๐ Examples
โข Average marks of a class
โข A bar chart showing monthly sales
โข Table of COVID-19 cases by state
โข Percentage of male vs female students
Unit I ยท Lectures 1โ3 of 40 ยท B.Sc. Data Science, 1st Year, Semester II
Statistics is the science of collecting, organising, presenting, analysing, and interpreting numerical data to make informed decisions. It provides methods for drawing conclusions about a large group (population) by studying a smaller part of it (sample).
Imagine a large pot of soup. You cannot taste the entire pot to decide if it needs salt. Instead, you take a small spoonful (sample), taste it, and make a decision about the whole pot (population). This is exactly what statistics does โ it studies a part to say something meaningful about the whole.
Descriptive statistics involves methods for collecting, organising, summarising, and presenting data in a meaningful way. It describes what the data shows without making predictions.
Think of a report card. It describes a student's marks in each subject, the total, the average, and the rank. It does not predict next year's performance โ it only summarises what has already happened.
โข Average marks of a class
โข A bar chart showing monthly sales
โข Table of COVID-19 cases by state
โข Percentage of male vs female students
Inferential statistics involves methods for making predictions, generalisations, and decisions about a population based on data collected from a sample. It goes beyond the immediate data.
Think of an exit poll during elections. Interviewers ask a sample of voters (a few thousand) and predict the outcome for the entire country (millions of voters). This prediction is inference.
โข Predicting election results from exit polls
โข Testing if a new drug is effective
โข Estimating average height of all Indians from 1,000 people
โข Quality testing in factories (test a sample, approve the batch)
Click on each type to explore its definition, tools, and a real-world example:
Summarise & Present
Predict & Generalise
| Feature | Descriptive Statistics | Inferential Statistics |
|---|---|---|
| Purpose | Summarise and present data | Make predictions and generalisations |
| Scope | Limited to the data at hand | Extends from sample to population |
| Tools Used | Tables, graphs, charts, mean, median, mode | Hypothesis testing, confidence intervals, regression |
| Certainty | Describes exact facts (no uncertainty) | Involves probability and uncertainty |
| Example | "Average marks of this class = 72" | "We estimate the average marks of all B.Sc. students in India is between 68 and 76" |
Statistics is applied across virtually every field where data-driven decisions are needed.
Clinical trials, drug effectiveness testing, epidemiology (disease spread analysis), public health surveys.
Market research, sales forecasting, demand analysis, GDP estimation, inflation measurement.
Production quality testing, defect rate analysis, process optimisation, Six Sigma methods.
Crop yield analysis, fertiliser effectiveness, weather pattern studies, field experiments (Design of Experiments).
Exam analysis, student performance trends, aptitude testing, survey research, behavioural studies.
Census, population projections, poverty estimation, policy evaluation, election forecasting.
While statistics is a powerful tool, it has inherent limitations that every student must understand. Ignoring these limitations leads to misuse and misleading conclusions.
โ Lecture 2 โ
A population (or universe) is the entire group of individuals, objects, or measurements about which we want to draw conclusions. It includes every member of the defined group.
โข All students enrolled in B.Sc. Data Science in India (2025)
โข Every light bulb manufactured by a factory in a month
โข The entire population of India (1.4 billion people)
โข All patients admitted to AIIMS Delhi in 2024
A sample is a subset (a smaller portion) of the population, selected for actual study. It is chosen to represent the population so that conclusions drawn from the sample can be generalised.
โข 200 B.Sc. Data Science students selected from across India
โข 50 light bulbs picked randomly from the factory's monthly production
โข A blood sample drawn from a patient
โข 1,000 voters surveyed in an exit poll
Think of a huge pot of dal (population). You take a spoonful (sample) to taste. If the spoonful is well-stirred (randomly selected), it represents the taste of the entire pot. If it is taken only from the top (biased selection), it may not represent the pot accurately.
| Feature | Population | Sample |
|---|---|---|
| Definition | Entire group of interest | A subset of the population |
| Size | Usually very large (may be infinite) | Much smaller than the population |
| Notation | Denoted by N (population size) | Denoted by n (sample size) |
| Census vs Survey | Studied through a census (complete enumeration) | Studied through a sample survey |
| Cost & Time | Expensive and time-consuming | Cheaper and faster |
| Accuracy | Results are exact (no sampling error) | Results have sampling error (margin of error) |
| Practicality | Often impossible to study fully | Practical and feasible |
| Example | All 140 crore Indians | 10,000 people surveyed for the Census |
A parameter is a numerical measure (such as mean, standard deviation, or proportion) that describes a characteristic of the population. Parameters are usually fixed but unknown because we rarely study the entire population.
Population mean = ฮผ (mu)
Population standard deviation = ฯ (sigma)
Population size = N
Population proportion = P
"The average income of all families in India is โน3,00,000/year." โ This is a parameter (it describes the entire population). In practice, we rarely know this exact value.
