2024 The concept of perceielts

Introduction. Other measures of location. Quartiles – for discrete data and continuous data. Deciles and percentiles. 1. Introduction. In section 2.1, we learnt how to find the three most common averages for a set of data – namely, the mode, the median and the mean. They are measures of central tendency which indicate the overall location .... Embryonic and fetal development

Basic concepts of perception and communication. Perception is the conscious reception, selection, processing and interpretation of information by our brain via all senses. Perception is also used to describe what is perceived. Communication can be several things. Regarding the process, communication is the reception, exchange, and transmission ...Example. Let us make an example. Let be a discrete random variable with support and probability mass function. The distribution function of is. Suppose that we want to compute the -quantile for . There is no such that. However, the smallest such that is because for and for . Thus, we have.Example question: Find out where the 25th percentile is in the above list. Step 1: Calculate what rank is at the 25th percentile. Use the following formula: Rank = Percentile / 100 * (number of items + 1) Rank = 25 / 100 * (8 + 1) = 0.25 * 9 = 2.25. A rank of 2.25 is at the 25th percentile. 3. Use the QUARTILE function shown below to calculate the 1st quartile. Excel returns the value 11.25. This means that 25% (5 out of 20) of the scores are lower or equal to 11.25. Note: The second argument of the QUARTILE function must be a number between 0 and 4. PERCENTILE (A1:A20,0.25) gives the exact same result. Boehm Test of Basic Concepts Third Edition helps evaluate basic concepts essential for school success. Boehm-3 is based on research that identified the 50 basic concepts most frequently used by teachers in kindergarten, first, and second grade classrooms. Dec 10, 2020 · This week, we will bust another myth – market percentiles. Users of salary surveys are accustomed to referring to the market data in terms of a percentile. The most common percentile of reference is the median average or 50 th percentile. Simply stated, the 50 th percentile of an array of values is the point where there are equal numbers of ... 14.2.1 Concepts Related to Probability Probability is a statistical concept which can be measured and analysed. Due to its much scientific applications, there are certain related concepts which you need to know. These concepts are: 1) Sample Space, Events and Power Set: The collection or set of all 3. Use the QUARTILE function shown below to calculate the 1st quartile. Excel returns the value 11.25. This means that 25% (5 out of 20) of the scores are lower or equal to 11.25. Note: The second argument of the QUARTILE function must be a number between 0 and 4. PERCENTILE (A1:A20,0.25) gives the exact same result. z=\dfrac {x-\mu} {\sigma} z = σx−μ x x represents an observed score, also known as a “raw score.”. As previously mentioned, \mu μ represents the mean and \sigma σ represents the standard deviation. To calculate a z-score, we simply subtract the mean from a raw score and then divide by the standard deviation.The first box plot tells the percentile values of the sepal length feature for three different ranges of iris flowers. 25ᵗʰ, 50ᵗʰ, 75ᵗʰ percentile values for Setosa flower when sepal length is taken as a feature are 4.8, 5, 5.25 (approx). When petal length is considered as the feature, 25ᵗʰ, 50ᵗʰ, 75ᵗʰ percentile values for ...A better measure of central tendency would be the median (15) or the mean (also 15) in this case. The mode is also a poor measure of central tendency when it happens to be a number that is far away from the rest of the values. For example, the mode of the following dataset is 30, but this doesn’t actually represent the “typical” number of ...11 data science statistics concepts. Here is a list of statistical concepts a data scientist might find useful: 1. Probability distribution. Probability distribution is a statistical concept that seeks to gauge the chances of something happening. For example, probability distribution estimates the chances that a team in a sport might make the ...Apr 21, 2021 · First, we go the Z table and find the probability closest to 0.90 and determine what the corresponding Z score is. For any normal distribution a probability of 90% corresponds to a Z score of about 1.28. We also could have computed this using R by using the qnorm () function to find the Z score corresponding to a 90 percent probability. Dec 10, 2020 · This week, we will bust another myth – market percentiles. Users of salary surveys are accustomed to referring to the market data in terms of a percentile. The most common percentile of reference is the median average or 50 th percentile. Simply stated, the 50 th percentile of an array of values is the point where there are