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Histogram - DOC

VIEWS: 51 PAGES: 11

									                                    Histograms

 Topic:
   Histograms

 Focus:
   Connections – Students will make connections to previous information on data
     displays that they have acquired. Students will compare bar graphs and
     histograms since many misconceptions of histograms stem from a lack of
     understanding in the distinction between the two data displays. Students will then
     compare histograms with stem and leaf plots to analyze which would be more
     helpful and/or efficient in different situations and compare the two representations
     of the same data.

 Sources:
   http://www.learnnc.org/lessons/DebbieNewton5232002546
   https://ims.ode.state.oh.us/ODE/IMS/Lessons/Content/CMA_LP_S05_BA_L06_I
     01_01.doc

 Objectives:

    Level One: Students will be able to create and analyze a histogram to interpret
     information.
    Level Two: Students will be able to explain the difference between a bar graph
     and a histogram.
    Level Three: Students will be able to explain the connection between a histogram
     and a stem and leaf plot.

 Materials:

    Transparencies, Over Head Projector
    Histogram/Barrel Graphic organizer
    Pencils

 Motivation: (1-3 minutes)

Students will enter the class and complete the Do Now written on the board. Students
will copy down their homework and the objectives of today’s class.

       Do Now:
       Think about what activities you do when you get home from school. What are
       your favorite TV shows? How many hours a week do you spend watching TV?
       Put a tally on the overhead projector in the box over the barrel that you belong
       in. W hen you are finished, immediately get together with your rows and discuss
       the answers to the homework and compare with the answers displayed on the
       overhead. Be sure to help each other out!
A picture of what will be on the board is attached, Attachment A, will be displayed on the
overhead projector.
    A student will then be selected at random to read the class goal for the day, which
       will also be written on the board before class:
        “What is a histogram?”

 Procedure:

   1. Address any individual questions with the homework.
   2. Group work and class discussion (5-10 minutes)
      Students will be given a picture of a Histogram (Attachment B). Students will get
      into groups with their rows (3 across) and will discuss the histogram. Each group
      will come up with some properties of a histogram based on the picture of the
      histogram.
   3. Students will discuss as a class a few properties of a histogram.
   4. The definition of a histogram will be presented:
      - Histograms are a graph that uses bars to display the frequency of data within
          equal intervals. Think of histograms as “sorting bins”. There is one variable
          and the data is sorted by this variable by placing the data into “bins”. The
          pieces of data in each bin are counted.
   5. Guided Discussion (30 minutes)
      Using the same histogram, students will view attachment B on the overhead and
      answer the questions that follow.
               - How many kids spend 20 minutes or less per week doing chores?
               - How many kids spend more than 80 minutes per week doing chores?
               - What is the most common amount of time spent doing chores?
               - What is the least common amount of time spent doing chores?
               - How is a bar graph different from a histogram?
                       o Histograms are often confused with bar graphs
                                Histograms:
                                         The height of the rectangle drawn on top of
                                            each bin is proportional to the number of pieces
                                            in that bin.
                                         Histograms show one set of data and are
                                            designed to show trends.
                                Bar graphs
                                         Have several measurements of different items
                                            that allow comparison.
                                         Bar graphs display numerical information with
                                            labels for each bar and a scale to show amount
                                            for each bar.
   6. The students will then refer back to the data from the Do Now. Students will total
      the tallies and transfer the tallies and totals from the barrels onto a frequency
      table.
               - What numbers go on the x-axis
             - What information goes on the y-axis
             - Where do the barrels fit on the histogram?
             - How can we construct a histogram of the number of hours a week our
                 class watches TV?
   7. The class will work together to construct the histogram onto Attachment D,
      through guided discussion, based on the data of the Do Now.
   8. Discussion (20 minutes)
      Students will work in groups of 6 (two rows of 3 will work together) on
      Attachment C. Each student will hand in their own work. In the event the group
      does not have time to finish, students will complete the assignment for homework.

 Closure:

    Using a piece of notebook paper, students will list at least two interesting facts
     that they learned today and something that is still unclear to them. Students will
     hand this in at the end of the period.

 Assessment:

    Students’ participation in the guided discussion will give an idea of how well the
     students are at drawing conclusions and how well they comprehend the data
     displayed on a histogram.
    The closure activity will help to assess how well the students understood the
     material. Based on the depth of detail used in their response, their understanding
     and clarity of histograms can be evaluated.
    The group work will assess the class’ abilities to work represent data correctly in
     a histogram and draw conclusions from the display.

