Business Analytics - Descriptive Analytic Techniques - Assessment Answer

Business Analytics Assignment

Assignment Task

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:

• Measure of Central Tendency:

1. Mean
2. Median
3. Mode

• Measure of Dispersion:

1. Range
2. Standard Deviation
3. Variance

• Measure of position:

1. Z-score
2. Percentiles
3. Quartiles
4. Interquartile

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