Empirical relation(mean, median and mode)
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This document provides information about the relationship between the mean, median, and mode of a moderately skewed distribution. It states that for a moderately skewed distribution, the difference between the mean and mode is equal to three times the difference between the mean and median. This relationship is represented by the formula: Mean – Mode = 3(Mean – Median). The document provides three examples of using this formula to calculate the missing statistical measure when given the other two. It concludes by providing three practice problems for the reader to solve on their own.
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This document discusses the relationship between mean, median, and mode for different types of distributions. It provides formulas for relating these measures in moderately skewed distributions. An example is given of a symmetrical distribution where the mean, median, and mode are equal. The distribution's frequencies are used to calculate each measure and confirm the distribution is symmetrical since all three values are the same.
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This document discusses the empirical relationship between the mean, median, and mode of a distribution. It states that if the mean, median, and mode are equal, the distribution is symmetrical. If they differ, the distribution is skewed. For a positively skewed distribution, the mode is less than the median, which is less than the mean. For a negatively skewed distribution, the mode is greater than the median, which is greater than the mean. Empirical formulas are provided relating the mode, median, and mean for moderately skewed distributions.
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Data processing, editing and coding
tribhuvan University
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if any mistakes, suggest me to improve it.
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hope its useful for all :)
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1) Skewness is a measure of the lack of symmetry in a distribution. It indicates if the distribution is balanced around the mean.
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1) Skewness is a measure of the lack of symmetry in a distribution. It indicates if the distribution is balanced around the mean.
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This document provides an overview of probability concepts including:
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- An experiment generates outcomes that make up the sample space. Events are collections of outcomes.
- Simple events have a defined probability based on being equally likely. The probability of an event is the sum of probabilities of the simple events it contains.
- Rules like the multiplication rule for independent events and additive rule for unions allow calculating probabilities of composite events.
- Complement and conditional probabilities relate the probabilities of events. Independent events do not influence each other's probabilities.
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This document defines and provides the formula for calculating mean deviation, which is a measure of variation that uses all the scores in a distribution. It is more reliable than range. Mean deviation is calculated by finding the absolute difference between each score and the mean, summing the absolute differences, and dividing by the number of observations. Two examples of calculating mean deviation for sets of data are provided, along with exercises asking students to find the mean deviation of additional data sets and define standard deviation.
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Normal distribution
The document discusses the normal distribution, which produces a symmetrical bell-shaped curve. It has two key parameters - the mean and standard deviation. According to the empirical rule, about 68% of values in a normal distribution fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. The normal distribution is commonly used to model naturally occurring phenomena that tend to cluster around an average value, such as heights or test scores.
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Empirical relationship between averages
The document discusses the empirical relationship among averages - mean, median and mode. It provides examples to calculate each average from values of other two averages using the empirical formula: Mode = 3Median - 2Mean. It also illustrates the differences between mean, median and mode. The mean is the average calculated by adding all values and dividing the sum by total numbers. The median is the middle number when values are arranged in ascending order. The mode is the value that occurs most frequently in a data set.
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Here are the steps to solve this problem:
1) Form a frequency distribution table with class intervals of width 1:
Marks Frequency
0-1 8
1-2 9
2-3 8
3-4 6
4-5 5
5-6 3
2) To find the mean:
Add all values and divide by total number of values = ∑fx/N
= 0*8 + 1*9 + 2*8 + 3*6 + 4*5 + 5*3 = 84/35 = 2.4
3) To find the median:
The median is the middle value when the data is arranged in ascending order. Since there are 35
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- An experiment generates outcomes that make up the sample space. Events are collections of outcomes.
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Mean Deviation
This document defines and provides the formula for calculating mean deviation, which is a measure of variation that uses all the scores in a distribution. It is more reliable than range. Mean deviation is calculated by finding the absolute difference between each score and the mean, summing the absolute differences, and dividing by the number of observations. Two examples of calculating mean deviation for sets of data are provided, along with exercises asking students to find the mean deviation of additional data sets and define standard deviation.
