5-Minute Check on Activity 7-2

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5-Minute Check on Activity 7-2

1. What were the graphs examined in the last lesson?
2. What type of graph was the Age-Gender Population
   graph?
3. Are pie-charts the same as a relative frequency
   chart?
4. What is a pareto chart?

Bar graphs and pie charts
Back to back bar graphs
Yes the both add up to 100
Pareto charts list s the bars in percentage order
from highest to lowest
Click the mouse button or press the Space Bar to
display the answers.
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Activity 7 - 3

• The Class Survey

3
Objectives

• Organize data with frequency tables, dotplots,
  and histograms
• Organize data using stem-and-leaf plots

4
Vocabulary

• Frequency the number of occurrences of each
  data value
• Dotplot a graph that represent each occurrence
  of a data value with a dot
• Frequency Distributions show how the data is
  distributed over all possible values
• Classes are frequency intervals (grouped data)
• Class width how wide a class is (upper limit
  lower limit)
• Stem the digit or group of digits with the
  greatest place value
• Leaf the remaining digits

5
Activity

• Decisions that are made in business, government,
  education, engineering, medicine, and many other
  professions depend on analyzing collections of
  data. As a result, data analysis has become an
  important topic in many mathematics classes. In
  this activity, you will collect and organize data
  from your class.

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Activity cont

• Fill in the requested data on the board

Gender of Siblings Miles from School Time doing Homework Yesterday














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Activity cont

• Using the data collected on the board, determine
  the following characteristics of your class
• Most common number of siblings (mode)
• Average number of miles from school (mean)
• More females or males in class (mode)
• The most hours studied last night (max)

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Activity cont

• Draw dot plots of the four categories of data

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TI-83 Graph Support

• 2nd Y gets into STAT PLOT where we find six
  graph types supported
• Dot plot
• Line Plot
• Histogram
• Boxplot with outliers marked
• Boxplot without outliers marked
• Normality Plot
• To graph things we need the values entered into
  the list variables L1, L2, etc
• Zoom 9 (ZoomStat) will do the windowing for
  us

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Histograms

• Histograms break the range of data values into
  classes and displays the count or of
  observations that fall into that class
• Divide the range of data into equal-width classes
• Count the observations in each class frequency
• Draw bars to represent classes height
  frequency
• Bars should touch (unlike bar graphs).

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Histogram versus Bar Chart

• Histogram Bar Chart
• variables quantitative categorical
• bar space no space spaces between

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Categorical Data Example
Body Part Frequency Relative Frequency
Back 12 0.4
Wrist 2 0.0667
Elbow 1 0.0333
Hip 2 0.0667
Shoulder 4 0.1333
Knee 5 0.1667
Hand 2 0.0667
Groin 1 0.0333
Neck 1 0.0333
Total 30 1.0000
Physical Therapists Rehabilitation Sample
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Categorical Data

• Items are placed into one of several groups,
  intervals or categories (to be counted)
• Typical graphs of categorical data
• Pie Charts emphasizes each categorys relation
  to the whole
• Bar Charts emphasizes each categorys relation
  with other categories

Pie Chart
Bar Chart
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Charts for Both Data Types
Pareto Chart
Relative Frequency Chart
Cumulative Frequency Chart
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Quantitative Data

• Quantitative Variable
• Values are numeric - arithmetic computation makes
  sense (average, etc.)
• Distributions list the values and number of times
  the variable takes on that value
• Displays
• Dotplots
• Stemplots
• Histograms
• Boxplots

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Dot Plot

• Small datasets with a small range (max-min) can
  be easily displayed using a dotplot
• Draw and label a number line from min to max
• Place one dot per observation above its value
• Stack multiple observations evenly
• First type of graph under STATPLOT

34 values
ranging from 0 to 8
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Stem Plots

• A stemplot gives a quick picture of the shape of
  a distribution while including the numerical
  values
• Separate each observation into a stem and a
  leafeg. 14g -gt 14 256 -gt 256 32.9oz -gt 329
• Write stems in a vertical column and draw a
  vertical line to the right of the column
• Write each leaf to the right of its stem
• Note
• Stemplots do not work well for large data sets
• Not available on calculator

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Stem Leaf Plots Example
Given the following values, draw a stem and leaf
plot 20, 32, 45, 44, 26, 37, 51, 29, 34, 32, 25,
41, 56
Ages Occurrences ----------------------
-------------------------------------------- 2
0, 6, 9, 5 3 2, 3, 4, 2 4 5,
4, 1 5 1, 6
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Splitting Stems

• Double the number of stems, writing 0-4 after the
  first and 5-9 after second.

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Back-to-Back Stemplots

• Back-to-Back Stemplots Compare datasets

Example1.4, pages 42-43 of YMS Literacy Rates in
Islamic Nations
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Example 2

• The ages (measured by last birthday) of the
  employees of Dewey, Cheatum and Howe are listed
  below.
• Construct a stem graph of the ages
• Construct a back-to-back comparing the offices
• Construct a histogram of the ages

22 31 21 49 26 42
42 30 28 31 39 39
20 37 32 36 35 33
45 47 49 38 28 48
Office A
Office B
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Example 2a Stem and Leaf
22 31 21 49 26 42
42 30 28 31 39 39
20 37 32 36 35 33
45 47 49 38 28 48
Ages of Personnel
2 0, 1, 2, 6, 8, 8, 3 0, 1, 1, 2, 3, 5,
6, 7, 8, 9, 9, 4 2, 2, 5, 7, 8, 9, 9,
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Example 2b Back-to-Back Stem
22 31 21 49 26 42
42 30 28 31 39 39
20 37 32 36 35 33
45 47 49 38 28 48
Office B Ages of Personnel
Office A Ages of Personnel
2 0, 8 3 2, 3, 5, 6, 7, 8, 4 5, 7,
8, 9,
1, 2, 6, 8 0, 1, 1, 9, 9 2, 2, 9
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Example 2c Histogram

• n 24
• k v24 4.9 so pick k 5
• w (49 20)/5
• 29/5 5.8 ? 6
• K range Nr
• 1 20 25 3
• 2 26 31 6
• 3 32 37 5
• 4 38 43 5
• 5 44 49 5

8
6
4
Numbers of Personnel
2
20-25
32-37
44-49
26-31
38-43
Ages
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Summary and Homework

• Summary
• Frequency Distribution describes how frequently
  each data value occurs
• Listed in a frequency table
• Visually depicted in a dot-plot or histogram
• Grouped histograms are useful for wide range of
  data by dividing groups in equal-width intervals
• Stem-and-leaf organizes data by splitting each
  data value into two parts (usually tens digit and
  singles digit)
• Homework
• pg 811-814 problems 2, 3, 7