Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there.
In this slide the discussed points are:
1. Dispersion & it's types
2. Definition
3. Use
4. Merits
5. Demerits
6. Formula & math
7. Graph and pictures
8. Real life application.
Measure of dispersion has two types Absolute measure and Graphical measure. There are other different types in there.
In this slide the discussed points are:
1. Dispersion & it's types
2. Definition
3. Use
4. Merits
5. Demerits
6. Formula & math
7. Graph and pictures
8. Real life application.
Topic: Variance
Student Name: Sonia Khan
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Measures of dispersion
Absolute measure, relative measures
Range of Coe. of Range
Mean deviation and coe. of mean deviation
Quartile deviation IQR, coefficient of QD
Standard deviation and coefficient of variation
students will be able to understand various measures of central tendency and also will be able to calculate mean median and mode for individual discrete and continuous series.
Topic: Variance
Student Name: Sonia Khan
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Measures of dispersion
Absolute measure, relative measures
Range of Coe. of Range
Mean deviation and coe. of mean deviation
Quartile deviation IQR, coefficient of QD
Standard deviation and coefficient of variation
students will be able to understand various measures of central tendency and also will be able to calculate mean median and mode for individual discrete and continuous series.
Unit-I Measures of Dispersion- Biostatistics - Ravinandan A P.pdfRavinandan A P
Biostatistics, Unit-I, Measures of Dispersion, Dispersion
Range
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standard deviation
Variance
coefficient of variation
standard error of the mean
MEANING OF DISPERSION In Statistics,
This term is used commonly to mean scatter,
Deviation, Fluctuation, Spread or variability of data.
The degree to which the individual values of the variate scatter away from the average or the central value, is called a dispersion
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Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
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The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
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2. MEASURES OF DISPERSIONS
• A quantity that measures the variability
among the data, or how the data one
dispersed about the average, known as
Measures of dispersion, scatter, or
variations.
3. • To know the average variation of different
values from the average of a series
• To know the range of values
• To compare between two or more series
expressed in different units
• To know whether the Central Tendency
truly represent the series or not
4. 2. Common Measures of
Dispersion
• The main measures of dispersion
1. Range
2. Mean deviation or the average deviation
3. The variance & the standard deviation
5. 5
The Range
• The range is defined as the difference
between the largest score in the set of
data and the smallest score in the set of
data, XL - XS
• What is the range of the following data:
4 8 1 6 6 2 9 3 6 9
• The largest score (XL) is 9; the smallest
score (XS) is 1; the range is XL - XS = 9 - 1 =
8
7. 1. RANGE
• Example:
1. Find the range in the following data.
31,26,15,43,19,10,12,37
Range = xm – xo 33 = 43 – 10
2. Find the range in the following F.D. (Ungrouped)
5 = 8 – 3
Range 5 = 8 – 3
3. Find the range in the following data.
Range = 60 – 10 = 50
X 3 4 5 6 7 8
f 5 8 12 10 4 2
X 10 - 20 20 - 30 30- 40 40 – 50 50 - 60
f 5 8 12 10 4
8. MEAN (OR AVERAGE) DEVIATION
• It is defined as the “Arithmetic mean of the
absolute deviation measured either from
the mean or median.
• or for ungroup.
• or for grouped.
n
xx
DM
∑ −
=..
N
xxf∑ −
=
N
medianx∑ −
N
medianxf∑ −
=
11. MEAN (OR AVERAGE) DEVIATION
• Exp: Calculate mean deviation from the FD (Grouped Data).
MD (x) = 33.6 / 20 = 1.68
M.D = 23.72 / 14 = 1.69
X f Class Mark
( x )
f.x I x – 6.57 I f I x – 6.57 I
2 – 4 2 3 6 3.57 7.14
4 - 6 3 5 15 1.57 4.71
6 – 8 6 7 42 0.43 2.58
8 – 10 2 9 18 2.43 4.86
10 – 12 1 11 11 4.43 4.43
Total Σf =14 Σ f.x =92 Σ f I x – 6.57 I =
23.72
=92/14=6.57ẋ
13. THE VARIANCE AND
STANDARD DEVIATION
• It is defined as “The mean of the squares
of deviations of all the observation from
their mean.” It’s square root is called
“standard deviation”.
• Usually it is denoted by (for population of
statistics) S2
(for sample)
• = for ungrouped
2
σ
2
σ
n
xx∑ − 2
)(
15. • = for grouped
• It is an absolute measure;
• It is relative measure is coefficient of
variation.
