MCA-205
Statistics and Data Analytics
Descriptive and inferential statistics with Python — central tendency and dispersion, probability distributions, hypothesis testing, ANOVA and regression.
- Semester
- Semester 3
- Credits
- 3
- Scheme
- 3 lectures a week
- Contact hours
- 40 across four units
- Category
- Core Elective - II
What the paper is
Statistics and Data Analytics is the paper that supplies the mathematics the machine learning papers assume. It runs in the conventional order — describe the data, model the randomness, infer from a sample, then test a claim — and every stage is meant to be done in Python rather than by hand.
The distinction the syllabus keeps returning to is descriptive versus inferential. Unit I is descriptive: measures that summarise data you already have. Units II and III are inferential: statements about a population you only have a sample of, with a stated confidence. Getting that distinction sharp early makes the whole paper easier.
Unit IV brings the tests together — ANOVA, chi-square, correlation and regression — and it is where the paper connects to Artificial Intelligence and Machine Learning, whose regression material assumes exactly this.
What to concentrate on
- Hypothesis testing is the centre of the paper and the most examined topic: state the null and alternative, choose the test, compute the statistic, compare with the critical value, conclude. Practise that five-step shape on t, z, F and chi-square until it is automatic.
- Know when each test applies rather than only how to compute it. “Which test would you use and why” is asked as often as the computation itself.
- For Unit I, be able to compute mean, median, mode, quartiles, standard deviation and coefficient of variation on a small frequency distribution, and to read a box-and-whisker plot. These are quick marks that come up every year.
Syllabus, unit by unit
Summarised from the approved scheme. Hours are the contact hours the scheme allots, which is a fair guide to where the marks sit.
Unit I · Introduction and descriptive statistics
10 hours- Definition, importance, scope, applications and limitations of statistics; descriptive versus inferential statistics
- Data analytics: definition, difference from statistics, uses and applications
- The role of statistics in data analytics; types of analytics — descriptive, diagnostic, predictive and prescriptive
- Types of data, data measurement and collection
- Measures of central tendency: mean, median, mode, partition values
- Measures of dispersion: range, quartile deviation, mean deviation, standard deviation, variance, coefficient of variation
- Measures of shape, the empirical rule, Chebyshev's theorem, box and whisker plots, z-scores
Unit II · Probability and probability distributions
10 hours- Theory of probability, sample spaces and events, conditional probability
- Basic relationships of probability, Bayes' theorem
- Random variables: discrete and continuous
- Binomial, Poisson and normal probability distributions
Unit III · Inferential statistics and hypothesis testing
10 hours- Reasons for sampling, sampling frame, sampling error, sample size, non-response
- Random and non-random sampling methods; the sampling distribution, large and small sample tests, the central limit theorem
- Types of estimate; using the z statistic to estimate a population mean; confidence intervals when the standard deviation is unknown; estimating with the t statistic
- Hypothesis formulation and testing, null and alternative hypotheses, Type I and Type II errors
Unit IV · Analysis of variance, regression and correlation
10 hours- Two population variances and the F distribution
- One-way and two-way classification
- The chi-square test
- Curve fitting and the principle of least squares, regression and correlation
How it is examined
- Question 1 is compulsory, covers the whole syllabus, and is made of objective or short-answer questions. It carries 12 marks.
- The rest of the paper is four units matching the four above. Each unit sets two questions and you attempt one, so there are four more answers at 12 marks each.
- Examiners are asked to map every question to a course outcome using Bloom's taxonomy, which is why questions are phrased as “apply”, “analyse” or “evaluate” rather than only “explain”.
The pass mark is 40 out of 100 in every paper.
Learning objectives
- Descriptive and inferential statistics and their application to real-world problems
- Data analysis using statistical tools and techniques
Assumed beforehand
- Python, for implementing the theoretical concepts
Paired in the scheme with MCA-265 Lab based on Core Elective II.
Books it is taught from
- TB1Anderson, Sweeney, Williams, Camm and Cochran, “Statistics for Business & Economics”, Cengage, revised 13th edition, 2018
- TB2S. C. Gupta, “Fundamentals of Statistics”, Himalaya Publishing, 7th edition, 2019
- TB3J. K. Sharma, “Business Statistics”, Pearson Education, 2nd edition, 2010
- TB4A. Maheshwari, “Data Analytics Made Accessible”, 2018
Notes for MCA-205
Lecture notes, question papers and assignments filed against MCA-205 are in the library. Everything there has been checked by a moderator before it appears, and an account is free — new ones are approved by hand, which is what keeps the shelf clean.