This document defines and compares measures of central tendency, including the arithmetic mean, median, and mode. It provides formulas and examples for calculating each measure. The arithmetic mean is the sum of all values divided by the total number of values and can be used for numerical data. The median is the middle value when values are arranged in order and is not influenced by outliers. The mode is the value that occurs most frequently and can be used for both numerical and categorical data. Each measure of central tendency has advantages and disadvantages depending on the characteristics of the data set.
Measures of Central Tendency-Mean, Median , Mode- Dr. Vikramjit SinghVikramjit Singh
This presentation discusses in details about different measures of central tendency like- mean, median, mode, Geometric Mean, Harmonic Mean and Weighted Mean.
Measures of Central Tendency-Mean, Median , Mode- Dr. Vikramjit SinghVikramjit Singh
This presentation discusses in details about different measures of central tendency like- mean, median, mode, Geometric Mean, Harmonic Mean and Weighted Mean.
This slideshow explains the important measures of central tendency in statistics. It deals with Mean, mode and median; its characteristics, its computation, merits and demerits. This slideshow will be useful to students, teachers and managers.
Lecture 3 Measures of Central Tendency and Dispersion.pptxshakirRahman10
Objectives:
Define measures of central tendency (mean, median, and mode)
Define measures of dispersion (variance and standard deviation).
Compute the measures of central tendency and Dispersion.
Learn the application of mean and standard deviation using Empirical rule and Tchebyshev’s theorem.
Measures of Central Tendency:
A measure of the central tendency is a value about which the observations tend to cluster.
In other words it is a value around which a data set is centered.
The three most common measures of central tendency are mean, median and mode.
A measure of the central tendency is a value about which the observations tend to cluster.
In other words it is a value around which a data set is centered.
The three most common measures of central tendency are mean, median and mode.
A measure of the central tendency is a value about which the observations tend to cluster.
In other words it is a value around which a data set is centered.
The three most common measures of central tendency are mean, median and mode.
A measure of the central tendency is a value about which the observations tend to cluster.
In other words it is a value around which a data set is centered.
The three most common measures of central tendency are mean, median and mode.
Why is it needed?
To summarize the data.
It provides with a typical value that gives the picture of the entire data set
Mean:
It is the arithmetic average of a set of numbers, It is the most common measure of central tendency.
Computed by summing all values in the data set and dividing the sum by the number of values in the data set Properties:
Applicable for interval and ratio data
Not applicable for nominal or ordinal data
Affected by each value in the data set, including extreme values.
Formula:
Mean is calculated by adding all values in the data set and dividing the sum by the number of values in the data set.
Median:
Mid-point or Middle value of the data when the measurements are arranged in ascending order.
A point that divides the data into two equal parts.
Computational Procedure:
Arrange the observations in an ascending order.
If there is an odd number of terms, the median is the middle value and If there is an even number of terms, the median is the average of the middle two terms.
Mode:
The mode is the observation that occurs most frequently in the data set.
There can be more than one mode for a data set OR there maybe no mode in a data set.
Is also applicable to the nominal data.
Comparison of Measures of Central Tendency in Positively Skewed Distributions:
Majority of the data values fall to the left of the mean and cluster at the lower end of the distribution: the tail is to the right Mean, median & mode are different When a distribution has a few extremely high scores, the mean will have a greater value than the median = positively skewed.
Majority of the data values fall to
the right of the mean and cluster at the upper end of the distribution= Negatively Skewed
This slideshow explains the important measures of central tendency in statistics. It deals with Mean, mode and median; its characteristics, its computation, merits and demerits. This slideshow will be useful to students, teachers and managers.
Lecture 3 Measures of Central Tendency and Dispersion.pptxshakirRahman10
Objectives:
Define measures of central tendency (mean, median, and mode)
Define measures of dispersion (variance and standard deviation).
Compute the measures of central tendency and Dispersion.
Learn the application of mean and standard deviation using Empirical rule and Tchebyshev’s theorem.
Measures of Central Tendency:
A measure of the central tendency is a value about which the observations tend to cluster.
In other words it is a value around which a data set is centered.
The three most common measures of central tendency are mean, median and mode.
A measure of the central tendency is a value about which the observations tend to cluster.
In other words it is a value around which a data set is centered.
The three most common measures of central tendency are mean, median and mode.
A measure of the central tendency is a value about which the observations tend to cluster.
In other words it is a value around which a data set is centered.
The three most common measures of central tendency are mean, median and mode.
A measure of the central tendency is a value about which the observations tend to cluster.
In other words it is a value around which a data set is centered.
The three most common measures of central tendency are mean, median and mode.
Why is it needed?
To summarize the data.
It provides with a typical value that gives the picture of the entire data set
Mean:
It is the arithmetic average of a set of numbers, It is the most common measure of central tendency.
Computed by summing all values in the data set and dividing the sum by the number of values in the data set Properties:
Applicable for interval and ratio data
Not applicable for nominal or ordinal data
Affected by each value in the data set, including extreme values.
Formula:
Mean is calculated by adding all values in the data set and dividing the sum by the number of values in the data set.
Median:
Mid-point or Middle value of the data when the measurements are arranged in ascending order.
A point that divides the data into two equal parts.
Computational Procedure:
Arrange the observations in an ascending order.
If there is an odd number of terms, the median is the middle value and If there is an even number of terms, the median is the average of the middle two terms.
Mode:
The mode is the observation that occurs most frequently in the data set.
There can be more than one mode for a data set OR there maybe no mode in a data set.
Is also applicable to the nominal data.
