5-minute check on activity 7-2
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5-Minute Check on Activity 7-25-Minute Check on Activity 7-25-Minute Check on Activity 7-25-Minute Check on Activity 7-2
Click the mouse button or press the Space Bar to display the answers.Click the mouse button or press the Space Bar to display the answers.
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
Activity 7 - 3
The Class Survey
Objectives
• Organize data with frequency tables, dotplots, and histograms
• Organize data using stem-and-leaf plots
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
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.
Activity contFill in the requested data on the board:
Gender # of Siblings Miles from School Time doing Homework Yesterday
Activity cont
Using the data collected on the board, determine the following characteristics of your class:
a)Most common number of siblings (mode)
b)Average number of miles from school (mean)
c)More females or males in class (mode)
d)The most hours studied last night (max)
Activity cont
Draw dot plots of the four categories of data
Gender Siblings
Miles from School Homework
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
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).
Histogram versus Bar Chart
Histogram Bar Chart
• variables quantitative categorical
• bar space no space spaces between
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 Therapist’s Rehabilitation Sample
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 category’s relation to the whole– Bar Charts; emphasizes each category’s relation with other
categories
0
2
4
6
8
10
12
14
Ba
ck
Wri
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Elb
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Hip
Sh
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Kn
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Ha
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Gro
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Ne
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Rehab
Rehab
Back40%
Wrist7%
Elbow3%
Hip7%
Shoulder13%
Knee17%
Hand7%
Groin3%
Neck3% Pie ChartBar Chart
Charts for Both Data Types
00.05
0.10.15
0.20.25
0.30.35
0.40.45
Ba
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Wri
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Elb
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Hip
Sh
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Kn
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Pe
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Rehab
00.05
0.10.15
0.20.25
0.30.35
0.40.45
Ba
ck
Kn
ee
Sh
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lde
r
Wri
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Ha
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Hip
Elb
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Gro
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Pe
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Rehab
Pareto ChartRelative Frequency Chart
0
0.2
0.4
0.6
0.8
1
1.2
Ba
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Wri
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Elb
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Hip
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Rehab
Cumulative Frequency Chart
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
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
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 leaf
eg. 14g -> 1|4 256 -> 25|6 32.9oz -> 32|9– 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
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
Splitting Stems
• Double the number of stems, writing 0-4 after the first and 5-9 after second.
Back-to-Back Stemplots
• Back-to-Back Stemplots: Compare datasets
Example1.4, pages 42-43 of YMSLiteracy Rates in Islamic Nations
Example 2
The ages (measured by last birthday) of the employees of Dewey, Cheatum and Howe are listed below.
a) Construct a stem graph of the ages
b) Construct a back-to-back comparing the offices
c) 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
Example 2a: Stem and Leaf
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,
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
Example 2b: Back-to-Back Stem
2 0, 8
3 2, 3, 5, 6, 7, 8,
4 5, 7, 8, 9,
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 PersonnelOffice A: Ages of Personnel
1, 2, 6, 8
0, 1, 1, 9, 9
2, 2, 9
Example 2c: Histogramn = 24
k = √24 ≈ 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
2
4
6
8
20-2526-31
32-3738-43
44-49
Num
bers
of
Per
sonn
el
Ages
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
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