Descriptive Statistics and Analytics

Descriptive Statistics

• ways of summarizing large sets of quantitative (numerical) information

• provides insights into

  • central tendencies
  • variability
  • patterns within datasets

• understand key characteristics of their data and identify anomalies, trends, and outliers by employing techniques such as

  • mean
  • median
  • mode
  • range
  • standard deviation
  • skewness
  • kurtosis

• serves as foundation for further data analysis

  • enable generation of actionable insights without relying on complex statistical modeling

Statistical Measurements

Mean

• the arithmetic average
• fundamental measure of central tendency $$mean=\frac{\sum _{i=0}^N{x}_i}{N}$$
• provides insight into the overall trend of a dataset  can be misleading when the data contains outliers or is highly skewed

import numpy as np
 
data = [100, 200, 150, 400, 500]
mean_value = np.mean(data)

Median

• the middle value in an ordered dataset
• more robust measure of central tendency when data is skewed
• less affected by extreme values
  • useful in financial and income-related analysis

import numpy as np
 
data = [100, 200, 150, 400, 500]
median_value = np.median(data)

Mode

• the value that appears most frequently in a dataset
• useful for categorical data analysis

from statistics import mode
 
data = [42, 37, 42, 45, 42, 38, 37]
mode_value = mode(data)

Range

• measure of dispersion that represents the difference between the maximum and minimum values in a dataset
• provides simple measure of variability
• does not account for how data is distributed between these extremes

data = [42, 37, 42, 45, 42, 38, 37]
range_value = max(data) - min(data)

Standard Deviation

• quantifies the amount of variation or dispersion in a dataset
  • Lower standard deviation: close to the mean
  • Higher standard deviation: greater variability

import numpy as python
 
std_dev = np.std(data, ddof=1)  # ddof=1 for sample standard deviation

Skewness

• measures the asymmetry of a distribution relative to its mean
  • positive skew: long right tail
  • negative skew: long left tail

from scipy.stats import skew
 
skewness_value = skew(data)

Kurtosis

• measures the “tailedness” of a distribution, indicating whether data points are concentrated around the mean or dispersed across the tails

from scipy.stats import kurtosis
 
kurtosis_value = kurtosis(data)