Comparison of Measures of Central Tendency in Positively Skewed Distributions:
Majority of the data values fall to the left of the mean and cluster at the lower end of the distribution: the tail is to the right Mean, median & mode are different When a distribution has a few extremely high scores, the mean will have a greater value than the median = positively skewed.
Majority of the data values fall to
the right of the mean and cluster at the upper end of the distribution= Negatively Skewed
Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...Subhajit Sahu
Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.
Explore our comprehensive data analysis project presentation on predicting product ad campaign performance. Learn how data-driven insights can optimize your marketing strategies and enhance campaign effectiveness. Perfect for professionals and students looking to understand the power of data analysis in advertising. for more details visit: https://bostoninstituteofanalytics.org/data-science-and-artificial-intelligence/
Techniques to optimize the pagerank algorithm usually fall in two categories. One is to try reducing the work per iteration, and the other is to try reducing the number of iterations. These goals are often at odds with one another. Skipping computation on vertices which have already converged has the potential to save iteration time. Skipping in-identical vertices, with the same in-links, helps reduce duplicate computations and thus could help reduce iteration time. Road networks often have chains which can be short-circuited before pagerank computation to improve performance. Final ranks of chain nodes can be easily calculated. This could reduce both the iteration time, and the number of iterations. If a graph has no dangling nodes, pagerank of each strongly connected component can be computed in topological order. This could help reduce the iteration time, no. of iterations, and also enable multi-iteration concurrency in pagerank computation. The combination of all of the above methods is the STICD algorithm. [sticd] For dynamic graphs, unchanged components whose ranks are unaffected can be skipped altogether.
2. STATISTICS
• Is a mathematical science pertaining to the
collection , presentation ,summarising ,analysis,
interpretation or explanation of data.
3. CENTRAL TENDENCY
• The tendency of the obseravtions to cluster round some central
value is known as central tendency
• are also called as averages.
• For any group of data ,that value is used to represent the whole set
of observations.
• It is used when to compare 2 or more minor set of observations.
4. • It is measured by
• ARITHMETIC MEAN
• MEDIAN
• MODE
• HARMONIC MEAN
• GEOMETRIC MEAN
Averages of position
Mathematical averages
5. ARITHMETIC MEAN
• It is the average of the data.
• It is obtained by summing up of all observations
by number of observations.
It is denoted by X.
6. • UNGROUPED DATA
• MEAN = SUM OF ALL OBSERVATIONS
NO: OF OBSERVATIONS
1 1 2
n
i
i n
X
X X X
X
n n
7. ????
• CALCULATE THE MEAN OF:
1.BP OF 8 INDIVIDUALS- 83, 75, 81, 79 .71 ,75 ,95 ,77
2. WEIGHT OF 5 INFANTS- 5,3,6,4,7
3.No of teeth erupted at 2yrs in 6 children
- 3 ,5 ,8 ,9 ,7 ,4
8. GROUPED DATA
• To find the Arithmetic Mean of 1,2,3,1,2,3,2.
• The arithmetic mean = 1+2+3+1+2+3+2/7 = 14/7 = 2
• In this case there are two 1's, three 2's and two 3’s.
• The number of times each number occurs is called its frequency.
X value Frequency ΣfX
1 2 1 * 2 = 2
2 3 2 * 3 = 6
3 2 3 * 2 = 6
9. • Step 1: Find Σf.
Σf = 7
• Step 2: Now, find ΣfX.
ΣfX = ((1*2)+(2*3)+(3*2)) = 14
Step 3: Now, Substitute in the above
formula
• Arithmetic mean = ΣfX / Σf = 14/7 = 2
10. • MERITS
• Simple To Calculate
• Easy To Understand
• Useful For Further Statistical Analysis
• Uses all information in the data
• DEMERITS
• Values of all items necessary for calculation
• May be ridiculous some times e.g. Average number of
children =4.76
• Influenced by extreme values
• Cannot be obtained for qualitative data.
11. MEDIAN
• It is the value of middle observation after placing the
observations in either ascending or descending order.
• Half the values lie above it and half below it.
12. • If n or N is odd, the median is the middle
number.
• If n or N is even, the median is the average
of the two middle numbers
13. Example 1: To find the median of 4,5,7,2,1 [ODD].
Step 1: Count the total numbers given.
There are 5 elements or numbers in the
distribution.
Step 2: Arrange the numbers in ascending order.
1,2,4,5,7
Step 3: The total elements in the distribution (5) is
odd.
The middle position can be calculated using the
formula. (n+1)/2
So the middle position is (5+1)/2 = 6/2 = 3
The number at 3rd position is = Median = 4
14. Example 2 : To find the median of 5,7,2,1,6,4.
step 1 : count the total numbers given.
there are 6 numbers in the distribution.
step 2 :arrange the numbers in ascending order.
1,2,4,5,6,7.
step 3 :the total numbers in the distribution is 6
(even).
so the average of two numbers which are respectively in
positions n/2 and (n/2)+1 will be the median of the given data.
Median = (2+1)/2 = 1.5.
15. Grouped series
simply divide the total observation by 2
If the number of observations is 200 then
median will be 100th observation.
If the number of observations is 201 then
median will be 101th observation
16. ADVANTAGES:
1.There will be only one median for a given
data set.
2 .It is unaffected by the extreme values.
DISADVANTAGES:
1.It doesn't take in to consideration all the
observations.
17. MODE
• A measure of central tendency
• Value that occurs most often
• Not affected by extreme values
• Used for either numerical or categorical data
PROPERTIES:
1. There could be more than one mode for a given data.
2. It is un affected by extreme values.
3. It does not use all the observations in the given data.
