Transcript 7.7 Statistics & Statistical Graphs

Exploring Data: Statistics
& Statistical Graphs
During this lesson, you will organize
data by using tables and graphs.
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Tables, frequency distributions, line plots,
histograms, circle graphs, and pictograms are all
ways to represent data.
Organizing Data
Data- information, facts, or numbers
that describe something
A collection of data is easier to
understand when it is organized in a
table or graph. While there is no “best
way” to organize such data; there are
many good ways. This lesson illustrates
several types of tabular and graphic
representations.
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REVIEW: Statistics
 Statistics – numerical values used to
summarize & compare sets of data (such
as ERA in baseball).
 Measures of Central Tendency – mean,
median, & mode are the three
“averages” which we will be using
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Three “Averages”
Mean – ( x ) average of n numbers (add all #s
& divide by n)
Median – the middle # when the #s are written
in order from least to greatest or greatest to
least. If there are two middle numbers, the
median will be the average of those numbers.
Mode – most frequently occurring number.
NOTE: It is possible to have more than 1
mode or even no mode.
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EXAMPLE:
Find the mean, median, &
mode of the following set of numbers: 36,
39, 40, 34, 48, 33, 25, 30, 37, 17, 42, 40,
24.
Mean -
445
 34.2
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Median – Put the numbers in order first!
17, 24, 25, 30, 33, 34, 36, 37, 39, 40, 40,
42, 48
Mode – most frequent!
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is McConaughy
the mode.
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Measures of Dispersion – tell how
spread out the data are
* Range – difference between the
largest and smallest values.
(for example: the range of the
last example would be 48-17=31)
* Standard Deviation - (σ –
“sigma”)
( x1  x) 2  ( x2  x) 2  ...  ( xn  x) 2 x is the mean

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n
x1, x2, x3, …, xn are
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n is the number of entries in the set
the entries in the
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data set.
EXAMPLE:
Find the standard
deviation of the data from the first
example.
(36  34.2) 2  (39  34.2) 2  (40  34.2) 2  ...  (24  34.2) 2

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856.32

13
  65.87
  8.12
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EXAMPLE: Box-and-whisker plots
Box
Whisker
0
Minimum
value
(17)
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10
20
30
Lower Quartile –
median of all
numbers in the list
to the left of the
median
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Median
(36)
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(25+30)/2 = 27.5
Whisker
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Maximum
value (48)
Upper Quartile –
median of all numbers
to the right of the
median
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(40+40)/2 = 40
Hints for making a
box-and-whiskers plot:
 Make sure data is in order from least to
greatest.
 Find the minimum value, median,
maximum value, upper & lower quartiles.
 Plot the points for this information
below a number line.
 Draw the box and whiskers.
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EXAMPLE: Frequency Distribution
Assign appropriate
intervals that will
include all data
values in the set.
Interval
0 to 9
10 to 19
20 to 29
30 to 39
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Put a tally mark
for each data
value in the
appropriate row.
Count the
number of tally
marks and put
the total in the
last column.
Title Goes Here
Tally
Frequency
0
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1
ll
2
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EXAMPLE: Histogram
Frequency
L
A
B
E
L
H
E
R
E
TITLE HERE
Bars should be
touching!
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5
4
3
2
1
0
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Intervals
LABEL HERE
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Final Checks for Understanding
1.
Give an example of a collection of data that
you could organize using a box-and-whiskers
plot.
2. Your classmates were asked to select their
favorite type of music from these choices:
classical, jazz, country, rock, and rap. How
would you organize the results?
3. Which technique do you think is best suited
to organize the results of a student council
election?
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Homework Assignment:
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