equal numbers of ... percentile = (number of ranks below x/total number of ranks) X 100. For example, in the table above, the number 58 with a rank = 6. Number of ranks below 58 = 5, total number of ranks = 50. The percentile for 58 = (5/50)X 100 = 10th. Using that formula, we can calculate the percentiles for all numbers in our data.Answer (1 of 7): Percentiles are a great tool to use when you need to know the relative standing of a value. Where does a value fall within a distribution of values?Start your trial now! First week only $4.99! arrow_forward Literature guides Concept explainers Writing guide Popular textbooks Popular high school textbooks Popular Q&A Business Accounting Business Law Economics Finance Leadership Management Marketing Operations Management Engineering AI and Machine Learning Bioengineering Chemical Engineering Civil Engineering Computer Engineering Computer ...Aug 31, 2017 · Percentage. Percentages are part of our everyday lives, from calculating how much to tip to determining your bank account’s interest. In simplest terms, a percentage is a number expressed as a fraction of 100. It is also uniquely signified with the use of a percent sign (%). A simple example might be a candidate’s score on a pre-employment ... An integrated diagnosis with multiple modalities appears a promising concept but requires further development and testing. Many basic issues in assessing fetal growth have yet to be addressed, such as whether fetuses of different race/ethnic groups have a similar growth pattern; how fast a normal fetus is supposed to grow at different stages of ...14.2.1 Concepts Related to Probability Probability is a statistical concept which can be measured and analysed. Due to its much scientific applications, there are certain related concepts which you need to know. These concepts are: 1) Sample Space, Events and Power Set: The collection or set of allBenefits of lifelong learning. Incorporating lifelong learning in your life can offer many long-term benefits, including: 1. Renewed self-motivation. Sometimes we get stuck in a rut doing things simply because we have to do them, like going to work or cleaning the house. Figuring out what inspires you puts you back in the driver’s seat and is ...Benefits of lifelong learning. Incorporating lifelong learning in your life can offer many long-term benefits, including: 1. Renewed self-motivation. Sometimes we get stuck in a rut doing things simply because we have to do them, like going to work or cleaning the house. Figuring out what inspires you puts you back in the driver’s seat and is ...Oct 21, 2022 · Your child’s test scores are only one part of the evaluation results. Your child is going through the evaluation process. Once the testing is done, you’ll get a report explaining the scores. The results of evaluation testing are presented statistically. So, when you get the report, you may see language you’re not familiar with. The concept of skewness is baked into our way of thinking. When we look at a visualization, our minds intuitively discern the pattern in that chart, whether we are data scientists or beginners working on a python dataset. As you might already know, India has more than 50% of its population below the age of 25 and more than 65% below the age of 35.May 21, 2012 · The score that is one standard deviation is higher than the 34% between the mean and one standard deviation above the mean, as well as than the 50% below the mean. That means, a score that lies one standard deviation above the mean is the 50 + 34 = 84th percentile. Thus, it’s higher than a score in the 80th percentile. Answer = A. Skewness is a measure of asymmetry or distortion of symmetric distribution. It measures the deviation of the given distribution of a random variable from a symmetric distribution, such as normal distribution. A normal distribution is without any skewness, as it is symmetrical on both sides. Hence, a curve is regarded as skewed if it is shifted ... Pages 118 ; Ratings 50% (4) 2 out of 4 people found this document helpful; This preview shows page 91 - 94 out of 118 pages.preview shows page 91 - 94 out of 118 Concept mapping is a technique for visualizing relationships among different concepts. A concept map is a diagram showing the relationships among concepts. In particular, constructivists hold that learners actively construct knowledge. Concepts are connected with labeled arrows, in a downward-branching hierarchical structure. Bell Curve: A bell curve is the most common type of distribution for a variable, and due to this fact, it is known as a normal distribution. The term "bell curve" comes from the fact that the ...Mar 18, 2005 · In contemporary philosophy, the phrase ‘the contents of perception’ means, roughly, what is conveyed to the subject by her perceptual experience. For example, suppose you are looking into a piano at the array of hammers and