statistics - frontier central school district / overview · web viewwhat percentage of the vehicles...

ALGEBRA 1UNIT 11

(11 LESSONS + 1 QUIZ + 1 STUDY GUIDE + 1 TEST = 14 DAYS)

Date Lesson Plan Standard(s) Other

W 5/15 11-N1 Measures of Central Tendency S.ID.2, S.ID.3 COMMON CORE WARM UP& Hand Out HW Set #31

Th 5/16 11-N2 Box Plot, Range, Interquartile Range S.ID.1 COMMON CORE WARM UP

F 5/17 11-N3 Outliers, Standard Deviation, Dot Plot S.ID.1 COMMON CORE WARM UP

M 5/20 11-N4 Histograms S.ID.2, S.ID.3 Warm Up Quiz

T 5/21 11-N5 Two-Way Frequency Table S.ID.5 COMMON CORE WARM UP & Collect HW Set #31

W 5/22 QUIZ COMMON CORE WARM UP

Th 5/23 11-N6 Independent and Dependent Variables, S.ID.6, S.ID.9 COMMON CORE WARM UP Correlation, Causation, Scatter Plot & Hand Out HW Set #32

F 5/24 11-N7 Linear Regressions S.ID.6, S.ID.8 Warm Up Quiz

T 5/28 11-N8 Exponential Regressions S.ID.6, S.ID.8 COMMON CORE WARM UP

W 5/29 11-N9 Interpolation and Extrapolation S.ID.6 COMMON CORE WARM UP & Collect HW Set #32

Th 5/30 11-N10 Correlation Coefficient S.ID.6, S.ID.8 COMMON CORE WARM UP& Hand Out HW Set #33

F 5/31 11-N11 Plotting and Analyzing Residuals S.ID.6 COMMON CORE WARM UP

M 6/3 STUDY GUIDE Warm Up Quiz

T 6/4 TEST Collect HW Set #33

11 – N1Today, you will be able to:

STATISTICS –

MEASURES OF CENTRAL TENDENCY:

MEAN –

MEDIAN -

MODE -

1. The table below shows the number of hits Marcus made for his team.Team Played

Hits

Badgers 3Hornets 8Bulldogs 5Vikings 2Rangers 3Panthers 9

What is the mean?

What is the median?

What is the mode?

2. Isaiah collects data from two different companies, each with four employees. The results of the study, based on each worker’s age and salary, are listed in the tables below.

Which statement is true about this data?

(1) The median salaries in both companies are greater than $37,000.

(2) The mean salary in company 1 is greater than the mean salary in company 2.

(3) The median salary in company 1 is less than the median salary in company 2.

(4) The mean salary in company 1 is equal to the mean salary in company 2.

3. The two sets of data below represent the number of runs scored by two different youth baseball teams over the course of a season.

Team A: 4, 8, 5, 12, 3, 9, 5, 2

Team B: 5, 9, 11, 4, 6, 11, 2, 7

Which set of statements about the mean and median is true?

(1) mean A < mean B ; median A > median B

(2) mean A > mean B ; median A < median B

(3) mean A < mean B ; median A < median B

(4) mean A > mean B ; median A > median B

4. The table below shows the annual salaries for the 24 members of a professional sports team in terms of millions of dollars.

The team signs an additional player to a contract worth 10 million dollars per year. Which statement about the median and mean is true?

(1) Both will increase.

(2) Only the median will increase.

(3) Only the mean will increase.

(4) Neither will change.


BOX PLOT -

LOWER EXTREME –

FIRST QUARTILE –

MEDIAN –

THIRD QUARTILE –

UPPER EXTREME –

1. The box plot below represents the ages of 12 people.

What percentage of these people is age 15 or older?

2. Construct a box plot for the 12 quiz scores below.

67 78 60 95 93 55 70 87 85 64 82 50

MEASURES OF SPREAD:

RANGE:

INTERQUARTILE RANGE:

3. Given the following box plot,

What is the range?

What is the interquartile range?

4. Robin collected data on the number of hours she watched television on Sunday through Thursday nights for a period of 3 weeks. The data is shown in the table below.

Using an appropriate scale on the number line below, construct a box plot for the 15 values.

What is the range?


5. The students in Mrs. Lankford’s 4th and 6th period Algebra classes took the same test. The results of the scores are shown in the following table:

Based on these data, which class has the largest spread of test scores? Explain how you arrived at your answer.

6. Santina is considering a vacation and has obtained high-temperature data from the last two weeks for Miami and Los Angeles.