A statistic is a numerical measure that describes a characteristic of the sample. Statistics are calculated from sample data and are used to estimate the corresponding population parameter. Statistics vary from sample to sample.
Sample mean = xฬ (x-bar)
Sample standard deviation = s
Sample size = n
Sample proportion = pฬ (p-hat)
"The average income of 500 surveyed families in India is โน2,80,000/year." โ This is a statistic (it describes a sample). We use it as an estimate of the true population mean.
A variable is a characteristic that assumes different numerical values for different individuals, objects, or events under study. It is something that varies (changes) from one observation to another.
โข Height of students: 150 cm, 162 cm, 175 cm...
โข Weight of newborn babies: 2.5 kg, 3.1 kg, 3.8 kg...
โข Marks in an exam: 45, 78, 92...
โข Temperature in Dehradun: 18ยฐC, 25ยฐC, 32ยฐC...
โข Age of employees: 22, 35, 48...
Discrete Variable: Takes only whole number values (countable). E.g., number of children in a family (0, 1, 2, 3โฆ), number of cars sold.
Continuous Variable: Takes any value within a range (measured, not counted). E.g., height, weight, temperature, time.
An attribute is a qualitative (non-numerical) characteristic that cannot be measured numerically but can only be observed or classified into categories. Attributes are expressed in words, not numbers.
โข Gender: Male, Female, Other
โข Blood group: A, B, AB, O
โข Marital status: Married, Unmarried
โข Eye colour: Brown, Blue, Black
โข Employment status: Employed, Unemployed
Variable โ Measured numerically โ Can calculate mean, SD, etc.
Attribute โ Classified into categories โ Can count frequencies, calculate proportions and percentages.
Click each card below to see whether it is a Variable or an Attribute, with an explanation:
Click "Reveal" to see how the six core terms relate to each other in the statistical workflow:
| Term | Meaning | Example |
|---|---|---|
| Population | Entire group under study (size = N) | All 1.4 billion Indians |
| Sample | A subset of the population (size = n) | 5,000 Indians surveyed |
| Parameter | Numerical measure of the population (ฮผ, ฯ) | True average height of all Indians |
| Statistic | Numerical measure of the sample (xฬ, s) | Average height of the 5,000 surveyed |
| Variable | Characteristic that takes numerical values | Height, weight, marks, temperature |
| Attribute | Qualitative characteristic (non-numerical) | Gender, blood group, eye colour |
โ Lecture 3 โ
Data collection is the process of gathering information (observations, measurements, responses) relevant to a statistical study. The quality of any statistical analysis depends critically on how the data was collected. Poor data collection leads to unreliable conclusions โ no amount of sophisticated analysis can fix bad data.
"Garbage in, garbage out." If you collect data poorly, your results will be poor โ regardless of how advanced your statistical techniques are. This is why understanding data sources is the foundation of all statistics.
Data can be collected from two broad sources:
Primary data is data collected originally (first-hand) by the researcher for a specific purpose or investigation. The investigator is the first person to collect and record this data.
1. Direct Personal Observation: The investigator personally collects data by observing the phenomenon. E.g., a researcher measuring plant growth in a field experiment.
2. Indirect Oral Investigation: Data is collected from third parties who have knowledge about the subject. E.g., interviewing neighbours about a person's health habits.
3. Questionnaire Method: A set of printed or digital questions is sent to respondents, who fill in and return them. E.g., online feedback forms, Google Forms surveys.
4. Interview Method: The investigator asks questions directly (face-to-face, phone, or video). E.g., Census workers visiting homes, exit pollsters at polling booths.
5. Schedule Method: Enumerators (trained data collectors) visit respondents with a pre-designed schedule (form) and fill in the responses on their behalf.
Primary data is like cooking a meal from scratch. You select the ingredients (choose what to measure), you prepare them (design the survey), and you cook (collect the data). The result is fresh, customised, and exactly what you need โ but it takes time, effort, and resources.
โข Data is original and collected for the specific research purpose
โข High reliability and accuracy (the investigator controls the process)
โข The investigator can choose the method, sample, and scope
โข Data is up-to-date and relevant
โข Expensive (requires personnel, travel, printing, technology)
โข Time-consuming (can take weeks, months, or years)
โข Risk of bias (interviewer bias, respondent dishonesty)
โข Requires trained investigators and proper planning
Secondary data is data that has already been collected, recorded, and published by someone else for a different purpose. The researcher uses this pre-existing data for their own study. The investigator is not the first person to collect it.
Published Sources:
โข Government reports (Census of India, Economic Survey, RBI Bulletin)
โข Journals, research papers, and books
โข Newspapers and magazines
โข Reports by international organisations (WHO, World Bank, UN)
Unpublished Sources:
โข Internal records of companies (sales data, HR records)
โข University records (student marks, attendance)
โข Research data maintained by organisations (not publicly available)
Secondary data is like buying a ready-made meal from a restaurant. Someone else did the cooking (collected the data). It is quick, convenient, and cheaper โ but you have less control over the ingredients (quality, accuracy, relevance).