strings. Example question: Find out where the 25th percentile is in the above list. Step 1: Calculate what rank is at the 25th percentile. Use the following formula: Rank = Percentile / 100 * (number of items + 1) Rank = 25 / 100 * (8 + 1) = 0.25 * 9 = 2.25. A rank of 2.25 is at the 25th percentile. Mar 10, 2023 · Range is one of the simplest measures of variation. It's the lowest point of data subtracted from the highest point of data. For example, if your highest point is 10 and your lowest point is three, your range would be seven. The range tells you a general idea of how widely spread your data is. Because range is so simple and only uses two pieces ... Quartiles, Deciles and Percentiles. Quartiles, Deciles and Percentiles Let us now extend the concept of partitioning of the frequency distribution by taking up the concept of quantiles (i.e. quartiles, deciles and percentiles) We have already seen that the median divides the area under the frequency polygon into two equal halves:Aug 23, 2023 · percentile: [noun] a value on a scale of 100 that indicates the percent of a distribution that is equal to or below it. Apr 21, 2021 · First, we go the Z table and find the probability closest to 0.90 and determine what the corresponding Z score is. For any normal distribution a probability of 90% corresponds to a Z score of about 1.28. We also could have computed this using R by using the qnorm () function to find the Z score corresponding to a 90 percent probability. There are two steps to follow: Find the location of the desired quartile. If there are n observations, arranged in increasing order, then the first quartile is at position n + 1 4, second quartile (i.e. the median) is at position 2 ( n + 1) 4, and the third quartile is at position 3 ( n + 1) 4. Find the value in that position for the ordered data. Mar 18, 2005 · In contemporary philosophy, the phrase ‘the contents of perception’ means, roughly, what is conveyed to the subject by her perceptual experience. For example, suppose you are looking into a piano at the array of hammers and strings. First, we go the Z table and find the probability closest to 0.90 and determine what the corresponding Z score is. For any normal distribution a probability of 90% corresponds to a Z score of about 1.28. We also could have computed this using R by using the qnorm () function to find the Z score corresponding to a 90 percent probability.A z-score measures the distance between a data point and the mean using standard deviations. Z-scores can be positive or negative. The sign tells you whether the observation is above or below the mean. For example, a z-score of +2 indicates that the data point falls two standard deviations above the mean, while a -2 signifies it is two standard ...Pages 118 ; Ratings 50% (4) 2 out of 4 people found this document helpful; This preview shows page 91 - 94 out of 118 pages.preview shows page 91 - 94 out of 118See full list on thoughtco.com Percentiles In this lesson: 1. Definition of a percentile and an interpercentile range. 2. Applications of a percentiles. 3. Calculating percentiles and interpercentile range.The values which divide an array (a set of data arranged in ascending or descending order) into four equal parts are called Quartiles. The first, second and third quartiles are denoted by Q1, Q2,Q3 respectively. The first and third quartiles are also called the lower and upper quartiles respectively. The second quartile represents the median ...When used properly, they accurately gather data for educators and administrators. Some standard measurements in education are raw scores, percentile ranks and standard scores. Assessment. One of the primary measurement tools in education is the assessment. Teachers gather information by giving tests, conducting interviews and monitoring behavior.also developed: Concepts & Applications, a standards-based measure of higher-order thinking skills and concepts. For Reading (Grades 2–8), minor revisions were made to improve the content and interest level of the Oral Reading Fluency stories. Moreover, two new measures were developed to assess vocabulary An integrated diagnosis with multiple modalities appears a promising concept but requires further development and testing. Many basic issues in assessing fetal growth have yet to be addressed, such as whether fetuses of different race/ethnic groups have a similar growth pattern; how fast a normal fetus is supposed to grow at different stages of ...Measures of Variability. Range, Inter-Quartile Range, Variance, Standard Deviation, Variance, Coefficient of Variation. Variance. Measure of variability that utilizes data. It is based on the difference between the value. of each observation (xi) and the mean x bar. Measures of Central Tendency/Location. Tendency of individual observations to ...In this chapter, we rst describe the concepts and application of percentiles and Z -scores in anthropometry and compare their limitations and strengths. Next, we address two important issues: the selection of anthropometric measure cut points and the statistical methods and techniques for growth curve tting and smoothing. 