Tag Archives: quantitative techniques
TRADITIONAL & MODERN METHODS OF MARKETING
Want to MASTER Derivatives? Watch This Now : Lecture II
Want to MASTER Derivatives? Watch This Now
Working strategy of unemployed white collared
Hi there , the unmployment rate increases due to excessive monopoly effect of few companies in india . The drastic ratio of unemployed youth is due to their unskilled bookish knowledge with no practical skill to be learnt with. Hyper rate is leading to depression in them . Let’s try to increase emplyment opportunities to them or make enterprenual skills in them , there should be proper export promotion activities and we should adopt chineses modal of development to enhance the opportunities of maximum exports as local agricultural and manufacturing industries have already boosted . The new strategy of export orientation must be launched to adjust the surplus labour by which economic development of the country will be done , thanks jatin
Dispersion : Quartile Deviation in Discrete Series
Quartile deviation is also known as the semi-interquartile range, is a measure of statistical dispersion. It indicates the spread of the middle 50% of a dataset. The quartile deviation is calculated using the first quartile (Q1) and the third quartile (Q3). The formula is:
Quartile Deviation=𝑄3−𝑄1/2
Coefficient of Quartile Deviation = 𝑄3−𝑄1/𝑄3+𝑄1
Here’s a step-by-step explanation:
Arrange Data: Organize the data set in ascending order.
Find Quartiles:
Q1 (First Quartile): The median of the lower half of the dataset (not including the median if the dataset has an odd number of observations).
Q3 (Third Quartile): The median of the upper half of the dataset (not including the median if the dataset has an odd number of observations).
Calculate Quartile Deviation: Subtract Q1 from Q3 and divide by 2.
The quartile deviation provides a robust measure of spread as it is not affected by extreme values or utliers. afterwards find coefficient of quartile deviation by formula QD = 𝑄3−𝑄1/𝑄3+𝑄1 you can watch the video for practical solution of this in various type of series like Individual Series , Discrete Series and Continuous Series. Here in this lecture you will find the Practical Solution in Discrete Series , kindly check the link here and do Subscribe to the channel :
Thanks a Lot
jatin
Quartile Deviation in Dispersion Individual Series
Quartile deviation is also known as the semi-interquartile range, is a measure of statistical dispersion. It indicates the spread of the middle 50% of a dataset. The quartile deviation is calculated using the first quartile (Q1) and the third quartile (Q3). The formula is:
Quartile Deviation=𝑄3−𝑄1/2
Coefficient of Quartile Deviation = 𝑄3−𝑄1/𝑄3+𝑄1
Here’s a step-by-step explanation:
Arrange Data: Organize the data set in ascending order.
Find Quartiles:
Q1 (First Quartile): The median of the lower half of the dataset (not including the median if the dataset has an odd number of observations).
Q3 (Third Quartile): The median of the upper half of the dataset (not including the median if the dataset has an odd number of observations).
Calculate Quartile Deviation: Subtract Q1 from Q3 and divide by 2.
The quartile deviation provides a robust measure of spread as it is not affected by extreme values or utliers. afterwards find coefficient of quartile deviation by formula QD = 𝑄3−𝑄1/𝑄3+𝑄1 you can watch the video for practical solution of this in various type of series like Individual Series , Discrete Series and Continuous Series. Here in this lecture you will find the Practical Solution in Individual Series , kindly check the link here and do Subscribe to the channel :
Thanks
Jatin
Statistical Analysis Practical Solutions for Various Topics
Multiplication of Matrices
Matrix multiplication is a binary operation that produces a new matrix from two matrices. Unlike addition and subtraction, the dimensions of the matrices involved in multiplication determine the possibility and the result of the operation. Matrix Multiplication involves two major conditions practically for finding AB where A assumes first matrix and B as Second matrix.
1.The no. of columns of first matrix should be equal to the no. of rows of second matrix only then multiplication is possible . if they are not equal then multiplication is not possible.
2. Multiply first row of first matrix with first column of second matrix then first row of first matrix with second column of second matrix then first row of first matrix with third column of second matrix then second row of first matrix with first column of second matrix and so on till the no. of row of first matrix and no. of column of second matrix.
Kindly check the link for practical solution of this method :
Matrix multiplication is a fundamental operation in linear algebra, widely used in various fields such as computer graphics, physics, economics, and statistics. Understanding its definition, properties, and application is crucial for effectively utilizing matrices in mathematical and applied contexts.
Addition & Subtraction of Matrices
A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The numbers in a matrix are called its elements or entries. A matrix with mmm rows and nnn columns is called an m×nm \times nm×n matrix, read as “m by n matrix”.
Addition of Matrices : Matrix addition is a binary operation that takes two matrices of the same dimensions and produces another matrix of the same dimensions, where each element of the resulting matrix is the sum of the corresponding elements of the input matrices.