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The document discusses the binomial and Poisson distributions. The binomial distribution describes the probability of success in a fixed number of yes/no trials, while the Poisson distribution models the occurrence of rare events. Examples of applications include defective items in manufacturing and accidents. Key characteristics of both distributions including their formulas are provided. The document concludes by noting the Poisson distribution is useful for modeling rare events with small probabilities of success.
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e. Example
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1. Correlation analysis measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 is a perfect negative correlation, 0 is no correlation, and 1 is a perfect positive correlation.
2. Scatter diagrams provide a visual representation of the relationship between two variables but do not provide a precise measure of correlation. Pearson's correlation coefficient (r) calculates the numerical strength of the linear relationship.
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Combined mean and Weighted Arithmetic Mean
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- The mean, median, and mode are measures of central tendency that provide a single value to represent the central or typical value in a data set.
- The mean is the average and is calculated by adding all values and dividing by the number of values. The median is the middle value when values are arranged from lowest to highest. The mode is the value that occurs most frequently.
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Measures of central tendency (ungrouped data)
This document defines and provides examples of the three measures of central tendency: mean, median, and mode. It explains that the mean is the average value found by summing all values and dividing by the total number. The median is the middle value when data is arranged in order. The mode is the most frequently occurring value. The document provides examples of calculating and interpreting these measures. It then gives practice problems asking to find and analyze these values for different data sets.
Measure of Central Tendency
What is mean?
Different types of mean, & their relation.
What is median?
What is mode?
Relation between mean, median, mode.
Usage in Business.
Sec 3.1 measures of center
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Chapter 3: Describing, Exploring, and Comparing Data
3.1: Measures of Center
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Empirical relation(mean, median and mode)
- 1. NADEEM UDDIN ASSOCIATE PROFESSOR OF STATISTICS https://www.slideshare.net/NadeemUddin17 https://nadeemstats.wordpress.com/listofbooks/
- 2. i) Median lies between mean and mode. ii) Median closer to mean than mode. iii) In the case of a moderately skewed distribution, the difference between mean and mode is equal to three times the difference between the mean and median. In moderately skewed distribution, the following approximate relation holds good. Mean – Mode = 3 (Mean – Median) OR Mode = 3 Median – 2 Mean This empirical relation does not hold in case of a J – shaped or an extremely skewed distribution.
- 3. Example -1 For a certain frequency distribution, the mean was 40.5 and median 36. Find the mode using the formula connecting the three. Solution: Given that: Mean = 40.5, Median = 36, Mode = ? We know that: Mean – Mode = 3 (Mean – Median) 40.5 – Mode = 3 (40.5 – 36) 40.5 – Mode = 3 4.5 40.5 – Mode = 13.5 Mode = 40.5 – 13.5 Mode = 27
- 4. Example -2 For a certain frequency distribution, the mode was 27 and median 36. Find the mean using the formula connecting the three. Solution: Given that: Median = 36, Mode = 27 , Mean = ? We know that: Mode = 3Median - 2Mean 27 = 3 (36) - 2Mean 27 = 108 - 2Mean 27 - 108 = - 2Mean - 81 = - 2Mean Mean = 81 2 Mean = 40.5
- 5. Example -3 For a certain frequency distribution, the mode was 27 and mean 40.5. Find the median using the formula connecting the three. Solution: Given that: Mode = 27 , Mean = 40.5, Median = ? We know that: Mode = 3Median - 2Mean 27 = 3Median – 2(40.5) 27 = 3Median – 81 27 + 81 = 3Median 108 = 3Median Median = 108 3 Median = 36
- 6. DO YOURSELF i) In a moderately asymmetrical series, the value of arithmetic mean and median is 20 and 18.67 respectively. Find out the value of Mode. (Answer = 16.01) ii) In a moderately skewed distribution, mode = 10 and median = 30, then find the mean. (Answer = 40) iii) In a moderately asymmetrical distribution the mode and mean are 32.1 and 35.4 respectively. Calculate the median. (Answer = 34.3)