3. Use the QUARTILE function shown below to calculate the 1st quartile. Excel returns the value 11.25. This means that 25% (5 out of 20) of the scores are lower or equal to 11.25. Note: The second argument of the QUARTILE function must be a number between 0 and 4. PERCENTILE (A1:A20,0.25) gives the exact same result. Mar 1, 2019 · November 1965 Parliamentary Affairs. If L is a Levy process and (Tt)t ≥ 0 is a positive increasing process, Xt = L (Tt) is called a time-changed Levy process with time change (Tt)t ≥ 0. When ... Mar 1, 2022 · z=\dfrac {x-\mu} {\sigma} z = σx−μ x x represents an observed score, also known as a “raw score.”. As previously mentioned, \mu μ represents the mean and \sigma σ represents the standard deviation. To calculate a z-score, we simply subtract the mean from a raw score and then divide by the standard deviation. Jun 17, 2023 · Benefits of lifelong learning. Incorporating lifelong learning in your life can offer many long-term benefits, including: 1. Renewed self-motivation. Sometimes we get stuck in a rut doing things simply because we have to do them, like going to work or cleaning the house. Figuring out what inspires you puts you back in the driver’s seat and is ... percentile definition: 1. one of the points into which a large range of numbers, results, etc. is divided to make 100…. Learn more.Look, it's just gonna be 0.5 repeating. So 55.5555%. So either of these would actually be a legitimate response to the percentile rank for the driver with the daily driving time of six hours. It depends on whether you include the six hours or not. So you could say either the 50th percentile or roughly the 55th, or actually the 56th percentile ...1. a [count] : the way you think about or understand someone or something — often + of. People's perceptions of this town have changed radically. the public/public's perception of nuclear power. — see also self-perception. b [noncount] somewhat formal : the ability to understand or notice something easily. She shows remarkable perception. IQ stands for intelligence quotient. Supposedly, it is a score that tells one how “bright” a person is compared to others. The average IQ is, by definition, 100; scores above 100 indicate a higher-than-average IQ, and scores below 100 indicate a lower-than-average IQ. Theoretically, scores can range from any number below or above 100.Example question: Find out where the 25th percentile is in the above list. Step 1: Calculate what rank is at the 25th percentile. Use the following formula: Rank = Percentile / 100 * (number of items + 1) Rank = 25 / 100 * (8 + 1) = 0.25 * 9 = 2.25. A rank of 2.25 is at the 25th percentile.Sep 1, 2023 · perception, in humans, the process whereby sensory stimulation is translated into organized experience. That experience, or percept, is the joint product of the stimulation and of the process itself. Concept mapping is a technique for visualizing relationships among different concepts. A concept map is a diagram showing the relationships among concepts. In particular, constructivists hold that learners actively construct knowledge. Concepts are connected with labeled arrows, in a downward-branching hierarchical structure.Estimation of percentiles. Percentiles can be estimated from N measurements as follows: for the p th percentile, set p(N + 1) equal to k + d for k an integer, and d , a fraction greater than or equal to 0 and less than 1. For 0 < k < N, Y(p) =Y[k] + d(Y[k+1] − Y[k])Measures of Variability. Range, Inter-Quartile Range, Variance, Standard Deviation, Variance, Coefficient of Variation. Variance. Measure of variability that utilizes data. It is based on the difference between the value. of each observation (xi) and the mean x bar. Measures of Central Tendency/Location. Tendency of individual observations to ...Percentiles In this lesson: 1. Definition of a percentile and an interpercentile range. 2. Applications of a percentiles. 3. Calculating percentiles and interpercentile range. Sep 18, 2018 · A better measure of central tendency would be the median (15) or the mean (also 15) in this case. The mode is also a poor measure of central tendency when it happens to be a number that is far away from the rest of the values. For example, the mode of the following dataset is 30, but this doesn’t actually represent the “typical” number of ... Anthropometry and Workspace Design DEA 3250/6510 Professor Alan Hedge Normal Man? Cranfield Man! cIdeal operator for lathe controls should be 4.5' (1.37m) tall, 2' (0.61m) across shoulders, and 8' (2.35m) arm span!Apr 14, 2020 · The first box plot tells the percentile values of the sepal length feature for three different ranges of iris flowers. 