Chapter Six: Collecting and Displaying Data

Section Objective Estimated Dates Section 6-1 Making a table Monday, Feb 2nd Section 6-2 Mean, Median, Mode, and Range Tuesday, Feb 3rd Section 6-3 Additional Data and Outliers Wednesday, Feb 4th Quiz Section 6-1 ----6-3 Friday, Feb 6th Section 6-4 Bar Graphs Monday, Feb 9th Section 6-5 Line Plots, Frequency Tables, and Tuesday, Feb 10th Histograms Section 6-6 Ordered Pairs Wednesday, Feb 11th Section 6-7 Line Graphs Thursday, Feb 12th Section 6-8 Misleading Graphs Friday, Feb 13th Section 6-9 Stem-and-leaf plots Tuesday, Feb 17th Section 6-10 Choosing an appropriate display Wednesday, Feb 18th Quiz Section 6-4 ------6-10 Thursday, Feb 19th Review Chapter six Friday, Feb 20th Chapter Six Test Monday, Feb 23rd

Why Learn This?

“After collecting data on animal populations, scientists must organize the data into useful forms like tables or graphs. Then, they can analyze the data and try to determine the cause of a population increase or decrease or make predictions about the future. Students will learn to organize and analyze data in Lessons 6-1 to 6-3. Students will also learn to display and interpret data in Lessons 6-4 to 6-10.”

-Holt McDougal text

Please make sure to take good notes as these will help serve as a study guide at the end of the chapter! Good luck. 

Mrs. Helmberger

______parent/s signature Section 6-1: Making a Table

You’ll learn: to use tables to record and organize data

1. Use the data about Hurricane Dean to make a table. Then use your table to describe how the hurricane’s strength changed over time.

On August 16, 2007, Hurricane Dean’s wind speed was 75 mi/hr. On August 17, its wind speed was 100 mi/hr. On August 18, its wind speed was 150 mi/hr. On August 21, its wind speed was 160 mi/hr. On August 22, its wind speed was 85 mi/hr.

How many rows should our table have? How many columns should our table have? What should we label the columns in our table?

Create your table in the space at the right ------

Later, we will be using our tables to display the information in a graph!

2. Use the temperature data to make a table. Then use your table to find a pattern in the data and draw a conclusion.

At 10:00 A.M., the temperature was 620 F. At noon, it was 650 F. At 2:00 P.M., it was 680 F. At 4:00 P.M., it was 700 F. At 6:00 P.M., it was 660 F.

How many rows should our table have? How many columns should our table have? What should we label the columns in our table?

Create your table in the space at the right ------

Do you see any patterns in your table?

What conclusions can you draw?

Why was the data in example #2 arranged from earliest to latest time instead of from lowest to highest temperature? Section 6-2: Mean, Median, Mode, and Range

You’ll learn: to find the mean, median, mode, and range of a data set.

Median:

Range:

1. Find the mean, median, mode and range of each data set.

Heights of Vertical Jumps (in) 13 23 21 20 21 24 18

Before you start to calculate the mean, median, mode, and range, notice that the numbers are given in no particular order. It is always was to analyze your table and take note of the order of the values given.

Always start by putting your numbers in order from least to greatest. Do this now.

Find the mean: _____ Find the median: _____ Find the mode: _____ Find the range: _____

2. Find the mean, median, mode, and range for the following data sets.

Number of Pets Owned 2 4 1 1 2

Mean: Median: Mode: Range:

NFL Career Touchdowns Marcus Allen 145 Franco Harris 100 Jim Brown 126 Walter Payton 125

Mean: Median: Mode: Range: Section 6-3: Additional Data and Outliers

You’ll learn: the effect of additional data and outliers

Outlier:

A. Find the mean, median, and mode of the following data set:

U.S. Winter Olympic Medals Won Year 2006 2002 1998 1994 1992 1988 1984 1980 Medals 25 34 13 13 11 6 8 12

Mean: Median: Mode:

B. Now add in the information that The United States also won 10 medals in 1976 and 8 medals in 1972. Add this data to the data in the table and find the mean, median, and mode again.

Mean: Median: Mode:

Compare your new data to the data in part A.

C. In 2001, 64-year-old Sherman Bull became the oldest American to reach the top of Mt. Everest. The table below shows the age of other climbers to reach the summit that day. Find the mean, median, and mode with and without Bull’s age and explain the changes.

Ages of people to reach the top of Mount Everest 33 31 31 32 33 28

With Bull: Mean: Median: Mode: Without Bull: Mean: Median: Mode:

What changes did you see in the data?

Which is most affected by the outlier? Section 6-4: Bar Graphs

You’ll learn: to display and analyze data in bar graphs.

Bar graph:

Double-bar graph:

Reading a Bar Graph

Use the bar graph to answer each question.

 Before using a bar graph to answer questions, what should you always look at first?

A. Which biome in the graph has the most rainfall? B. Which biomes in the graph have an average yearly rainfall less than 40 inches?

Making a Bar Graph

Use the given data to make a bar graph. (Use unattached piece of graph paper to make the graph) Coal Reserves (billion metric tons) Asia Europe Africa 695 404 66

Words to know: Interval: Scale: Y-axis (vertical): X-axis (horizontal):

Step 1: Find an appropriate scale and interval. The scale must include all of the data values. The interval separates the scale into equal parts. Step 2: Use the data to determine the lengths of the bars. Draw bars of equal width. The bars cannot touch. Step 3: Title the graph and label the axes

Double bar graphs

Make a double-bar graph to compare the data in the table.

