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An in-depth review of descriptive analytics techniques mentioned below.You are required to develop a taxonomy for descriptive analytics techniques, describing for each technique its purpose, functionality, assumptions, method of validation and sample use case. The sample use case must be from a business analytics scenario (600 words) so 100 words per technique( 100 for mean, 100 for Median and so on) . please do as shown in example.
Descriptive Analytic Techniques:
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Measures of Central Tendency
Technique:The mean
Purpose:One of the best measures of central tendency. The mean is very effective when the distribution of the variable of interest follows normal distribution
Functionality:Adding all the values in the variable and dividing the result by the sample size of the variable
Assumptions:Should validate the assumption of normality
Method of validation:The histogram is constructed for the data. If the distribution has equal tail width on both sides of the histogram, then the distribution follows normal distribution, and therefore, the mean is considered as the appropriate measure of central tendency
Sample use case:To determine the mean waiting time of customers who wait in line to pay their bills in the supermarket
Technique:The median
Purpose:The median is the best measure when the distribution of the variable of interest violate the assumption of normal distribution
Functionality:The median is the middle value of the dataset after arranging it in ascending or descending order of magnitude. To calculate the median, we first need to arrange the data either in ascending or descending order of magnitude. The sample size of the variable of interest is then calculated and if n is odd, then the median is calculated by using the formula (n+1)/2. On the other hand, when n is even, then the median is calculated by using the formula [n/2 + (n/2+1)]/2
Assumptions:No assumption is required
Method of validation:Either histogram or box plot to validate the median
Sample use case:The median age of students in class 10
Technique:The mode
Purpose:The mode is defined as the most repeated value in the dataset. In discrete probability distribution, the mode is defined as the value x which take the maximum probability value in its probability mass function
Functionality:The mode is the maximum value in the dataset and it is obtained by calculating the frequency distribution of the discrete data. For continuous data, the value that takes the maximum probability is considered as the mode.
Assumptions:No assumption is required
Method of validation:Bar chart and pie chart are the appropriate method to validate mode
Sample use case:To determine the number of points scored in the series of the football games
Measures of Dispersion
Technique:The Range
Purpose:The range is defined as the difference between the two extreme values (maximum and minimum values in the dataset). It is highly affected by outliers in the dataset
Functionality:Range is calculated by taking the difference between the maximum and minimum value in the dataset and it mainly explains the spread of a set of data.
Assumptions:Normality assumption is required. If the distribution is skewed, then the variation will be high and it leads to biased results. To test the normality assumption, it is found that the skewness should be within range ± 2
Method of validation:Box plot or histogram provides the validation for Range
Sample use case:To determine the range of the test scores of students studying in class 10
Technique:The standard deviation
Purpose:The standard deviation is the square root of the differences squared from the mean. It is usually helps us to determine the spread of the data. It is usually represented by the Greek symbol ?
Functionality:The standard deviation is calculated by using the formula given below
Assumptions:Normality assumption is required. If the distribution has extreme values, then using the standard deviation to represent the variability of the data is not the appropriate measure
Method of validation:Box plot or histogram provides the validation for standard deviation
Sample use case:To determine the standard deviation of student’s height studying in class 10
Technique:The variance
Purpose:The variance is the differences squared from the mean. It is usually helps us to determine the spread of the data. It is usually represented by the Greek symbol ?2. It is the square of standard deviation
Functionality:The variance is calculated by using the formula given below
Assumptions:Normality assumption is required. If the distribution has extreme values, then using the variance to represent the variability of the data is not the appropriate measure
Method of validation:Box plot or histogram provides the validation for variance
Sample use case:To determine the variance of student’s height studying in class 10
Measure of Position
Technique:Z score
Purpose:The Z score represents the measure of how many standard deviations the raw score falls either below or above the population mean and it is also measured as the standard score which is normally placed in a normal distribution
Functionality:The variance is calculated by using the formula given below
Z = (x - µ)/?
Assumptions:Normality assumption is required.
Method of validation:The point is always plotted in the normal curve and it represent the probability of the value that falls below the number of standard deviations of the mean
Sample use case:To determine the probability of students who fall below 170 cm of height in class 10 where the height of students follows normal distribution with mean 165 cm with a standard deviation of 10 cm
Technique:The percentiles
Purpose:The percentiles represents the value below with a certain percentage of dataset fall
Functionality:The percentile is calculated by using the formula given below
Assumptions:Normality assumption is required.
Method of validation:The point is always plotted in the normal curve and it represent the probability of the value that falls below the number of standard deviations of the mean. It is normally used in the school reports to represent the reporting of scores computed from students test marks (norm referenced tests)
Sample use case:To determine the 20th percentile of the student score which means that 20% of the students falls below a certain score
Technique:The quartiles
Purpose:The quartile divide the dataset into four equal groups in such a way that it divides the population with respect to the distribution of values for the variable of interest
Functionality:The quartile is calculated by using the formula given below
Q1 = (n+1)/4th item, Q2 = Median and Q3 = 3(n+1)/4th item
Assumptions:Normality assumption is required.
Method of validation:Box plot is the appropriate method to validate the quartiles. In normal distribution Q1 represents that the first quartile which means that 25% of the data falls below first quartile, Q2 represents that the first quartile which means that 50% of the data falls below second quartile and Q3 represents that the third quartile which means that 75% of the data falls below third quartile
Sample use case:To determine the first quartile of the student score which means that 25% of the students falls below a certain score
Technique:The interquartile range
Purpose:The interquartile range is the difference between the third quartile and the first quartile. It is used to measure the variability of the dataset
Functionality:The quartile is calculated by using the formula given below
IQR = Q3 – Q1
Assumptions:Normality assumption is required.
Method of validation:Box plot is the appropriate method to validate the quartiles. The IQR is the appropriate measure of dispersion when the distribution is skewed. When there are extreme values, then either standard deviation or variance cannot be used to measure the dispersion of the dataset. In this situation, IQR can be used
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