Subtraction of Matrices : Matrix subtraction is a binary operation that takes two matrices of the same dimensions and produces another matrix of the same dimensions, where each element of the resulting matrix is the difference of the corresponding elements of the input matrices.
Kindly check the link for practical implication of these methods :
How to Solve Crammer’s Rule of Matrix
Cramer’s rule is a mathematical theorem used to solve a system of linear equations with as many equations as unknowns, provided that the system has a unique solution. It is applicable to systems of linear equations represented in matrix form. The rule is named after Gabriel Cramer, an 18th-century Swiss mathematician.
Kindly check the link for practical solution of Cramar’s Rule.
Probable Error & Standard Error in Coefficient of Correlation
In statistics, the “standard error of the correlation coefficient” measures the accuracy of the estimated correlation coefficient. It indicates how much the observed correlation coefficient may vary if the study were repeated multiple times.Whereas The probable error (PE) of the correlation coefficient is another measure of the accuracy of the estimated correlation. It provides Kindly see the practical solution of these formulas via link :
Probable Error can be calculated as:
𝑃𝐸=0.6745×𝑆𝐸𝑟
Here, 0.6745 is a constant derived from the normal distribution.
Both SE_r and PE are useful in assessing the reliability of the estimated correlation coefficient. If the PE is large relative to the correlation coefficient, it suggests that the observed correlation might not be very reliable due to sampling variability.
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Factor Reversibility Test : Test of Adequacy in Index Numbers
The “Factor Reversibility Test” and the “Index Number Test of Adequacy” are both methods used in econometrics and statistics to assess the validity and reliability of certain statistical models, particularly those related to index numbers and factor analysis.
Factor Reversibility Test: it can be solved by practical ways . kindly Check the link
In factor analysis, the factor reversibility test is used to determine the number of factors to retain in the analysis. The basic idea is to assess whether rotating the factors back to the original variables reproduces the original correlation matrix well. If the factors are correctly identified, the correlation matrix should be reproduced accurately. Deviations from this can indicate that too few or too many factors have been retained.
Index Number Test of Adequacy
Index numbers are used to represent changes in a set of related variables over time. The index number test of adequacy assesses whether the chosen index formula adequately represents the underlying relationships between the variables it’s supposed to measure. It usually involves comparing the calculated index numbers with some benchmark or theoretical expectations. The test checks if the index reflects the intended changes accurately and if it is free from significant biases or distortions.
Both tests are crucial for ensuring the reliability and validity of statistical models and indices used in various fields, including economics, finance, and social sciences.
Time Reversibility Test (TRT) Index Numbers
“Test of Adequacy TRT in Index Number” likely refers to a statistical evaluation specifically aimed at assessing the adequacy of a Time Reversibility Test (TRT) in the context of index numbers.
This can be solved in practical easy way for this kindly check the link for practical solution:
In this context, the Time Reversibility Test (TRT) could be a statistical test used to examine whether a time series or a set of data can be reversed in time without losing information.
The “Test of Adequacy” would then involve examining whether this Time Reversibility Test is appropriate or sufficient for assessing the properties or characteristics of an index number. This could involve evaluating how well the TRT captures the essential features or dynamics of the index number, such as its trend, seasonality, volatility, or other patterns.
Typically, such a test would involve statistical analysis to determine whether the TRT effectively detects any inherent time reversibility in the index number data. This might include conducting hypothesis tests, assessing the statistical significance of the results, and potentially comparing the performance of the TRT against alternative methods or benchmarks.
In summary, the “Test of Adequacy TRT in Index Number” would likely involve evaluating the suitability and effectiveness of a Time Reversibility Test in analyzing index number data, ensuring that it provides meaningful insights into the temporal behavior of the index series.
Binomial Expansion Method of Interpolation (Two Values Missing )
The binomial method of interpolation, also known as binomial interpolation, is used to estimate missing values within a sequence of values. This method utilizes the concept of finite differences and binomial coefficients. To demonstrate the process, let’s go through the steps required to interpolate Two missing values using the binomial method.
Steps for Binomial Interpolation with Two Missing Values
Define the Sequence: Let’s consider a sequence with Two missing values.like Y0, Y1, Y2 , Y3, Y4………….Ym Out of which Two values are missing Use PASCAL TRIANGLE and apply it with checking the value which is missing. And Solve the sum accordingly .
Let’s do it with practical example
MEDIAN in Measures of Central Tendency
MEDIAN IN MEASURES OF CENTRAL TENDENCY
The median is a statistical measure that identifies the middle value in a data set when the numbers are arranged in numerical order. It effectively divides the data set into two equal halves, with half of the values lying below the median and half above it.
- Odd Number of Observations: If a data set contains an odd number of values, the median is the value that lies exactly in the middle of the sorted data set.
