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

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Rehab

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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

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00.05

0.10.15

0.20.25

0.30.35

0.40.45

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Pareto ChartRelative Frequency Chart

0

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0.4

0.6

0.8

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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

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20-2526-31

32-3738-43

44-49

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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