25ᵗʰ, 50ᵗʰ, 75ᵗʰ percentile values for Setosa flower when sepal length is taken as a feature are 4.8, 5, 5.25 (approx). When petal length is considered as the feature, 25ᵗʰ, 50ᵗʰ, 75ᵗʰ percentile values for ... Definition and meaning. Percentile or centile is a value or number that represents a percentage position on a range or list of data – the person or thing at that number of value is above that number in percentage. For example, if the exam results of schoolchildren at a specified school in a nationwide study is at the 65th percentile, it means ...The formula for finding the interquartile range takes the third quartile value and subtracts the first quartile value. IQR = Q3 – Q1. Equivalently, the interquartile range is the region between the 75th and 25th percentile (75 – 25 = 50% of the data). Using the IQR formula, we need to find the values for Q3 and Q1.Range is one of the simplest measures of variation. It's the lowest point of data subtracted from the highest point of data. For example, if your highest point is 10 and your lowest point is three, your range would be seven. The range tells you a general idea of how widely spread your data is. Because range is so simple and only uses two pieces ...4.2 - The Normal Curve. Many measurement variables found in nature follow a predictable pattern. The predictable pattern of interest is a type of symmetry where much of the distribution of the data is clumped around the center and few observations are found on the extremes. Data that has this pattern are said to be bell-shaped or have a normal ...Pages 118 ; Ratings 50% (4) 2 out of 4 people found this document helpful; This preview shows page 91 - 94 out of 118 pages.preview shows page 91 - 94 out of 118Collectively, the quartiles, deciles and percentiles and other values obtained by equal sub-division. of the data are called Quartiles. Quartiles: The values which divide an array (a set of data arranged in ascending or descending order) into four equal parts are called Quartiles. The first, second and third quartiles are denoted by.One way to think of this concept is that sensation is a physical process, whereas perception is psychological. For example, upon walking into a kitchen and smelling the scent of baking cinnamon rolls, the sensation is the scent receptors detecting the odor of cinnamon, but the perception may be “Mmm, this smells like the bread Grandma used to ...Percentile definition: one of 99 actual or notional values of a variable dividing its distribution into 100... | Meaning, pronunciation, translations and examplesThe concept of skewness is baked into our way of thinking. When we look at a visualization, our minds intuitively discern the pattern in that chart, whether we are data scientists or beginners working on a python dataset. As you might already know, India has more than 50% of its population below the age of 25 and more than 65% below the age of 35.Imagine you have the marks of 20 students. Now, try to calculate the 90th percentile. Step 1: Arrange the score in ascending order. Step 2: Plug the values in the formula to find n. P90 = 94 means that 90% of students got less than 94 and 10% of students got more than 94. Let’s look at another way how you can find the percentile in statistics.The entry in the row and column for z = 1.56 is the area under the distribution to the left of the score. This is often expressed in the form of a probability: P ( z ≤ 1.56) = 0.9406. The ...W3Schools offers free online tutorials, references and exercises in all the major languages of the web. Covering popular subjects like HTML, CSS, JavaScript, Python, SQL, Java, and many, many more. Example: You are the fourth tallest person in a group of 20. 80% of people are shorter than you: That means you are at the 80th percentile.. If your height is 1.85m then "1.85m" is the 80th percentile height in that group.1. a [count] : the way you think about or understand someone or something — often + of. People's perceptions of this town have changed radically. the public/public's perception of nuclear power. — see also self-perception. b [noncount] somewhat formal : the ability to understand or notice something easily. She shows remarkable perception. A quartile is a type of quantile. Quantiles are values that split sorted data or a probability distribution into equal parts. In general terms, a q -quantile divides sorted data into q parts. The most commonly used quantiles have special names: Quartiles (4-quantiles): Three quartiles split the data into four parts.Aug 31, 2023 · The following are the steps to calculate the kth percentile (where k is any number between zero and one hundred). Step 1: Arrange all data values in the data set in ascending order. Step 2: Count the number of values in the data set where it is represented as 'n'. Step 3: calculate the value of k/100, where k = any number between zero and one ...