- Even Number of Observations: If a data set contains an even number of values, the median is the average of the two middle values in the sorted data set.
There are three type of Series I which Median can be calculated like Individual Series , Discrete Series & Continuous Series.
Kindly Check the link for Practical Solution of this formula :
Median in individual series
In statistics, an individual series refers to a data set where values are listed individually without any frequency distribution.
Median in discrete series
In a discrete series, data are presented along with their corresponding frequencies. To calculate the median in a discrete series, the data set is first arranged in ascending order, and then cumulative frequencies are calculated to determine the median class.
Median in Continuous series
In continuous series, data is grouped into class intervals with their corresponding frequencies. Calculating the median in a continuous series involves identifying the median class and then applying a formula to find the precise median value.
Median in Different Contexts
- Descriptive Statistics: The median is commonly used to summarize the central tendency of a data set.
- Economics: Median income is often reported to understand the income distribution of a population without the distortion caused by very high incomes.
- Real Estate: Median home prices give a better sense of typical property values compared to average prices, which can be skewed by very expensive homes.
Hope you enjoyed the topic.
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How to Find Mode in Measures of Central Tendency
MODE IN MEASURES OF CENTRAL TENDENCY
In measures of central tendency, “mode” refers to the value that appears most frequently in a dataset. Unlike mean and median, which focus on the average and middle value respectively, mode highlights the most common occurrence. It’s particularly useful in categorical data or when dealing with data where certain values occur with higher frequency than others. For example, in the dataset {1, 2, 2, 3, 4, 4, 4, 5}, the mode is 4 because it appears more frequently than any other number. In some cases, a dataset may have multiple modes (bimodal, trimodal, etc.) if two or more values occur with the same highest frequency.
In an individual series (also known as raw data series), where each observation is unique, finding the mode is straightforward. You simply identify the value that occurs most frequently in the dataset.
Here’s how to find the mode in an individual series:
- Count Frequencies: Count the frequency (number of occurrences) of each distinct value in the dataset.
- Identify the Mode: The mode is the value that appears with the highest frequency.
Let’s go through an example:
Suppose you have the following individual series: 5,7,9,7,2,4,7,5,9,3,7,55, 7, 9, 7, 2, 4, 7, 5, 9, 3, 7, 55,7,9,7,2,4,7,5,9,3,7,5
1. Count the frequency of each distinct value:
- Value 2 occurs once.
- Value 3 occurs once.
- Value 4 occurs once.
- Value 5 occurs three times.
- Value 7 occurs four times.
- Value 9 occurs twice.
2. Identify the mode: The value that occurs with the highest frequency is 7 (which occurs four times), so the mode of this dataset is 7.
So, in this example, the mode is 7.
To find the mode in a discrete series (a set of data with distinct values), you can follow these steps:
- Organize Data: Arrange your data in ascending or descending order to make it easier to identify repeated values.
- Count Frequencies: Count the frequency (number of times each value appears) for each distinct value in the dataset.
- Identify the Mode: The mode is the value that occurs with the highest frequency. It’s the value that appears most frequently in the dataset.
Here’s a step-by-step example:
Let’s say you have the following dataset: 3,4,5,5,6,6,6,7,8,8,8,83, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8, 83,4,5,5,6,6,6,7,8,8,8,8
- Organize the data in ascending order: 3,4,5,5,6,6,6,7,8,8,8,83, 4, 5, 5, 6, 6, 6, 7, 8, 8, 8, 83,4,5,5,6,6,6,7,8,8,8,8
- Count the frequency of each distinct value: 3:1,4:1,5:2,6:3,7:1,8:43: 1, 4: 1, 5: 2, 6: 3, 7: 1, 8: 43:1,4:1,5:2,6:3,7:1,8:4
- Identify the mode: The value with the highest frequency is 8, which appears 4 times. So, the mode of this dataset is 8.
If there are multiple values with the same highest frequency, then the dataset is said to be multimodal, and it has multiple modes. If all values occur with the same frequency, then the dataset is said to be uniform or there is no mode.
In continuous series (where data is presented as intervals or ranges rather than individual values), finding the mode involves determining the interval with the highest frequency density.
Here’s how you can find the mode in a continuous series:
- Group Data: If not already grouped, create intervals or classes for the continuous data. Each interval should be mutually exclusive and collectively exhaustive, covering the entire range of the data.
- Count Frequencies: Count the frequency of data points falling within each interval.
- Identify the Modal Interval: Determine which interval has the highest frequency density. Frequency density is calculated by dividing the frequency of each interval by its width (the difference between the upper and lower limits of the interval).
- Estimate Mode: Once you’ve identified the modal interval, you can estimate the mode within that interval. This is usually done by assuming a uniform distribution within the interval and finding the midpoint of the modal interval.
Here the formula to calculate Mode in practical form . kindly check the link for this :
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