Data Distributions Interactive Presentation. Data Collection and Frequency Tables 1. Why does sample...
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Data Distributions Interactive Presentation. Data Collection and Frequency Tables 1. Why does sample size matter? 2. How could the way data is collected
Data Collection and Frequency Tables 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?
Slide 3
Vocabulary Data facts or numbers that are collectedData Types
of Data Categorical data data that is a name or category Numerical
data data that is a number
Slide 4
Vocabulary Sample a group of people within a population
EXAMPLE: Population the entire group you want to find information
about EXAMPLE: Sample or population?
Slide 5
REMEMBER! Sample Statistics will be more accurate as sample
size INCREASES!!
Slide 6
Vocabulary Survey given to investigate behaviors or opinions by
questioning a sample from the populationSurvey Click link for
examples examples
Slide 7
Vocabulary Census a survey of an entire population
Slide 8
Vocabulary Parameter a measured characteristic of a population
Statistic a measured characteristic of a sample A number that
represents the average shoe size of ALL 7 th graders The average
shoe size of our class (the representative length from the
sample)
Slide 9
Vocabulary Review Definition Facts or numbers that are
collected A measured characteristic of a sample Data that is a
number Given to investigate opinions or behaviors by questioning a
group of people A group of people within a population Survey of an
entire population A measured characteristic of a population Data
that is a name or category The group you want to find information
about
Slide 10
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.
Slide 11
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?
Slide 12
Frequency Table After you choose a question, you need to
collect and organize your data. A good way to do this is to use a
frequency table (frequency distribution).
Slide 13
Frequency distribution (frequency table) a table that organizes
data to show how many times each item or group of items
appearsFrequency distribution
Slide 14
Your Turn! Maxine took a census of all the students in Ms.
Alvarezs class. The data below show the number of pets owned by
each student: 0, 1, 3, 2, 1, 4, 2, 1, 0, 3, 5, 2, 2, 1, 3, 2, 1, 4,
5, 0, 0, 1, 2, 1, 2 Organize the data in an ungrouped frequency
table. Use the data to determine how many more students have 1 pet
than have no pets. # of petsTalliesFrequency 0 1 2 3 4 5 Questions:
1._______ students have 1 pet. 2._______ students have no pets.
3.How many more students have 1 pet than have no pets? _______ 4.
The data are organized in the frequency table above. The data show
that _____ more students have 1 pet than have no pets.
Slide 15
Try another frequency table problem: 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:
TransportationNumber of people Airplane125 Automobile6 Boat42
Train27 1.What percent of those surveyed chose boat? 2.What percent
did not chose airplane? Challenge Question:
Slide 16
1.21% of those surveyed chose boat 2.37.5% of those surveyed
did not choose airplane
Slide 17
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. We will show you a variety of graphs
you can use to display your data later on in this unit!
Slide 18
Ticket-out-the-door 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? 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 _________. 5.A good way to
organize this data is to use a ________ __________. population
sample data survey Frequency table
Slide 19
How can I describe and interpret a data set in a meaningful
way? VOCABULARY: central tendency, mean, median, mode
Slide 20
Measures of central tendencyMeasures of central tendency:
1.Mean 2.Median 3.Mode
Slide 21
Vocabulary 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 These are measures of central tendency!
Slide 22
EXAMPLE 1 Find the mean, median, and mode of the data in the
table: 9, 8, 9, 8, 7, 8, 9, 10, 10, 7, 8, 9, 8, 8, 10, 8, 8, 9, 10,
8, 8, 10, 9, 9, 9 ScoreFrequency 10 9 8 7 *Hint to help with mean*
Use the frequency column to find the TOTAL number of students
Slide 23
Example1 Answers:
Slide 24
EXAMPLE 2 Zack wants to have a mean score of 80 on his health
quizzes. He scored 70, 75, 82, and 90 on his first four quizzes.
What score must he earn on his fifth quiz to have a mean score of
exactly 80 for all five quizzes? SMART STRATEGY: Use what you know
about MEAN! Step 1: Find the sum of the 4 scores you know. Step 2:
Find the sum if Zack has a mean score of 80 on all 5 quizzes. Step
3: What number would you need to add 317 to get a sum of 400? Step
4: Check your answer
Slide 25
Example 3 This stem and leaf plot shows the number of miles
Jamal biked per week for each of the past 10 weeks: This week,
Jamal was ill so he only biked 11 miles. How does this change the
median and mean of the data? StemLeaf 345345 6 0 3 3 5 7 8 9 3 Key:
5 3 = 53 miles
Slide 26
Which would be the best measure for each situation? 1.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?
