Transcript Lesson 25 - algebra2PCHS

Lesson 25
Finding measures of central
tendency and dispersion
statistics
Statistics is the branch of mathematics
that involves the collection, analysis and
comparison of numerical data.
 A measure of central tendency is used
to represent the middle of a set of data
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Measures of central tendency
Mean ( average) of n numbers is the sum of the
numbers divided by n, mean is denoted by "x
bar" or "x" with a bar over it.
 Median of n numbers is the middle number
when the numbers are written in order. If n is
even, the median is the mean of the 2 middle
numbers.
 Mode of n numbers is the number that appears
most frequently in the list. There may be one
mode, no mode, or more than one mode.
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Finding measures of central
tendency
The following are Anne's grades for
algebra quizzes: 18,15,20,16,17,19,19
 Calculate the mean, median and mode
 mean = 124/7 = 17.7
 Median= 18
 Mode = 19
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Measure of dispersion
 A measure
of dispersion is a
statistic that indicates how spread
out, or dispersed, data values are.
 Three common measures of
dispersion are the range,
variance, and standard
deviation
Measures of dispersion
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The range of a set of data is the difference between
the largest and smallest data values.
The variance of a data set is the average of the
squared differences from the mean.
The standard deviation measures, on average, how
far away from the mean the data values are. The
standard deviation, which is represented by the
Greek letter sigma  , is the square root of the
variance and is calculated using the following
formula
2
2
2

bx  x g bx  x g...bx  x g
1
2
n
n
Finding measures of dispersion
Find the range and standard deviation for the
following sets of data: 5, 7, 12, 14, 17
 Range = 17-5 = 12
 Mean = 11
 Standard deviation =
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a5  11f  a7  11f  a12  11f  c14  11h a17  11f
2

2
2
5
36  16  1  9  36
98


 4.4
5
5
2
2
Find the range and standard
deviation for the following sets of
data
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10,12,7,11,20,7,6,8,9
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3,4,5,7,9
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12,13,15,16,17
outlier
An outlier is an item in a data set that is
much larger or much smaller than the
other items in the set.
 The presence of an outlier in a data set
can have a misleading effect on the
measures of central tendency and
dispersion.
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Examining the effect of an outlier
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Identify the outlier in the set. Then find the mean,
median, mode, range, and standard deviation when
the outlier is included and when it is not.
2,2,3,3,4,4,4,6,68
Outlier is 68
With outlier
without outlier
Range
66
4
Mode
4
4
Median
4
3.5
Mean
10.7
3.5
Stan dev 20.3
1.2
Box-and-whisker plot
A box-and-whisker plot is a convenient
way to organize data.
 The first quartile is the median of the
lower half of the data set.
 The third quartile is the median of the
upper half of the data set
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Draw box-and-whisker plots to
display the following data
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31,29,28,20,35,22,32,22,32
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32,44,42,34,40,34,33,30,46
Lab 5
Storing
and
plotting a list of
data
P. 153 -storing a list of data
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Press STAT to open the statistics menu
Press ENTER to edit the list
Go to the L1 column and enter your data. Press
Enter after each number.
Go to L2 column and enter the data from the
second data set
Plotting data
Turn on the plot feature by going to 2nd Y= which
is stat plot
Press ENTER to turn plot 1 on
Pick the type of graph you want
Graph
Lab 6-
Calculating
1 and
2 variable
statistical data
P. 178
Enter data sets into L1 and L2 as in lab 5
 To calculate 1-variable statistics:
 Press STAT, then open the CALC menu
 select 1:1-var stats
 Input L1 by pressing 2nd 1
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Calculating statistics for 2variable data
Press Stat , then go to Calc
 Go to 2:2-var stats
 Press enter
 It will analyze for values in L1 and L2
 L1 will be referred to as x and L2 will be
referred to as y
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Box-and-whisker plot
Press 2nd y= to open stat plot
 Press enter to turn plot on
 Choose box-and-whisker plot
 L1 should be displayed
 Move down to Freq
 Press Enter
 Go to zoom stat,
 Enter
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