Sample Data and Display

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Chapter 1

• Sample Data and Display

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Section 1-1

• Surveys and Sampling

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Population an entire group of peopleSuch as
Students at Fairland High School, Residents of
Proctorville, Citizens of the United States
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Sampling surveying a group of people from a
population, instead of the entire populationWhy
would we do this?
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Random SamplingEach member of the population
has an equal chance of being selected
Example All students names are in a box. Draw
out 50 names.
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Cluster SamplingMembers of the population are
randomly selected from particular parts of the
population and surveyed in clusters
Example Certain classrooms surveyed
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Convenience SamplingMembers of a population are
selected because they are readily available, and
all are surveyed
Example Everyone entering the mall Saturday
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Systematic SamplingMembers of a population that
have been organized in some way are selected
according to a pattern
Example Every tenth person in the cafeteria line
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Biased a survey finding that is not truly
representative of the entire population
How does this happen?
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ExampleA cereal manufacturer puts a survey in
every tenth box of cereal packaged to identify
the most popular brand.
What method of sampling was used?
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Answer Systematic Sampling
Are the results likely to be biased? Why or why
not?
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Section 1-2

• Measures of Central Tendency and Range

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Measures of Central Tendency

• Mean
• Median
• Mode
• All of these represent a central, or middle,
  value of a data set.

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Mean the sum of the values in the data set
divided by the number of data
Such asmean age of students in class
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Median the middle value of the data when the
data are arranged in numerical order
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What is the median?12, 25, 37, 21, 16, 35, 17
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What is the median?14, 23, 58, 35, 46, 17
If there are an even number of data, you must
take the average of the two middle data
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Mode the number that occurs most often in a set
of data
There may be one or more modes in a single set of
data
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What is the mode?23, 25, 14, 16, 32, 24, 23,
57, 64, 48, 14, 26, 25, 17
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Example 1Find the mean, median and mode for
the following set4, 12, 21, 33, 9, 4, 78
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Range the difference between the greatest and
least values in a set
What is the range? 4, 12, 21, 33, 9, 4, 78
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Section 1-3

• Histograms and Stem-and-leaf Plots

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Frequency Table records the number of times a
response occurs but does not offer a visual
display
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Histogram a bar graph with no space between the
bars
The bars represent a grouped interval of numbers
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Stem-and-Leaf Plot Another way to organize and
visually display data
Each number is represented by a leaf and a stem
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Leaf the digit in the place farthest to the
right in the number
Stem the digit or digits that remain when the
leaf is dropped
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Grades in our Class
9 8 7 6 5
3, 6, 8 1, 5, 6, 9 2, 4, 4, 7 5, 7, 7, 8 2
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Outliers values much greater or less than most
of the other values
Clusters isolated groups of values
Gaps large spaces between values
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Find the following

• 14, 23, 26, 3, 29, 34, 12, 28, 16
• Possible outliers, clusters, and gaps
• Mean
• Median
• Mode
• Range

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Section 1-4

• Scatter Plots and Lines of Best Fit

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Scatter Plot shows the relationship of two sets
of data using ordered pairs
What does a scatter plot look like?
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Example 1 pg. 20

• How many people were at the pool on the days the
  temperature reached 94 F?
• Find the mode of the daily attendance.

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Correlations

• A scatter plot displays a relationship called a
  correlation
• It can be positive or negative
• It can display no correlation

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Positive Correlation -
As the horizontal axis values increase, so do the
vertical axis values.
What does this look like?
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Negative Correlation -
As the horizontal values increase, the vertical
values decrease.
What does this look like?
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Line of Best Fit -

• The line which is most closely related to each
  point
• Called Linear Regression
• How do you find the line of best fit?

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Section 1-5

• Problem Solving Skills
• Coefficient of Correlation

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Coefficient of Correlation-

• A statistical measure of how closely data fits a
  line.
• The coefficient, r, is between -1 and 1
• The closer it is to -1 or 1, the stronger the
  correlation

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Section 1-6

• Quartiles and Percentiles

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Quartiles-

• Three numbers that group the data into four equal
  parts

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Finding Quartiles

• First find the median, also called the second
  quartile
• Second, find the median of the data above the
  median, this is the third quartile

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Finding Quartiles

• Then find the median of the data below the
  median, this is the first quartile

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Interquartile Range-

• The difference between the first and third
  quartiles

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Find the following

• 18, 29, 56, 42, 58, 31, 40, 28, 37, 46
• median
• first quartile
• third quartile
• interquartile range

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Box-and-Whisker Plot

• A graph that uses quartiles and a box to
  illustrate the interquartile range
• Drawn using a number line.

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Whiskers

• The lines that are drawn from the ends of boxes
  to the least and greatest values of the data

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Outliers

• Data that are at least 1.5 times the
  interquartile range above the third quartile or
  at least 1.5 times the interquartile range below
  the first quartile

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Example

• Make a box-and-whisker plot for the data.

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Percentile

• The percent of those who achieved at or below
  your score
• Formula for percentile

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Example

• Bernardo took a placement test. His score is
  48th from the highest out of the 760 students who
  took the test. Find the percentile rank that
  Bernardo achieved.

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Section 1-7

• Misleading Graphs
• and Statistics

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Misleading data

• Data that leads to a false perception
• One way to present correct data so that it is
  misrepresented is to alter a scale or show only a
  certain segment of the results

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Example page 35

• Furniture World has seven salespeople. The
  commission they earned last week was 493, 283,
  301, 299, 304 and 299. The owner of the
  store places an ad in the newspaper for
  additional salespeople.

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Section 1-8

• Using Matrices to Organize Data

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Matrix

• A rectangular arrangement of data in rows and
  columns and enclosed by brackets

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Element

• Each number in a matrix is an element, or an entry

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Rows and Columns

• Rows are the horizontal sets of numbers in a
  matrix
• Columns are the vertical sets of numbers in a
  matrix

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Dimensions

• The number of rows and columns determine the
  dimensions of the matrix
• The number of rows is read first, with the number
  of columns second

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Example

• How many rows does a 3 x 4 matrix have?
• 3
• How many columns?
• 4

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Square Matrix

• A matrix with the same number of rows and columns
• 2 x 2 or a 3 x 3 is a square matrix

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Corresponding Elements

• The elements in the same position of each matrix
• When adding or subtracting matrices, add or
  subtract corresponding elements

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Adding and Subtracting

• When adding and subtracting matrices, they must
  have the same dimensions

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Example

• 13 7 5 9 4 2 10 3 ?
• 9 5 -5 6
• 1 22 16 9 15 8 ?
• 10 37 24