 Homework:
   Since the group work is very detailed and will most likely take them much more
    than 20 minutes, students will finish the group work for homework. Each student
    will hand in their homework and it will be graded on an individual basis. Each
    student will be graded on their accuracy, detailed responses to questions, and
    neatness.
   Textbook
     Spiral Review pg 324 #19-30
     This will not be collected. Answers will be on a transparency in the beginning
        of class tomorrow and students will ask questions on individual problems.
        This is assigned at the request of the teacher since this is a routine for the
        students. It does not cover the material we are teaching and she normally does
        not take much time to review this homework.

 Reflections/ Self Evaluations:
What Barrel do you
   belong in?




 <1 hour                                         6-10 hours
                         1-5 hours




           11-15 hours

                                     16+ hours
1. How many kids spend 20 minutes or less per week doing chores?

2. How many kids spend more than 80 minutes per week doing chores?

3. What is the most common amount of time spent doing chores?

4. What is the least common amount of time spent doing chores?

5. How is a bar graph different from a histogram?
Histograms
                        Jumping Into Histograms
Name_______________________________                  Date__________________________

Work in groups to complete the activity. Each person will hand in their own work. Each
person will be graded on their accuracy, detailed responses to questions, and neatness.

Ms. Varacallo had her students measure how high each student could jump. The students
were then instructed to graph their data as a class. Use the information in the table below
to create a histogram, stem and leaf plot, and box and whisker plot. Be sure to label
the x-axis, y-axis and title. Use both the histogram, stem and leaf, and box and whisker
plot to answer the questions below.

Name             Jump            Name            Jump           Name               Jump
                 Height (cm)                     Height (cm)                        Height(cm)
Frank            5               Mack            29             Brianne            27
Christian        11              Vicente         50             Ms. Schenker       13
Nicole           75              Anish           37             Ayesha             51
Carlos           55              Michael         14             Avik               54
Sana             25              Lauren          62             Kathleen           62
Kaitlyn          27              Amy             73             Kunal              56
Ms. Varacallo    6               John            10             Aakash             12
Kevin Jackson    62              Karen           44             Logan              79
Jennifer         52              Paul            14             Sabrina            29
Kevin Joyce      36              Ryan            65             Sarah              32
Lily             15              Veronica        15             Tiffany            20
Hope             53              Allison         60             Emily              27
Kevin Lim        44              Mr. Canik       47             Mr. McGurney       70
Po               13              Will            33             Ms. Perhacs        19
Alex             47              Andy            66             Corey              49
Name:
Date:

              Histogram

                 <<Title>>
 <<Y Axis>>




               <<X Axis>>
Stem and leaf plot




1. What are the mean, median, mode, and range of this data?
(You can use a calculator to calculate the mean)



2. How many people jumped a height of 30 centimeters or less? ____________________

3. How many people jumped a height of 61 centimeters or more? ___________________

4. What is the most common height jumped in centimeters? _______________________
                                                                  (using histogram)
5. What is the least common height jumped in centimeters? ________________________
                                                                  (using histogram)
 6. Turn the stem and leaf plot on its side so that the “stem” is on the bottom and the
“leaves” are vertical. Compare the shape of the stem and leaf plot and the histogram.
What do you notice about their appearances? Explain how a stem and leaf plot and a
histogram are related.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
Name:______________________________________________ Date:_______________

                               Histogram Lesson
Directions: Use the notes discussed in class to define the term below.

Histogram:

Directions: Use the lines below to list some properties of the histogram discussed in
            group work.

                                      Properties

      __________________________________________________________________
      __________________________________________________________________
      __________________________________________________________________
      __________________________________________________________________
      __________________________________________________________________


Directions: Identify the differences between a bar graph and histograms.



                Histogram                                       Bar graph
                              Answer Key:
Attachment B
1.   10
2.   15
3.   41-60 minutes
4.   0-20 minutes
5.   Answers will very, however a main difference is that bar graphs
     are categorical while histograms display the frequency within an
     interval. A discussion should include ideas related to the physical
     appearances of both graphs.
                               Answer Key
                          Jumping into Histograms




Stem                       Leaves
0            56
1            0123344559
2            0577799
3            2367
4            44779
5            0123456
6            022256
7            0359
1.
mean: 1745  45  38.8
median: 37
mode(s): 27, 62
range: 79 – 5 = 74
2.   19 students
3.   9 students
4.   11-20 centimeters
5.   0- 10 centimeters
6.   A stem-and-leaf plot does resemble a histogram turned sideways. The stem
     values could represent the intervals of a histogram, and the leaf values could
     represent the frequency for each interval.

								
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