Week 5

Scatter PlotsA scatter plot is a graph of plotted points that shows the relationship between two sets of data.To make a scatter plot given two sets of data, x and y, - Label the x- and y- axis on a coordinate plane.- Then plot each point (x, y) on the plane.

A linear relationship exists when data points in a scatter plot easily surround a straight line. A non-linear relationship exists when data points are spread out and can not easily surround a straight line.

The pattern of the points is known as the correlation!Correlation describes tendency – not a definite cause and effect. Data sets can have a positive correlation, a negative correlation, or no correlation.

Important Words:

• ExampleEmily measured the depth of water in a bathtub at two-minute intervals after the tap was turned on. The table shows her data. Make a scatter plot for the data.

Time (min) 2 4 6 8 10 12 14 16 18 20 22Depth (cm) 7 8 13 19 20 24 32 37 38 41 47

Step 1: On graph paper, represent the time in minutes along the x-axis and the depth of water in the bathtub along the y-axis.

Step 2: Plot the values in the table. The scatter plot would look like the one below.

This graph has a positive correlation. As the time is increasing, so is the depth!

Cluster: data points that are closely grouped togetherIf data points cluster in a horizontal direction, no correlation exists.If data points in a vertical direction, an undefined correlation exists.

Outlier: a data point that is set apart from most of the other points.

Example: Below is a scatterplot of grade on exam 2 versus time spent playing video games in hours for the Exam 2 week for 40 students.

Describe the important features of the relationship between two variables:Form: linear or nonlinear?Answer: Linear

Direction: positive, negative, or no association? Answer: Negative

Strength: strong, moderate, weak? Answer: Strong

Are their any outliers –NO

You Try:

0 5 10 15 20 25 300

50

100

150

Exam 2

Time spent playing video games

Grade

Lines of Best Fit

A line of best fit is a line that goes through the data points on a scatter plot. - The distance between the line and the points above the line should be the same as the distance

between the line and all the points below the line

A line of best fit does not connect all the data points. It goes between the data to show the trend, or pattern of the data! A trend line is an approximate line of best fit. A trend line is surrounded by the data points and follows the general direction of the data.

Lines of best fit are straight lines when linear relationships exist. - The general equation for a straight line is y=mx+b,

o The slope will always represent the rate of change for the data o The y-intercept will often represent the starting value of the data

Example: Find the line of best fit for this scatter plot:

You Try: 1) The scatter plot shows the number of years since a new science initiative for girls was started and the

number of girls enrolled in science classes at several high schools. The data is modeled by the function y=25x+150 .

Find the y-intercept and slope, then interpret what they mean for this model.

a) y-intercept: ___________y – intercept represents: _________________________

b) slope: ___________________slope represents: ______________________

2)) The scatter plot shows the numbers of hours that students spent using social media the night before a

test, and their scores. The data is modeled by the function y=−8 x+100 . Which is the best interpretation of the y-intercept of this model?

A. The use of social media the night before a test does not affect a student's score. B. Students who use social media for 8 hours the night before are most likely to score 100.C. Students who use social media for 0 hours the night before are most likely to score 100. D. Using social media for 100 hours the night before lowers a student's score by 0 points.

4) Mr. Art collected data from a sample of 14 students to determine the association between the numbers of hours they studied for a test and their test scores. He created this scatter plot to show his data. The line of best fit shows the general trend of the data.

Find the y-intercept and slope, then interpret what they mean for this model.

a) y-intercept: ___________________

c) slope: ___________________

c) Write an equation for the linear model: ______________________________

5) A scatterplot is shown on the graph.Which equation could be a line of best fit?

a. y = x + 100b. y = x – 100c. x = 100d. y = 100

Two-Way Tables

A two-way table is a table that shows the frequency, or count, of two pieces of data. Two way tables can be used to analyze data and make conclusions. One variable of data in a two-way table is displayed in rows. The other is displayed in columns. Look for patterns or trends in the table to make conclusions

Example: This table shows the salary ranges of each employee in a different job class at a company. Job Class

Salary Range A B C$0-$25,000 0 11 58$25,001 - $50,000 10 41 22$50,001 - $100,000 44 48 0$100,001 + 16 0 0

A) A new employee will join the company with a starting salary of $23,850. What job class will this employee likely be in?

Solution: The data in this table shows employees with lower salaries tend to be in a higher letter job class. Most employees with salaries less than $25,000 are in job class C. So it is likely that this new employee will be in job class C.

B) What fraction of all employees are in job class A and have salaries greater than $50,000? Count the number of employees in job class A and have salaries greater then $50,000 : 44+16 = 60 Count the total number of employees:10 + 44 + 16 + 11 + 41 + 48 + 58 + 22 = 250

Write and simplify a fraction60

250= 6

25

So, 6

25 of all employees are in job Class A and have salaries greater than $50,000.

Example 2: In the school chorus, there are 9 sixth graders, 13 seventh graders, and 18 eighth graders. In the school orchestra, there are 6 sixth graders, 12 seventh graders, and 21 eighth graders. Make a two-way table to show this data.

Identify the two variables to be Grade Level and School Activity Have the rows represent the grade level Have the columns represent the school activity.

Chorus OrchestraGrade 6 9 6Grade 7 13 12Grade 8 18 21

You Try: 1) This table shows the relationship between the number of house and condo listings for sale by one

Real-estate Company and the number of bedrooms in each listing. Bedrooms Houses Condos1 3 172 8 163 18 54 or more 13 0What fraction of the 2-bedroom listings are houses? __________________

2) What is a reasonable conclusion that can be made from the data in this table?Work Start Time More than 7 hours of sleep?

Yes NoBefore 7:00 5 197:00-8:00 12 11After 8:00 20 23

a) The workers starting after 8:00 get the most hours of sleepb) About half of all workers get more than 7 hours of sleep each night.c) Most workers starting before 7:00 get less sleep than workers starting later?d) More than half of the workers starting after 8:00 get 8 hours of sleep.

3) A city bus company has a red line, a blue line, and a green line that travel different routes. Last

month’s arrival data for each route is listed below:- The red line was early 21 times, on-time 64 times, and late 18 times- The blue line was early 15 times, on-time 84 times, and late 27 times- The green line was early 8 times, on time 55 times, and late 22 times.

In the space below, create a two-way table to show the data:

From Last Years State Test:

Answer BWhy?

More Scatter Plot Practice:

2.