Slide 27
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!
Slide 28
EQ: What are measures of variation? VOCABULARY: Variation,
Range, Quartiles, Interquartile Range, outlier, 5 Number
Summary
Slide 29
Vocabulary Variability How a data set is spread out Range The
difference between the greatest and least values in a data set 27,
39, 40, 22, 19, 41, 58, 40, 53, 49 *HINT: Largest Number Smallest
Number
Slide 30
58 19 = 39
Slide 31
Quartile: The three numbers that split an ordered data set in
four equal groups Lower Quartile (median of the lower half of the
data) The median of the data set Upper Quartile (median of the
upper half of the data)
Slide 32
5 Number Summary: the 5 numbers that divide a set of data into
4 equal groups.5 Number Summary 1. Minimum or Lower Extreme 2.
Lower Quartile (Q1) 3. Median (Q2) 4. Upper Quartile (Q3) 5.
Maximum or Upper Extreme
Slide 33
Interquartile range: The difference between the first and third
quartiles. (Note that the first and third quartiles are sometimes
called upper and lower quartiles.) IQR = UQ - LQ
Slide 34
Outlier a number that is much greater than or much less than
the rest of the numbers in a data set
Slide 35
EXAMPLE 1 Below are the weekly earnings for eight Kroger
Employees. Find all measures of variation: $260, $175, $215, $350,
$320, $235, $240, $280 You are looking for: 1.Lower extreme
2.Quartile 1 3.Median 4.Quartile 3 5.Upper Extreme 6.Range
7.IQR
Slide 36
EQ: How can I use box-and-whisker plots to display and analyze
data?
Slide 37
Box-and-Whisker Plot: a five number summary of data organized
into quartiles
Slide 38
The box-and-whisker plot below shows the weights, in pounds, of
the dogs that were weighed this morning at a veterinarians office.
Approximately what percent of the dogs weighed less than 25 pounds?
1.The box-and-whisker plot shows that the lower quartile of the
data is _______ pounds. 2.The lower quartile is the median of the
lower __________ of the data set. 3.The quartiles divide the data
into ____________. 4.What fraction of the data is less than the
lower quartile? _______ 5.What percent is equivalent to that
fraction? 0102030405060708090100
Slide 39
The double box-and-whisker plot below shows the number of
points scored in games by two basketball players on the same team.
Find the range and interquartile range for each player. Who was the
most consistent scorer?
Slide 40
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
Slide 41
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
Slide 42
How do I collect data on a population that is too large to
study? VOCABULARY: sample, population
Slide 43
Vocabulary A sample is a _________ selected group that is
___________ of the population. If the sample is __________ of the
population, then the measures of central tendency and of variation
for the ________ and the __________ should be similar. The larger
the _______ size, the more accurate the _________.
Slide 44
Example 1 Owen took a random sample of 10 students who take
piano lessons at a music school and recorded their ages. The
director of the school took a census of all 30 students who take
piano lessons at the school and recorded their ages. Owens sample
data and the directors census data are show below: Owens Sample
Data: 5, 12, 12, 12, 12, 13, 13, 17, 17, 25 Directors Census Data:
5, 7, 8, 9, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13,
13, 14, 15, 16, 17, 17, 17, 18, 19, 21, 21, 25, 30 Find and compare
the mean, median, mode, and range of the sample and the
census.
Slide 45
Example 2 Which of the two samples has measures that are closer
to those of the actual population?
Slide 46
Example 3 The manager of an online bookstore kept track of the
number of books in each box that was shipped for 100 orders. His
assistant randomly selected two samples from his data and
calculated the mean and median for each: Sample A: 4, 7, 9, 9, 10,
11, 12, 15, 20, 26 Sample B: 1, 4, 4, 9, 12 Which sample is more
likely to have a mean and a median that are good approximations of
the actual mean (12.5) and the actual median (11.5) of the
population? Calculate the mean and median of each sample to
determine if your guess was correct or not.
Slide 47
How can best organize categorical and numerical data?
VOCABULARY: categorical data, numerical data, line plot,
pictograph
Slide 48
Vocabulary Categorical data data that is a name or category
Numerical data data that is a number What are some examples?
Slide 49
Vocabulary Line plot each data item is shown as a mark above a
number line; good for showing numerical data Class Example How many
brothers and sisters do you have?