Which location has the least variability in temperatures? Explain how you arrived at your answer.


OUTLIER:

1. Quinn took eight math quizzes this quarter. His grades are as follows:88, 89, 94, 90, 40, 91, 82, 88

Identify any outliers in the data.

STANDARD DEVIATION:

A LOW standard deviation means the data is ________________,

or ______________________________.

A HIGH standard deviation means the data is ________________,

or ______________________________.

2. Ed surveys his classmates to find out how many electronic gadgets each person has in their home.

9, 10, 11, 6, 9, 11, 9, 8, 11, 8, 7, 9, 11, 11, 5

Find the mean.

Find the standard deviation, to the nearest integer.3. Caleb tracked his calorie intake for a week.

1950, 2000, 2100, 2000, 1900, 2100, 2000

Find the standard deviation, to the nearest calorie.

Interpret the meaning of this standard deviation.

4. The heights, in inches, of 12 students are listed below.

61, 67, 72, 62, 65, 59, 60, 79, 60, 61, 64, 63

Which statement best describes the spread of these data?

(1) The set of data is evenly spread.

(2) The median of the data is 59.5.

(3) The set of data is skewed because 59 is the only value below 60.

(4) 79 is an outlier, which would affect the standard deviation of these data.

DOT PLOT:

5. The dot plot shown below represents the number of pets owned by students in a class.

Which statement about the data is not true?

(1) The median is 3.

(2) The interquartile range is 2.

(3) The mean is 3.

(4) The data contains no outliers.

6. The 15 members of the French Club sold candy bars to help fund their trip to Quebec. The table below shows the number of candy bars each member sold.

When referring to the data, which statement is false?

(1) The mode is the best measure of central tendency for the data.

(2) The data have two outliers.

(3) The median is 53.

(4) The range is 120.

7. Noah conducted a survey on sports participation. He created the following two dot plots to represent the number of students participating by age, in soccer and basketball.

Which statement about the given data sets is correct?

(1) The data for soccer players are skewed right.

(2) The data for soccer players have less spread than the data for basketball players.

(3) The data for basketball players have the same median as the data for soccer players.

(4) The data for basketball players have a greater mean than the data for soccer players.


HISTOGRAM -

1. The following histogram shows the ages of people that view a blog in an hour:

How many people in the 28-32 year old range viewed the blog?

How many total people viewed the blog?

How many people in the 33-42 year old range viewed the blog?

Is the distribution of data skewed or symmetric?

2. The following histogram represents the mileage of 38 different types of vehicles.

Is the distribution of the data skewed or symmetric?

What percentage, to the nearest percent, of the vehicles has gas mileages that are 16-25 miles per gallon?

What percentage of the vehicles has gas mileages that are greater than 25 miles per gallon?

3. The test scores for 16 students in Ms. Mosher’s class are listed below:

86, 80, 79, 70, 65, 87, 52, 71, 87, 87, 76, 64, 94, 77, 68, 98

Complete the frequency table.

Draw and label a frequency histogram on the grid below.

Which interval contains the lower quartile of the data?

Which interval contains the upper quartile of the data?


When researchers collect data, they often ask more than one question.Comparing the results of those questions can reveal relationships among the data.

TWO-WAY FREQUENCY TABLE:

1. The two-way frequency table shows the results of a survey in which ninth-grade students were asked which foreign language class they most wanted to take next semester.

Spanish French Italian

Boys 80 30 10

Girls 30 20 30

MARGINAL FREQUENCIES:

What percent of ninth-grade students want to take Spanish next semester?

CONDITIONAL FREQUENCIES:

What percent of girls want to take Spanish next semester?

2. A radio station did a survey to determine what kind of music to play by taking a sample of middle school, high school, and college students. They were asked which of three different types of music they prefer on the radio: hip-hop, alternative, or classic rock. The results are summarized in the table below.

What percentage of students prefer hip-hop?

What percentage of students prefer alternative?

What percentage of college students prefer classic rock?

What percentage of middle school students prefer hip-hop?

3. The school newspaper surveyed the student body for an article about club membership. The table below shows the number of students in each grade level who belong to one or more clubs.

If there are 180 students in ninth grade, what percentage of the ninth grade students belong to more than one club?

4. A public opinion poll was taken to explore the relationship between age and support for a candidate in an election. The results of the poll are summarized in the table below.

What percent of the 21-40 age group was for the candidate?

5. A survey of 100 students was taken. It was found that 60 students watched sports, and 34 of these students did not like pop music. Of the students who did not watch sports, 70% liked pop music. Complete the two-way frequency table.