•
• Shortcut method
N
xxf∑ − 2
)(2
σ
100. ×=
µ
σ
VC 100
..
.. ×=
x
DS
VC
22
2
−=
∑∑
N
x
N
x
σ
22
2
.
−=
∑∑
N
fx
N
xf
σ
THE VARIANCE AND
STANDARD DEVIATION
16. VARIANCE AND STANDARD
DEVIATION• Example:
1. Calculate Variance and SD from the FD (Ungrouped Data).
Using Short cut method
var = (564 / 20) - (98 / 20) ^ 2 = 28.2 – 24.01 = 4.09
Sd = √ σ^2 = √ 4.09 = 2.02
X f f.x X^2 f.x^2
2 3 6 4 12
4 9 36 16 144
6 5 30 36 180
8 2 16 64 128
10 1 10 100 100
Total Σf =20 Σf.x = 98 Σ f.x^2=564
22
2
.
−=
∑∑
N
fx
N
xf
σ
17. VARIANCE AND STANDARD
DEVIATION
• Exp: Calculate Variance and Standard deviation from the FD (Grouped Data).
Using Short cut method:
var = (670 /14) - (92 / 14) ^ 2 = 47.85 – 43.18 = 4.67
Sd = √ σ^2 = √ 4.67 = 2.16
X f Class Mark
( x )
f.x x^2 f.x^2
2 – 4 2 3 6 9 18
4 - 6 3 5 15 25 75
6 – 8 6 7 42 49 294
8 – 10 2 9 18 81 162
10 – 12 1 11 11 121 121
Total Σf =14 Σ f.x =92 Σ f.x^2 =670
22
2
.
−=
∑∑
N
fx
N
xf
σ
19. Relative Measures ofRelative Measures of
DispersionDispersion
Coefficient of Range
Coefficient of Quartile Deviation
Coefficient of Mean Deviation
Coefficient of Variation (CV)
20. Relative Measures of VariationRelative Measures of Variation
Largest Smallest
Largest Smallest
Coefficient of Range
X X
X X
−
=
+
3 1
3 1
Coefficient of Quartile Deviation
Q Q
Q Q
−
=
+
Coefficient of Mean Deviation
MD
Mean
=
21. Coefficient of Variation (CV)Coefficient of Variation (CV)
Can be used to compare two or more
sets of data measured in different
units or same units but different
average size.
100%
X
S
CV ⋅
=
22. Use of Coefficient of VariationUse of Coefficient of Variation
Stock A:
Average price last year = $50
Standard deviation = $5
Stock B:
Average price last year = $100
Standard deviation = $5
but stock B is
less variable
relative to its
price
10%100%
$50
$5
100%
X
S
CVA =⋅=⋅
=
5%100%
$100
$5
100%
X
S
CVB =⋅=⋅
=
Both stocks
have the
same
standard
deviation
24. Skewness
A fundamental task in many statistical analyses is to
characterize the location and variability of a data set
(Measures of central tendency vs. measures of dispersion)
Both measures tell us nothing about the shape of the
distribution
It is possible to have frequency distributions which differ
widely in their nature and composition and yet may have
same central tendency and dispersion.
Therefore, a further characterization of the data includes
skewness
25. Positive & Negative Skew
Positive skewness
There are more observations below the mean than
above it
When the mean is greater than the median
Negative skewness
There are a small number of low observations and a
large number of high ones
When the median is greater than the mean
26. Measures of Skew
Skew is a measure of symmetry in the distribution
of scores
Positive
Skew
Negative Skew
Normal
(skew = 0)
29. The Kurtosis is the degree of peakedness or flatness of a
unimodal (single humped) distribution,
• When the values of a variable are highly concentrated around
the mode, the peak of the curve becomes relatively high; the
curve is Leptokurtic.
• When the values of a variable have low concentration
around the mode, the peak of the curve becomes relatively
flat;curve is Platykurtic.
• A curve, which is neither very peaked nor very flat-toped, it
is taken as a basis for comparison, is called
Mesokurtic/Normal.
Measures of Kurtosis
31. Measures of Kurtosis
1. If Coefficient of Kurtosis > 3 ----------------- Leptokurtic.
2. If Coefficient of Kurtosis = 3 ----------------- Mesokurtic.
3. If Coefficient of Kurtosis < 3 ----------------- is Platykurtic.
( )
( )
4
22
n X-X
Coefficient of Kurtosis=
X-X
∑
∑
