Data Distributions

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Data Distributions

• Interactive Presentation

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Lesson 1

• Collecting Data

1. Why does sample size matter? 2. How could the
way data is collected affect answers to survey
questions? 3. What are some ways to make random
selection and why is randomness desirable?
EQ
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Math Dictionary
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Vocabulary

• Data facts or numbers that are collected
• Survey given to investigate behaviors or
  opinions by questioning a group of people

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Types of Data

• Categorical data data that is a name or
  category
• Numerical data data that is a number

the month you were born
How old you are
What are some examples?
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Vocabulary

• Population the group you want to find
  information about

The 7th grade class
EXAMPLE
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Vocabulary

• Sample a group of people within a population

Our math class
EXAMPLE
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Vocabulary

• Census a survey of an entire population

EXAMPLE
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Vocabulary
Example
A number that represents the average shoe size of
ALL 7th graders

• Parameter a measured characteristic of a
  population
• Statistic a measured characteristic of a sample

The average shoe size of our class (the
representative length from the sample)
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REMEMBER!

• Sample Statistics will be more accurate as sample
  size INCREASES!!

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Discussion 1

• A school principal wants to know the average
  amount of time it takes her students to reach
  school each morning. To find this out, she asked
  20 students in each grade How long does it
  usually take you to reach school in the morning?

Explain how the words population, sample, data,
and survey fit this situation.
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Discussion 2

• An automotive shop has 25 workers. The owner
  wants to reward his workers with a company
  outing. He is considering a day at a baseball
  game, a day at an amusement park, or a dinner for
  the workers at a restaurant. He decides to
  conduct a survey so he can make the best choice.

Formulate a single question he could ask. Should
he use a sample or a census?
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Ticket-out-the-door
1. The 2,000 members of the club represent
_____________. 2. The 150 members who sent back
the postcards represent the ___________. 3. What
the members write on the postcards is called
________. 4. The act of collecting the
information on the postcards is called a
_________.

• The 2,000 members of a club were mailed
  postcards, asking them to suggest locations for
  next years annual meeting. Only 150 returned
  the postcards. How do the new ideas from this
  lesson fit this situation?

data
population
sample
survey
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Categorical
VS
Numerical
Line plot
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Lesson 2

• How can I collect, organize, and analyze data in
  a meaningful way?
• VOCABULARY central tendency, mean, median, mode

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• Measures of central tendency
• Mean
• Median
• Mode

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Vocabulary
These are measures of central tendency!

• Mean the average (add up the values and divide
  by the of values)
• Median the middle number in a list of numbers
  (Hint write the numbers in order)
• Mode the value that occurs the most

Find the mean, median, and mode
13, 18, 13, 14, 13, 16, 14, 21, 13
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Discussion

• Find the mean, median, and mode of the data below

Hint to help with mean Use the frequency column
to find the TOTAL number of students
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Answers
Mean 8.64
Median 9
Mode 8
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Discussion

• In Ms. Lins 7th grade class, there are 21
  people, including Ms. Lin. There ages are
• 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12,
  12, 12, 12, 12, 12, 12, 12, 12, 37
• Find the mean, median, and mode
• Analyze the datawhich measure of central
  tendency would be the most appropriate to use?

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Which would be the best measure for each
situation?

• Would you use mean, median, or mode to describe
  the typical selling price of a bicycle?
• 2. Would you use mean, median, or mode to
  determine the most popular toy sold at a store?

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MMMR Rap

• M to the M to the M to the R, Remember this rhyme
  and youll go far
• Mode, Median, Mean Range, Now singing this song
  might feel strange.
• Mode, Mode now Ive been told, is the number you
  will see the most
• Median now hes the man, the one in the middle,
  line HIM up the best you can
• From small to large, small to large remember this
  your in charge

• Now mean mean you may wonder, just add add add
  all your numbers
• Then you just simply divide youll have one
  number to your surprise
• Last but not least is our friend the range
• Hes not the best hes kind of strange
• You start with the high subtract the low,
  thats the range now thats fo sho!

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The Dice Activity
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Lesson 3

• How can I collect, organize, and analyze data in
  a meaningful way?
• VOCABULARY frequency distribution, histogram,
  bar graph, pictograph

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Vocab
Frequency Distributions

• Frequency distribution (frequency table) a
  table that organizes data to show how many times
  each item or group of items appears

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Lets make our own frequency table!

• What is your favorite season?

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Sometimes, data is grouped before it is organized
into a frequency distribution

• What is your shoe size?

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Summary

• A survey of 200 people asked On your dream
  vacation, how would you get where you are going?
  The results are shown in the frequency table

• What percent of those surveyed chose boat?
• What percent did not chose airplane?

Challenge Question
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Answers

• 21 of those surveyed chose boat
• 37.5 of those surveyed did not choose airplane

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Getting the Idea

• A frequency distribution presents data in a
  table. It is easy to read the data in a
  frequency distribution, but it is not easy to get
  the whole picture from the list of numbers.
  Graphs are used to show data

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Bar Graphs

• Graphs that show data using vertical or
  horizontal bars
• The bars have spaces between them
• All the bars are the same width

Washington Warriors Victories
Number of Victories
Year
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Steps to making a BAR GRAPH

• Study your data from the frequency table and
  determine a scale
• Draw and label the graph.