6. Students were asked to name their favorite sport from a list of basketball, soccer, or tennis. The results are shown in the table below.

What percentage of the students chose soccer as their favorite sport?

(1) 39.6% (2) 41.4% (3) 50.4% (4) 58.6%

7. An outdoor club conducted a survey of its members. The members were asked to state their preference between skiing and snowboarding. Each member had to pick one. Of the 60 males, 45 stated they preferred to snowboard. Twenty-two of the 60 females preferred to ski. What is the relative frequency that a male prefers to ski?

(1) 0.125 (2) 0.25 (3) (4)

8. A statistics class surveyed some students during one lunch period to obtain opinions about television programming preferences. The results of the survey are summarized in the table below.

Based on the sample, predict how many of the school’s 351 males would prefer comedy. Justify your answer.


____________________ variables depend on __________________ variables.

The independent variable represents the __________________ of the graph.

The dependent variable represents the __________________ of the graph.

Identify the independent and dependent variables in the following examples:

1. The table below shows the cost of mailing a postcard in different years.

Independent variable (x):

Dependent variable (y):

2. An application developer released a new app to be downloaded. The table below gives the number of downloads for the first four weeks after the launch of the app.



3. The table below shows the average diameter of a pupil in a person’s eye as he or she grows older.



4. The table below shows the year and the number of households in a building that had high-speed broadband internet access.



When you study the relationship between two variables, you are working with

_____________________________.

This data can be written as a set of ordered pairs, ( x, y ) and graphed on a coordinate plane.

This kind of graph is called a ________________________.

CORRELATION:

Positive Correlation Negative Correlation No Correlation

5. There is a negative correlation between the number of hours a student watches television and his or her social studies test score. Which scatter plot below displays this correlation?

1) 3)

2) 4)

6. The scatter plot below represents the relationship between the number of peanuts a student eats and the student’s bowling score.

Which conclusion about the scatter plot is valid?

(1) No bowlers eat peanuts.

(2) Students who eat more peanuts have higher bowling scores.

(3) Students who eat more peanuts have lower bowling scores.

(4) There is almost no relationship between eating peanuts and bowling score.

CAUSATION:

7. Which relationship can best be described as causal?

(1) The alarm goes off and the sun rises.

(2) The car is moving slowly and the driver is singing.

(3) The birds are chirping and the rain is coming down.

(4) The snow is falling and the stores run out of snow shovels.

8. What type of relationship exists between the number of pages printed on a printer and the amount of ink used by that printer?

(1) positive correlation, but not causal

(2) positive correlation, and causal

(3) negative correlation, but not causal

(4) negative correlation, and causal

9. The data obtained from a random sample of track athletes showed that as the foot size of the athlete decreased, the average running speed decreased. Which statement is best supported by the data?

(1) Smaller foot sizes cause track athletes to run slower.

(2) The sample of track athletes shows a causal relationship between foot size and running speed.

(3) The sample of track athletes shows a correlation between foot size and running speed.

(4) There is no correlation between foot size and running speed in track athletes.


“TOP FIFTEEN” TOPIC

A scatter plot often will have a LINE OF BEST FIT. This is the line that best represents the pattern of the data.

The LINE OF BEST FIT can also be called the

___________________________________________.

1. A scatter plot was constructed on the graph below and a line of best fit was drawn.

What is the equation for this line of best fit?

Today, we will use the graphing calculator to find an exact equation for the line of best fit.

This is called a _______________________.

2. The data table below shows water temperatures at various depths in an ocean.

Write the LINEAR REGRESSION equation for this set of data, rounding all values to the nearest hundredth.

3. The mid-September statewide average gas prices, in dollars per gallon, for different years are given in the table below.

Year 2001 2002 2003 2004Price Per Gallon 1.345 1.408 1.537 1.58

Write a linear regression equation for this set of data when x=0 is used to represent the year 2001 and y is used to represent the price per gallon.

4. Omar has a piece of rope. He ties a knot in the rope and measures the new length of the rope. He then repeats this process several times. Some of the data collected are listed in the table below.

State, to the nearest tenth, the linear regression equation that approximates the length, y, of the rope after tying x knots.

Explain what the y-intercept means in the context of the problem.

Explain what the slope means in the context of the problem.

5. The graph of a linear equation contains the points and

. Which point also lies on the graph?

(1) (3)

(2) (4)


“TOP FIFTEEN” TOPICYesterday, we learned how to perform a

_________________________________ on the calculator.

Today, we will perform an ________________________________________.