Slide 50
Pictograph a graph that shows data using symbols or
pictures
Slide 51
Slide 52
Example 2 Jenny keeps statistics during basketball practice.
She recorded the number of free throws each player on the team
successfully made out of 15 attempts. Her data are listed below:
10, 14, 15, 12, 12, 9, 8, 14, 12, 5, 13, 10, 10, 12, 11 Create a
line plot to display these data. Then identify the mode.
Slide 53
Example 3 Leslie surveyed a sample of her classmates. She asked
them to name the number of different states they have lived in. She
displayed the results of her survey in the line plot below:
Identify any outliers for the data. Then find the median and the
range, with and without the outlier(s). Does removing the
outlier(s) change those measures?
Slide 54
How can I collect, organize, and analyze data in a meaningful
way? VOCABULARY: histogram, bar graph
Slide 55
Bar graph uses bars to display categorical data The bars have
spaces between them All the bars are the same width Washington
Warriors Victories Number of Victories Year
Slide 56
Steps to making a BAR GRAPH 1.Study your data from the
frequency table and determine a scale 2.Draw and label the graph.
DayMTWRF Visitor1151131335684
Slide 57
Your turn to try Using the frequency table below, draw a bar
graph CountrySchool Days Belgium175 Japan243 Nigeria190 S. Korea220
USA180 School Days Per Year
Slide 58
Histogram uses bars to show the frequency of data within equal
intervals Since the intervals leave no gaps, the bars of a
histogram do not have spaces between them!!
Slide 59
Steps to Creating a Histogram 1.Draw and label the axes of your
histogram 2.List the intervals from the frequency table on the
horizontal axes 3.Use the totals from the table to set the scale on
the vertical axes 4.Draw the bar for each interval 5.The bars
should be touching, the same width and shaded Example-Top 30
requested songs WeeksFrequency 1-54 6-1011 11-159 16-204 21-250
26-302
Slide 60
Example 1: Double Bar Graph The double bar graph shows the
number of tickets sold by four theatres yesterday. What was the
mean number of tickets sold by these theatres?
Slide 61
Example 2: Histogram 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.
25,19,23,29,34,26,30,34,33, 20,35,35,25,29,36,22,34, 15 Question 1:
What percent of students can type 30 or more words per minute
Question 2: How many students type 24 or less words per
minute?
Slide 62
EQ: How can I use line graphs and circle graphs to display and
analyze data?
Slide 63
Line graph a type of graph that shows change over time using a
line connecting data points Shows trends over time!!
Slide 64
People at the Sandwich Shop During what time interval did the
greatest number of people come into the sandwich shop? By how much
did it increase?
Slide 65
Slide 66
Circle Graph displays categories of data as parts of a whole
Shows Percents! ?
Slide 67
Example 1 As they exited the voting booths, 2,000 people were
asked to identify the mayoral candidate for whom they had voted. Of
the people surveyed, how many voted for Milton? How many voted for
Johnson? How many voted for Dunbar?
Slide 68
Example 2 Mandy asked a sample of students at her school to
name their favorite subject. Her results are shown above. If 12
students chose social studies as their favorite subject, what is
the total number of students surveyed? SMART STRATEGY: Set up a
PROPORTION!
Slide 69
Making a Circle Graph Type of Movie Number of Students Percent
of Total (# if students/Total) Degrees in a circle Size of angle
(Percent x 360) Funny Scary Romantic Action
Slide 70
Interactivate: Circle Graph
Slide 71
Ticket-out-the-door Create your own circle graph based on the
survey data below. *HINT: A total of 50 students were surveyed!!
Favorite type of ice cream Number of Students Percent of Total (#
of students/Total) Degree s in a circle Size of angle (Percent x
360) Vanilla15360 Chocolate25360 Strawberry10360
Slide 72
EQ: How can I use scatter plots to display and analyze
data?
Slide 73
Scatter Plot: a graph in which ordered pairs of data are
plotted. You can use a scatter plot to determine whether a
relationship, or correlation, exists between 2 sets of data
Slide 74
HINT: LOOK FOR TRENDS (PATTERNS)! As x increases, y
______________.
Slide 75
Slide 76
Slide 77
Interactivate: Scatter Plot
Slide 78
Graphs that help us analyze data: Pictographs Histograms Bar
graphs Line graphs Circle graphs Line plots Box-and-whisker plots
Scatter plots NLVM CNLVM Check it out!