14.2.1 Concepts Related to Probability Probability is a statistical concept which can be measured and analysed. Due to its much scientific applications, there are certain related concepts which you need to know. These concepts are: 1) Sample Space, Events and Power Set: The collection or set of all. Bay windows at lowe

Mar 7, 2022 · Bell Curve: A bell curve is the most common type of distribution for a variable, and due to this fact, it is known as a normal distribution. The term "bell curve" comes from the fact that the ... Anthropometrics and Design. 1. Design Limitations a. Myth of designing for the "average" person - since there are no people whose body dimensions are all at the 50th percentile. Body dimensions aren't linearly correlated so people with short arms don't necessarily have short legs, etc. While the use of the 5th and 95th percentiles on one body ...Pages 118 ; Ratings 50% (4) 2 out of 4 people found this document helpful; This preview shows page 91 - 94 out of 118 pages.preview shows page 91 - 94 out of 118z=\dfrac {x-\mu} {\sigma} z = σx−μ x x represents an observed score, also known as a “raw score.”. As previously mentioned, \mu μ represents the mean and \sigma σ represents the standard deviation. To calculate a z-score, we simply subtract the mean from a raw score and then divide by the standard deviation.Quantiles. A further generalization is to note that our order statistics are splitting the distribution that we are working with. The median splits the data set in half, and the median, or 50th percentile of a continuous distribution splits the distribution in half in terms of area. The first quartile, median and third quartile partition our ...Estimation of percentiles. Percentiles can be estimated from N measurements as follows: for the p th percentile, set p(N + 1) equal to k + d for k an integer, and d , a fraction greater than or equal to 0 and less than 1. For 0 < k < N, Y(p) =Y[k] + d(Y[k+1] − Y[k]) Percentiles: Interpretations and Calculations. By Jim Frost 59 Comments. Percentiles indicate the percentage of scores that fall below a particular value. They tell you where a score stands relative to other scores. For example, a person with an IQ of 120 is at the 91 st percentile, which indicates that their IQ is higher than 91 percent of ...Jun 25, 2021 · The values which divide an array (a set of data arranged in ascending or descending order) into four equal parts are called Quartiles. The first, second and third quartiles are denoted by Q1, Q2,Q3 respectively. The first and third quartiles are also called the lower and upper quartiles respectively. The second quartile represents the median ... There are two steps to follow: Find the location of the desired quartile. If there are n observations, arranged in increasing order, then the first quartile is at position n + 1 4, second quartile (i.e. the median) is at position 2 ( n + 1) 4, and the third quartile is at position 3 ( n + 1) 4. Find the value in that position for the ordered data.Concept 7: Measures of Dispersion. Range is the difference between the maximum and minimum values in a data set. The annual returns of a portfolio manager for the past 4 years are 4%, 2%, 6%, 8%. Calculate the range. Mean absolute deviation (MAD) is the average of the absolute values of deviations from the mean.The data in the online ranking can help you identify your stronger and weaker points in terms of conditioning. For example, if you rank in the top quartile for the 1 hour piece and the bottom quartile for 500 meters, that suggests you have good endurance but are lacking in power. You can then adopt a training plan to improve your weakness.Range is one of the simplest measures of variation. It's the lowest point of data subtracted from the highest point of data. For example, if your highest point is 10 and your lowest point is three, your range would be seven. The range tells you a general idea of how widely spread your data is. Because range is so simple and only uses two pieces ...percentile definition: 1. one of the points into which a large range of numbers, results, etc. is divided to make 100…. Learn more.lems, we hope this reference helps to clarify some of the concepts and methodologies used in our process. It is our goal to provide a better un-derstanding of how the science of Ergonomics is used to make products that help employees work more comfortably, efﬁ ciently, and effectively.P = (nth percentile/100) × Total number of values in the list. Here, n = Ordinal rank of the given value or value below the number. N = Number of values in the data set. P = Percentile. Rank = Percentile/100. Ordinal rank for Percentile value = Rank × Total number of values in the list.Percentiles In this lesson: 1. Definition of a percentile and an interpercentile range. 2. Applications of a percentiles. 3. Calculating percentiles and interpercentile range.4.2 - The Normal Curve. Many measurement variables found in nature follow a predictable pattern. The predictable pattern of interest is a type of symmetry where much of the distribution of the data is clumped around the center and few observations are found on the extremes. Data that has this pattern are said to be bell-shaped or have a normal ... Basic Statistics. When performing statistical analysis on a set of data, the mean, median, mode, and standard deviation are all helpful values to calculate.There are two steps to follow: Find the location of the desired quartile. If there are n observations, arranged in increasing order, then the first quartile is at position n + 1 4, second quartile (i.e. the median) is at position 2 ( n + 1) 4, and the third quartile is at position 3 ( n + 1) 4. Find the value in that position for the ordered data.Example. Let us make an example. Let be a discrete random variable with support and probability mass function. The distribution function of is. Suppose that we want to compute the -quantile for . There is no such that. However, the smallest such that is because for and for . Thus, we have..

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