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Your turn to try

• Using the frequency table below, draw a bar graph

School Days Per Year
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Vocab

• Histogram A special kind of bar graph in which
  the data has been grouped into equal-sized
  intervals

Since the intervals leave no gaps, the bars of a
histogram do not have spaces between them!!
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Steps to Creating a Histogram

• Draw and label the axes of your histogram
• List the intervals from the frequency table on
  the horizontal axes
• Use the totals from the table to set the scale on
  the vertical axes
• Draw the bar for each interval
• The bars should be touching, the same width and
  shaded

• Example-Top 30 requested songs

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Try a Histogram on your own

• The number of words that students in a typing
  class can type in a minute are listed below.
  First make a frequency table and then a histogram
  of the data.
• 25,19,23,29,34,26,30,40,33,20,35,35,25,29,36,22,31

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Vocab

• Pictograph a graph that shows data using
  symbols or pictures

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Activity
Jelly Beans!
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Lesson 4

• EQ What are measures of variation?
• VOCABULARY Variation, Range, Quartiles,
  Interquartile Range, outlier, 5 Number Summary

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Vocabulary

• Variability How a data set is spread out
• Range The difference between the greatest and
  least values in a data set

What's the range?
27, 39, 40, 22, 19, 41, 58, 40, 53, 49
HINT Largest Number Smallest Number
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Answer 39

• 58 19 39

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Vocab

• Quartile The three numbers that split an ordered
  data set in four equal groups

Lower Quartile (median of the lower half of the
data)
First Quartile
Second Quartile
The median of the data set
Upper Quartile (median of the upper half of the
data)
Third Quartile
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Vocab

• 5 Number Summary the 5 numbers that divide a
  set of data into 4 equal groups.
• 1. Lower Extreme
• 2. Lower Quartile (Q1)
• 3. Median (Q2)
• 4. Upper Quartile (Q3)
• 5. Upper Extreme

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Vocab

• Interquartile range The difference between the
  first and third quartiles. (Note that the first
  and third quartiles are sometimes called upper
  and lower quartiles.)

Formula
IQR UQ - LQ
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Vocab

• Outlier a number that is much greater than or
  much less than the rest of the numbers in a data
  set

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• Heres a freestyle, about the quartiles
• And I know you wanna know more, BUT were gonna
  work it in our head, you dont need that TI-84,
• First things first, Ima get it out quick and its
  only gonna take awhile, were gonna start things
  off with Q 1 or the first quartile.
• If you dont like math, dont be a hatar,
• Its the median of the lower half of the data.
• The second quartile, you can bet, is the median
  of the data set
• So finding the second quartile aint a tough
  riddle,
• All you gotta do, look right in the middle.
• Whats got attitude , swagga, and style, the
  highest number called the third quartile.
• It aint hard, but it does matter, its the
  median of the upper half of the data.
• WORD TO YOUR MOTHER!

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Activity
Classwork 5 Number Summary Strip Homework
Workbook pg. 165
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Lesson 5
Box-and-Whisker Plot
EQ How can I use box-and-whisker plots to
display and analyze data?
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Vocab

• Box-and-Whisker Plot a way of organizing data
  into quartiles that is useful for showing data
  distribution

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Steps for Creating a Box-and-Whisker Plot

• Step 1 Put the data in order from least to
  greatest
• Step 2 Find the median
• Step 3 Find the Lower Quartile
• Step 4 Find the Upper Quartile
• Step 5 Draw a number line
• Step 6 Place a point above the median, lower
  quartile, and upper quartile
• Step 7 Draw a box (with a vertical line thru
  the median)
• Step 8 Place a point above the lower extreme
• Step 9 Place a point above the upper extreme
• Step 10 Draw the whiskers

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Example

• 15 shoppers rated a brand of paper towel on a
  scale from 0-10
• 2, 6, 6, 6, 7, 8, 8, 8, 9, 10, 10

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Popcorn Activity

• Homework Box-and-whisker handout

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Lesson 6
Scatter Plots
EQ How can I use scatter plots to display and
analyze data?
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Vocab

• Scatter Plot a display of the relationship
  between two sets of data that are represented by
  points on a grid

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HINT LOOK FOR PATTERNS!
Examples
As x increases, y ______________.
As x increases, y ______________.
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As x increases, y ______________.
As x increases, y ______________.
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As x increases, y ______________.
As x increases, y ______________.
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Check it out!

• Interactivate Scatter Plot

Manatee Activity
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Lesson 7
Line graphs and Circle graphs
EQ How can I use line graphs and circle graphs
to display and analyze data?
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Vocab

• Line graph a type of graph that shows change
  over time using a line connecting data points

Shows trends over time!!
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Example
People at the Sandwich Shop
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Example
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Vocab

• Circle Graph a type of graph in which data is
  represented as part of a circle

?
Shows Percents!
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Making a Circle Graph
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Let's Create our Circle Graph!

• Interactivate Circle Graph

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Ticket-out-the-door

• Create your own circle graph based on the survey
  data below. HINT A total of 50 students were
  surveyed!!

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• Classwork/Homework Titanic Handout

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Graphs that help us analyze data

• Pictographs
• Histograms
• Bar graphs
• Line graphs
• Circle graphs
• Line plots
• Box-and-whisker plots
• Scatter plots

NLVM Check it out!