Measures of dispersion describe how similar or different scores in a data set are from each other. The more similar the scores, the lower the measure of dispersion, and the more varied the scores, the higher the measure. Common measures include the range, semi-interquartile range (SIR), variance, and standard deviation. Variance is the average of the squared deviations from the mean, while standard deviation is the square root of variance. Skew and kurtosis also describe the shape and symmetry of a distribution.
Topic: Frequency Distribution
Student Name: Abdul Hafeez
Class: B.Ed. (Hons) Elementary
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Topic: Frequency Distribution
Student Name: Abdul Hafeez
Class: B.Ed. (Hons) Elementary
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
this ppt gives you adequate information about Karl Pearsonscoefficient correlation and its calculation. its the widely used to calculate a relationship between two variables. The correlation shows a specific value of the degree of a linear relationship between the X and Y variables. it is also called as The Karl Pearson‘s product-moment correlation coefficient. the value of r is alwys lies between -1 to +1. + 0.1 shows Lower degree of +ve correlation, +0.8 shows Higher degree of +ve correlation.-0.1 shows Lower degree of -ve correlation. -0.8 shows Higher degree of -ve correlation.
Introduction to Statistics - Basic concepts
- How to be a good doctor - A step in Health promotion
- By Ibrahim A. Abdelhaleem - Zagazig Medical Research Society (ZMRS)
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.
This presentation gives you a brief idea;
-definition of frequency distribution
- types of frequency distribution
-types of charts used in the distribution
-a problem on creating types of distribution
-advantages and limitations of the distribution
Mpc 006 - 02-03 partial and multiple correlationVasant Kothari
3.2 Partial Correlation (rp)
3.2.1 Formula and Example
3.2.2 Alternative Use of Partial Correlation
3.3 Linear Regression
3.4 Part Correlation (Semipartial correlation) rsp
3.4.1 Semipartial Correlation: Alternative Understanding
3.5 Multiple Correlation Coefficient (R)
this ppt gives you adequate information about Karl Pearsonscoefficient correlation and its calculation. its the widely used to calculate a relationship between two variables. The correlation shows a specific value of the degree of a linear relationship between the X and Y variables. it is also called as The Karl Pearson‘s product-moment correlation coefficient. the value of r is alwys lies between -1 to +1. + 0.1 shows Lower degree of +ve correlation, +0.8 shows Higher degree of +ve correlation.-0.1 shows Lower degree of -ve correlation. -0.8 shows Higher degree of -ve correlation.
Introduction to Statistics - Basic concepts
- How to be a good doctor - A step in Health promotion
- By Ibrahim A. Abdelhaleem - Zagazig Medical Research Society (ZMRS)
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.
This presentation gives you a brief idea;
-definition of frequency distribution
- types of frequency distribution
-types of charts used in the distribution
-a problem on creating types of distribution
-advantages and limitations of the distribution
Mpc 006 - 02-03 partial and multiple correlationVasant Kothari
3.2 Partial Correlation (rp)
3.2.1 Formula and Example
3.2.2 Alternative Use of Partial Correlation
3.3 Linear Regression
3.4 Part Correlation (Semipartial correlation) rsp
3.4.1 Semipartial Correlation: Alternative Understanding
3.5 Multiple Correlation Coefficient (R)
Ppt By Mandar Abhyankar One of the serious problems India is facing today is ‘Population Explosion’. It has become one of the most serious problems our country is facing.
Frequency distribution, central tendency, measures of dispersionDhwani Shah
The presentation explains the theory of what is Frequency distribution, central tendency, measures of dispersion. It also has numericals on how to find CT for grouped and ungrouped data.
this is a presentation of probability and statistic on the topic of variance..its a detail presentation i will also upload a word document ....https://www.slideshare.net/ShahwarKhan16/statistics-and-probability-234750150
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
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!