1. The accompanying table shows the percent of the adult population that married before age 25 in several different years.

Using x=0 to represent the year 1971, find the LINEAR REGRESSION equation. Round the regression coefficients to the nearest hundredth.

2. A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees Fahrenheit, of the soup recorded over a 10-minute period.

Write an EXPONENTIAL REGRESSION equation for the data, rounding all values to the nearest thousandth.

3. Jill invests $400 in a savings bond. The value of the bond, V(x), in hundreds of dollars after x years is illustrated in the table below.

Which equation and statement illustrate the approximate value of the bond in hundreds of dollars over time in years?

(1) , and it grows.

(2) , and it decays.

(3) , and it grows.

(4) , and it decays.4. Write an exponential equation for the graph shown below.

Explain how you determined your equation.


1. Based on the least-squares line drawn below, which value could be expected for the data in June 2015?

(1) 230 (2) 310 (3) 480 (4) 540

2. The scatter plot below shows the relationship between the number of members in a family and the amount of the family’s weekly grocery bill.

The most appropriate prediction of the grocery bill for a family that consists of six members is

(1) $100 (2) $300 (3) $400 (4) $500

INTERPOLATION:

EXTRAPOLATION:

3. Each day, Toni records the height of a plant for her science lab. Her data are shown in the table below.

The plant continues to grow at a constant daily rate. Write a linear equation to represent h(n), the height of the plant on the nth day.

Using this equation, approximate the height of the plant on day 14.

4. A population of single-celled organisms was grown in a Petri dish over a period of 16 hours. The number of organisms at a given time is recorded in the table below.

Determine the exponential regression equation model for these data, rounding all values to the nearest thousandth.

Using this equation, approximate the number of single-celled organisms, to the nearest whole number, there were at the end of the 9th hour.

5. The data table below shows the median diameter of grains of sand and the slope of the beach for 9 naturally occurring ocean beaches.

Write the linear regression equation for this set of data, rounding all values to the nearest thousandth.

Using this equation, predict the slope of a beach, to the nearest tenth of a degree, on a beach with grains of sand having a median diameter of 0.65mm.

6. An application developer released a new app to be downloaded. The table below gives the number of downloads for the first four weeks after the launch of the app.

Write an exponential equation that models these data.

Use this model to predict how many downloads the developer would expect in the 26th week if this trend continues. Round your answer to the nearest download.

Would it be reasonable to use this model to predict the number of downloads past one year? Explain your reasoning.

11 – N10

Today, you will be able to:

“TOP FIFTEEN” TOPIC

CORRELATION COEFFICIENT:

The value of r is always in the range _____________________.

If r is close to 1, the data shows a ________________________ correlation.

If r is close to -1, the data shows a _______________________ correlation.

If r = 0, the data shows a ____________________________ correlation.

If r=1 , the graph looks like: If r=−1 , the graph looks like:

1. Which scatter plot shows the strongest positive correlation?

2. Which value of r represents data with a strong positive linear correlation between two variables?

(1) 0.99 (2) 0.34 (3) 1.04 (4) -0.99

3. What is the correlation coefficient of the linear fit of the data shown below, to the nearest hundredth?

(1) 1.00 (2) 0.93 (3) -0.93 (4) -1.00

4. Beverly did a study this past spring using data she collected from a cafeteria. She recorded data weekly for ice cream sales and soda

sales. Beverly found the line of best fit and the correlation coefficient, as shown in the diagram below.

Given this information, which statement(s) can be correctly be concluded?

I. Eating more ice cream causes a person to become thirsty.II. Drinking more soda causes a person to become hungry.III. There is a strong correlation between ice cream sales and soda

sales.

(1) I, only (3) I and III

(2) III, only (4) II and III

5. Bella recorded data and used her graphing calculator to find the equation for the line of best fit. She then used the correlation coefficient to determine the strength of the linear fit.

Which correlation coefficient represents the strongest linear relationship?

(1) 0.9 (3) -0.3

(2) 0.5 (4) -0.8

6. Analysis of data from a statistical study shows a linear relationship in the data with a correlation coefficient of −0 . 524 . Which statement best summarizes this result?

(1) There is a strong positive correlation between the variables.

(2) There is a strong negative correlation between the variables.

(3) There is a moderate positive correlation between the variables.

(4) There is a moderate negative correlation between the variables.

**In order to find a correlation coefficient on the calculator, you must

_____________________________________________!!!!

7. As shown in the table below, a person’s target heart rate during exercise changes as the person gets older.

Which value represents the linear correlation coefficient, rounded to the nearest thousandth?