Life Expectancies in Atlantic South America Brazil Argentina Uruguay Paraguay Make (yr) 59 71 73 70 Female (yr) 69 79 79 74

 The difference between a single-bar graph and a double-bar graph is that a double-bar graph will have a key to show what the two bars are representing.  Usually the bars are color-coded or through shading or something to show they are different.

Try it! Section 6-5: Line Plots, Frequency Tables, and Histograms

You’ll learn: to organize data in line plots, frequency tables, and histograms

Frequency:

Frequency table:

Line plot:

Histogram:

Using Tally Marks to make a Frequency Table

Each student in Mrs. Choe’s class recorded their fingerprint pattern. Which type is most common in Mrs. Choe’s class?

whorl loop loop loop loop arch loop whorl arch loop arch loop arch whorl

Make a table to show each type of fingerprint. Step #1: For each fingerprint, make a tally mark in the appropriate row. Step #2: Count the number of tally marks for each pattern. This is the frequency.

Making a Line Plot

Students in Mr. Lee’s class each ran several miles in a week. Make a line plot of the data. Number of Miles Run 8 3 5 6 7 8 5 5 3 6 10 7 5

Step #1: Draw a number line Step #2: For each student, use an x on the number line to represent how many miles he or she ran. Making a Frequency Table with Intervals

Use the data in the table to make a frequency table with intervals.

Number of Representatives per State in the U.S. House of Representatives 7 1 6 4 52 6 6 1 1 23 11 2 2 20 10 5 4 6 7 2 8 10 16 8 5 9 1 3 2 2 13 3 31 12 1 19 6 5 21 2 6 1 9 30 3 7 11 9 3 9

Step #1: Choose equal intervals Step #2: Find the number of data values in each interval. Write these numbers in the “Frequency” row.

Making a Histogram

Use the frequency table that you just made in Example 3 to make a histogram.

Step#1: Choose an appropriate scale and interval. Step #2: Draw a bar for the number of states in each interval. The bars should touch but not overlap Step #3: Title the graph and label the axes. Section 6-6: Ordered Pairs

You’ll learn: to graph ordered pairs on a coordinate grid.

Coordinate grid

Ordered pair: Section 6-7: Line Graphs

You’ll learn: to display and analyze data in the line graphs.

Line graph:

Double-line graph:

The first permanent English settlement in the New World was founded in 1607. It contained 104 colonists. Population increased quickly as more and more immigrants left Europe for North America. The table shows the estimated population of English American colonies from 1650 to 1700.

Populations of American Colonies Year 1650 1670 1690 1700 Population 50,400 111,900 210,400 250,900

Step #1: Place years on the horizontal axis and population on the vertical axis. Label the axes. Step #2: Determine an appropriate scale and interval for each axis. Step #3: Mark a point for each data value. Connect the points with straight lines Step #4: Title the graph. Making a double-line graph

Use the data in the table to make a double-line graph. United States Trade (Billions of $) 1980 1985 1990 1995 200 2005 Export 272 289 535 794 1,071 1,289 Import 291 411 616 890 1,450 1,997 Step #1: Determine an appropriate scale and interval Step #2: Mark a point for each export value and connect the points Step #3: Mark a point for each import value and connect the points Step #4: Title the graph and label both axes. Include a key so we know which line is for which piece of information. ------Line Graph Double-line Graph Section 6-8: Misleading Graphs

You’ll learn: to recognize misleading graphs Section 6-9: Stem-and-Leaf Plots

You’ll learn: to make and analyze a stem-and-leaf plot

Stem-and-leaf plot:

Bray Berg holds the Guinness World Record for card stacking. The Explorer Scouts had a competition to see who could build the highest card tower. The table shows the number of levels reached by each scout.

Number of Card-Tower Levels 12 23 31 50 14 17 25 44 51 20 23 18 35 15 19 15 23 42 21 13

Creating Stem-and-Leaf Plots

Step #1: Group the data by tens digits Step #2: order the data from least to greatest. Step #3: List the tens digits of the data in order from least to greatest. Write these in the “stems” column. Step #4: For each tens digit, record the ones digits of each data value in order from least to greatest. Write these in the “leaves” column. Step #5: Title the graph and add a key.

Reading Stem-and-Leaf Plots Find the least value, greatest value, mean, median, mode, and range of the data!

Least value:

Greatest value:

Median:

Mode: Range: Section 6-10: Choosing an Appropriate Display

You’ll learn: to choose an appropriate way to display data

Common Uses of Data Displays You can use a line You can use a bar plot to show how graph to display and often each number compare data in occurs. separate categories. You can use a line You can use a stem- graph to show how and-leaf plot to data change over a show how often data period of time. values occur and how they are distributed.

Choosing an Appropriate Data Display

A. The table shows the number of miles of coastline for states bordering the Gulf of Mexico. Which graph would be more appropriate to show the data—a bar graph or a line graph? Draw the more appropriate graph.

State AL FL LA MS TX Miles of Coastline 33 770 397 44 367

Think: is the information in the table describing a change over time? Is the information in the table divided into different categories?

B. The table shows the lengths of some animals. Which graph would be more appropriate to show the data—a stem-and-leaf plot or a line graph? Draw the more appropriate graph. Lengths of Animals (in) 70 43 42 50 35 32 Think: The table shows a number of different 32 45 61 35 40 30 lengths. It does not show data changing over time.

Graph for A. Graph for B.