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
2. Definition
Measures of dispersion are descriptive
statistics that describe how similar a set of
scores are to each other
The more similar the scores are to each other,
the lower the measure of dispersion will be
The less similar the scores are to each other, the
higher the measure of dispersion will be
In general, the more spread out a distribution is,
the larger the measure of dispersion will be
2
3. Measures of Dispersion
Which of the
distributions of scores 125
has the larger 100
75
dispersion? 50
25
The upper distribution 0
1 2 3 4 5 6 7 8 9 10
125
100
That is, they are less 75
50
similar to each other 25
0
1 2 3 4 5 6 7 8 9 10
3
4. Measures of Dispersion
There are three main measures of
dispersion:
The range
The semi-interquartile range (SIR)
Variance / standard deviation
4
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, X L -
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 =
5
8
6. When To Use the Range
The range is used when
you have ordinal data or
you are presenting your results to people with
little or no knowledge of statistics
The range is rarely used in scientific work
as it is fairly insensitive
It depends on only two scores in the set of data,
XL and XS
Two very different sets of data can have the
same range:
1 1 1 1 9 vs 1 3 5 7 9 6
7. The Semi-Interquartile Range
The semi-interquartile range (or SIR) is
defined as the difference of the first and
third quartiles divided by two
The first quartile is the 25th percentile
The third quartile is the 75th percentile
SIR = (Q3 - Q1) / 2
7
8. SIR Example
What is the SIR for the 2
data to the right? 4
← 5 = 25th %tile
25 % of the scores are 6
below 5 8
5 is the first quartile 10
25 % of the scores are 12
above 25 14
25 is the third quartile
20
SIR = (Q3 - Q1) / 2 = (25 - ← 25 = 75th %tile
30
5) / 2 = 10 60 8
9. When To Use the SIR
The SIR is often used with skewed data as it
is insensitive to the extreme scores
9
11. What Does the Variance Formula
Mean?
First, it says to subtract the mean from each
of the scores
This difference is called a deviate or a deviation
score
The deviate tells us how far a given score is
from the typical, or average, score
Thus, the deviate is a measure of dispersion for
a given score
11
12. What Does the Variance Formula
Mean?
Why can’t we simply take the average of
the deviates? That is, why isn’t variance
defined as:
σ 2
≠
∑ ( X − µ)
N
This is not the
formula for
variance!
12
13. What Does the Variance Formula
Mean?
One of the definitions of the mean was that
it always made the sum of the scores minus
the mean equal to 0
Thus, the average of the deviates must be 0
since the sum of the deviates must equal 0
To avoid this problem, statisticians square
the deviate score prior to averaging them
Squaring the deviate score makes all the
squared scores positive 13
14. What Does the Variance Formula
Mean?
Variance is the mean of the squared
deviation scores
The larger the variance is, the more the
scores deviate, on average, away from the
mean
The smaller the variance is, the less the
scores deviate, on average, from the mean
14
15. Standard Deviation
When the deviate scores are squared in variance,
their unit of measure is squared as well
E.g. If people’s weights are measured in pounds,
then the variance of the weights would be expressed
in pounds2 (or squared pounds)
Since squared units of measure are often
awkward to deal with, the square root of variance
is often used instead
The standard deviation is the square root of variance
15
17. Computational Formula
When calculating variance, it is often easier to use
a computational formula which is algebraically
equivalent to the definitional formula:
( ∑ X) 2
∑X ∑( X −µ)
2
− 2
N
σ
2
= =
N N
σ2 is the population variance, X is a score, µ is the
population mean, and N is the number of scores
17
19. Computational Formula Example
( ∑ X) 2
∑X ∑( X −µ)
2 2
−
N
σ
2
σ =
2
=
N N
2
12
306 − 42 =
= 6 6
6 =2
306 − 294
=
6
12
=
6
=2
19
20. Variance of a Sample
Because the sample mean is not a perfect estimate
of the population mean, the formula for the
variance of a sample is slightly different from the
( )
formula for the variance of a population:
2
2 ∑ X −X
s =
N −1
s2 is the sample variance, X is a score, X is the
sample mean, and N is the number of scores
20
21. Measure of Skew
Skew is a measure of symmetry in the
distribution of scores
Normal
(skew = 0)
Positive Negative Skew
Skew
21
22. Measure of Skew
The following formula can be used to
determine skew:
(
∑ X− X )
3
3 N
s =
(
∑ X− X )
2
N
22
23. Measure of Skew
If s3 < 0, then the distribution has a negative
skew
If s3 > 0 then the distribution has a positive
skew
If s3 = 0 then the distribution is symmetrical
The more different s3 is from 0, the greater
the skew in the distribution
23
24. Kurtosis
(Not Related to Halitosis)
Kurtosis measures whether the scores are
spread out more or less than they would be
in a normal (Gaussian) distribution
Mesokurtic
(s4 = 3)
Leptokurtic (s4 > Platykurtic (s4
3) < 3)
24
25. Kurtosis
When the distribution is normally
distributed, its kurtosis equals 3 and it is
said to be mesokurtic
When the distribution is less spread out than
normal, its kurtosis is greater than 3 and it is
said to be leptokurtic
When the distribution is more spread out
than normal, its kurtosis is less than 3 and it
is said to be platykurtic 25
26. Measure of Kurtosis
The measure of kurtosis is given by:
4
X−X
∑
∑ (X − X)
2
s4 =
N
N
26
27. s2, s3, & s4
Collectively, the variance (s2), skew (s3), and
kurtosis (s4) describe the shape of the
distribution
27