbook page 42

MAKING PREDICTIONS

Example: If Intricate Design profits are more than $190,000 in Year 6, it will open a new storefront. Based on the graph, are profits likely to be over $190,000?

To make a prediction about the future, look at current trends. From Year 3 to Year 5, profits increased slightly. To exceed $190,000 in Year 6, profits would have to increase by more than $10,000. Look closely at the graph to see if that is likely to happen.

In Year 4, profits increased by about $10,000. In year 5, profits increased by only about $5,000. This suggests that Intricate Design profits are starting to level off. Profits will probably not be greater than $190,000 in Year 6.

11 of 27

Workbook page 43

You can make predictions when a graph shows change. Line graphs, tables, and bar graphs can all be used to show trends.

Use the line graph for problems 1 – 3.

  1. Describe the trends in the graph of customers leaving MPE Networks.

2007 – 2011 : # of customer leaving increased.

2011 – 2012 : # of customers leaving decreased.

2013 : # of customers leaving remained the same.

12 of 27

Workbook page 43

You can make predictions when a graph shows change. Line graphs, tables, and bar graphs can all be used to show trends.

Use the line graph for problems 1 – 3.

  1. Describe the most current trend.
  1. Explain. Based on the data, how many customers do you predict left MPE Networks in 2014?

The number of customers leaving has remained constant at 1.5 million during the last year.

HOMEWORK # 3

13 of 27

Workbook page 43

Use the bar graph for problems 4 – 6.

  1. What trends do you see in the sale of tickets to R-rated movies at the Dollar Theater?
  1. Do you think the current trend will continue?
  1. Based on the current trend, what types of movies would you recommend the Dollar Theater show in the future?

The number of R rated tickets sold has mostly decreased since 2000. Over the last 3 years, sales have leveled off at around 200,000

HOMEWORK # 5 & 6

14 of 27

Workbook page 43

Use the table for problems 7 – 10.

The table shows the average stock price per month for three different stocks.

  1. What trends do you see in
    1. The price of RAO?

    • The price of LEC?

    • The price of KBW?
  1. What kind of graph would you use to best show the trends in the table?

A line graph would probably be most useful.

HOMEWORK # 7

15 of 27

Workbook page 43

Use the table for problems 7 – 10.

The table shows the average stock pile per month for three different stocks.

  1. Based on the current trends, estimate the price of each stock in June.
  1. Explain. Could you use the table to make predictions about stock prices for the rest of the year? Explain your answer.

RAO : around 2.27

LEC : around 5.46

KBW : around 10.24

No, you couldn’t use the table for the rest of the year. This table represents only 5 months. It does not give enough information to predict the remaining 7 months.

16 of 27

Workbook page 44

Understanding Correlation

You’ve already learned that data can have a positive or negative correlation. Groups of data are said to have a linear correlation when the points on the scatter plot approximately form a line.

The scatter plot here compares the diameter and height of tree trunks.

This data has a linear correlation because all of the plotted points are close to the black line.

The black line is call the line of best fit. This line estimates the relationship between the two groups of data.

17 of 27

Workbook page 44

USING THE LINE OF BEST FIT

Example: Using the line of best fit graphed above, find the trunk diameter for a tree with a height of 20 meters.

Find 20m on the vertical axis and follow it to the black line.

Read the corresponding value on the horizontal axis. A trunk with a height of 20m probably has a diameter of about 21 cm

18 of 27

Workbook page 44

Some groups of data have a nonlinear correlation.

Even though the points don’t’ form a line, you can still find a relationship between the groups of data.

19 of 27

Workbook page 44

ANALYZING NONLINEAR CORRELATION

Example: A beverage company does a taste test to determine how much added sugar produces the most popular taste. How much sugar results in the best taste?

From 0 to 8 tsp, sugar and taste have a positive correlation. More sugar seems to be good.

From 8 to 11 tsp, sugar and taste have a negative correlation. Too much sugar ruins the drink.

The highest results in the taste test are for 8 tsp of sugar per gallon. The company shouldn’t add more than 8 tsp of sugar.

20 of 27

Workbook page 45

Use the scatter plot for problems 1 – 3.

  1. Describe the correlation between car weight and average mileage.
  1. Based on the line of best fit, what would you expect the average mileage to be for a car weighing 3,000 pounds?
  1. Tim’s car weighs 2,500 pounds and averages 20 mpg. Does his car fall above or below the line of best fit?

Car weight and average mileage have a negative linear correlation.

20 mpg

Below

21 of 27

Workbook page 45

Use the scatter plot for problems 4 – 6.

  1. When is the correlation between study time and final exam score positive? When is it negative?
  1. Based on the data, how long should you study to get the highest grade?

Positive : 1 – 10 hours

Negative : greater than 10 hours

About 10 hours

22 of 27

Workbook page 45

Use the scatter plot for problems 4 – 6.

  1. Explain. Why do you think this data is nonlinear? What are some reasons that greater study time doesn’t always mean a higher grade?

There are other factors involved in getting a good grade.

Such as how well you slept before the test. Students who are studying more than 10 hours before a test might be staying up too late and hurting their score.

23 of 27

PUT YOUR PENCIL IN YOUR BOOK SO YOU CAN GO BACK TO THE PAGE, THEN CLOSE YOUR BOOKS FOR A MINUTE.

24 of 27

Workbook page 45

CORE CONNECTIONS: CORRELATION AND CAUSATION

A study done at an elementary school shows that students with a larger shoe size know more math. These two groups of data have a correlation. Does this mean that having big feet causes students to be better at math?

That doesn’t make sense. In elementary school, students with larger feet are older, so they have been taught more math.

When you analyze correlation, use your common sense to determine whether one data group might cause the outcome you observe.

There is a correlation between show size and math knowledge, but not causation.

25 of 27

OPEN YOUR BOOKS

26 of 27

Workbook page 45

CORE CONNECTIONS: CORRELATION AND CAUSATION

Decide whether you think the following correlations also have causation.

  1. When ice cream sales increase, homicide rates also increase.
  1. When the speed limit decreases, the number of accidents also decreases.
  1. When people consume more calories, they gain more weight.
  1. When umbrella sales are high, the number of traffic accidents is also high.

HOMEWORK, 1 - 4

27 of 27

HOMEWORK

Page 43, numbers 3, 5, 6, 7

Page 45, Core Connections