(1) -0.999 (2) -0.664 (3) 0.998 (4) 1.503

8. A nutritionist collected information about different brands of beef hot dogs. She made a table showing the number of Calories and the amount of sodium in each hot dog.

a) Write the correlation coefficient for the line of best fit. Round your answer to the nearest hundredth.

b) Explain what the correlation coefficient suggests in the context of this problem.

9. The table below shows the attendance at a museum in select years from 2007 to 2013.

State the linear regression equation represented by the data table when x=0 is used to represent the year 2007 and y is used to represent the attendance. Round all values to the nearest hundredth.

State the correlation coefficient to the nearest hundredth and determine whether the data suggest a strong or weak association.


1. Erica, the manager at Stellarbeans, collected data on the daily high temperature and revenue from coffee sales. Data from nine days this past fall are shown in the table below.

State the linear regression function, f(t), that estimates the day’s coffee sales with a high temperature of t. Round all values to the nearest integer.

State the correlation coefficient, r, of the data to the nearest hundredth. Does r indicate a strong linear relationship between the variables? Explain your reasoning.

RESIDUAL =

2. The days of absences for a group of students and their math grades were recorded for six students. Calculate the residuals in the following table:

Days of Absences

Math Grade Predicted Math Grade

Residual

1 96 982 94 953 93 925 86 876 85 847 81 828 81 799 77 7610 74 7310 72 7312 68 6512 63 65

Make a residual plot for the data.

If the points in a residual plot are random, then a _________ is the best fit.

The closer the residuals are to the x-axis, the better the fit.

If the points in a residual plot have a pattern or a curve, then

________________________________________________.

Based on your residual plot in question #2, is a line the best fit for the data?

3. The table below represents the residuals for a line of best fit.

Plot these residuals on the set of axes below.

Using the plot, assess the fit of the line for these residuals and justify your answer.

4. The residual plots from two different sets of bivariate data are graphed below.

Explain, using evidence from graph A and graph B, which graph indicates that a linear model for the data is a good fit.

UNIT 11 – STUDY GUIDE

11-N11. Using the data in the accompanying dot plot,

What is the mean?

What is the median?

What is the mode?

11-N2 through 11-N3

2. Based on the box plot:

What is the median?

What is the range?


3. Six of the Earth Science test grades are 100, 95, 55, 85, 75, and 100. For this sample, what is the standard deviation, to the nearest tenth?

11-N44. The accompanying histogram shows the height distribution of

students in a high school mathematics class.

What is the total number of students in the class?

11-N5

5. Based on the survey below,Intramural Basketball

Chess Club Jazz Band Did Not Participate

Female 25 4 31 33Male 41 12 27 29

What percentage, to the nearest percent, of the girls played intramuralbasketball?

11-N6

6. If the value of the dependent variable y increases as the value of the independent variable x increases, the graph of this relationship could be a

(1) horizontal line (3) line with a negative slope

(2) vertical line (4) line with a positive slope

7. A set of data is graphed on the scatter plot below.

The scatter plot shows

(1) no correlation (3) negative correlation

(2) positive correlation (4) undefined correlation

8. Which relationship can best be described as causal?

(1) height and intelligence

(2) shoe size and running speed

(3) number of correct answers on a test and test score

(4) number of students in a class and number of students with brown hair

11-N7 through 11-N10

9. Jean invested $380 in stocks. Over the next several years, the value of her investment grew, as shown in the accompanying table.

Year (x) Value of Stock, in Dollars (y)

2006 3802008 3952011 4112014 4272015 445

Write the exponential regression equation for this set of data when x=0 is used to represent the year 2006 and y is used to represent the value of the stock, rounding all values to two decimal places.

10. What could be the approximate value of the correlation coefficient for the accompanying scatter plot?

(1) -0.85 (2) -0.16 (3) 0.21 (4) 0.90

11. The table below displays data collected from the census. Years of Education

past 8th gradeAverage Yearly Salary

2 23,0884 32,5526 39,8848 53,9769 66,14411 80,600

a) Write a linear regression equation, to the nearest integer.

b) Use this equation to predict the salary for someone with 15 years of education past 8th grade.

c) What is the linear correlation coefficient, to the nearest hundredth?

d) Explain what the correlation coefficient suggests in the context of this problem.

11-N11

12. What does the following residual plot indicate about the linear fit for the data?

What does the following residual plot indicate about the linear fit for the data?

statistics - frontier central school district / overview · web viewwhat percentage of the vehicles...

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