โข Less expensive (data already exists; no collection cost)
โข Saves time (data is readily available)
โข Useful when primary collection is impossible (e.g., historical data, census data)
โข Can provide a broad overview and context for research
โข May not perfectly fit the current research purpose
โข Accuracy and reliability cannot be verified by the current researcher
โข Data may be outdated or incomplete
โข Possible bias in the original collection method (unknown to the user)
| Feature | Primary Data | Secondary Data |
|---|---|---|
| Source | Collected first-hand by the investigator | Already collected by someone else |
| Purpose | Collected for the current specific study | Originally collected for a different purpose |
| Cost | Expensive | Cheaper (or free) |
| Time | Time-consuming | Quick (data is already available) |
| Accuracy | Generally more reliable | Reliability depends on original source |
| Control | Full control over collection method | No control over how data was gathered |
| Relevance | Directly relevant to the research | May not perfectly match the need |
| Example | A survey you conduct among your classmates | Census data from the Government of India website |
Click each scenario to identify whether it is Primary or Secondary data, with an explanation:
Based on their nature, statistical data is classified into two fundamental types:
Qualitative data describes attributes or qualities that cannot be measured numerically but can only be classified or categorised. It answers the question: "What kind?"
โข Gender: Male, Female, Other
โข Blood group: A, B, AB, O
โข Nationality: Indian, American, British
โข Brand preference: Samsung, Apple, Xiaomi
โข Satisfaction level: Poor, Average, Good, Excellent
โข Eye colour: Brown, Blue, Green, Black
Quantitative data consists of numerical values that represent counts or measurements. It answers the question: "How much?" or "How many?"
โข Height: 150 cm, 172 cm, 185 cm
โข Age: 18, 25, 40 years
โข Income: โน2,00,000, โน5,00,000
โข Temperature: 22.5ยฐC, 36.8ยฐC
โข Number of children: 0, 1, 2, 3
โข Exam marks: 45, 78, 95 out of 100
Discrete data can take only specific, countable values (usually whole numbers). You count discrete data โ there are no values "in between."
โข Number of students in a class: 30, 31, 32โฆ (never 30.5)
โข Number of cars in a parking lot: 0, 1, 2, 3โฆ
โข Number of goals in a football match: 0, 1, 2, 3โฆ
โข Number of defective items in a batch: 0, 1, 2โฆ
โข Number of children in a family: 0, 1, 2, 3โฆ
If the question starts with "How manyโฆ?", the data is likely discrete.
Continuous data can take any value within a given range, including fractions and decimals. You measure continuous data โ there are infinitely many possible values between any two points.
โข Height: 165.4 cm, 170.23 cm, 180.0 cmโฆ
โข Weight: 55.5 kg, 62.3 kg, 78.1 kgโฆ
โข Temperature: 36.6ยฐC, 37.2ยฐC, 22.8ยฐCโฆ
โข Time: 9.58 seconds, 12.34 secondsโฆ
โข Distance: 5.27 km, 100.0 mโฆ
If the question starts with "How muchโฆ?", the data is likely continuous.
Nominal data consists of categories with no natural order or ranking. The categories are simply labels or names โ one is not "higher" or "better" than another.
โข Gender: Male, Female, Other (no ranking)
โข Blood group: A, B, AB, O (no "best" blood group)
โข Nationality: Indian, American, Japanese
โข Religion: Hindu, Muslim, Christian, Sikh
โข Hair colour: Black, Brown, Blonde
Ordinal data consists of categories that have a natural order or ranking, but the difference between categories is not measurable.
โข Education level: Primary โ Secondary โ Graduate โ Post-graduate
โข Satisfaction: Poor โ Average โ Good โ Excellent
โข Economic status: Low โ Middle โ High
โข Grade: A+ โ A โ B+ โ B โ C
โข Rating: 1 star โ 2 stars โ 3 stars โ 4 stars โ 5 stars
Click "Build Tree" to see the complete classification of statistical data types:
Click each scenario below and choose whether it is Nominal, Ordinal, Discrete, or Continuous:
Q1: Which type of statistics involves making predictions about a population based on a sample?
Q2: A numerical measure that describes a characteristic of the sample is called a:
Q3: "Blood group" is an example of which type of data?
Q4: Data collected by the researcher for the first time for a specific purpose is called:
Q5: The number of students in a classroom is an example of:
Q6: Which of the following is a limitation of statistics?
Q7: "Customer satisfaction: Poor โ Average โ Good โ Excellent" is an example of:
Q8: The symbol ฮผ (mu) represents:
1. Explain the difference between Descriptive and Inferential statistics. Give two real-life examples of each.
2. A researcher wants to study the average income of all workers in a factory. She surveys 50 workers out of 500.
(a) Identify the population and the sample.
(b) Is the average income of 50 workers a parameter or a statistic? Why?
(c) Is "income" a variable or an attribute?
3. Classify each of the following as Nominal, Ordinal, Discrete, or Continuous:
(a) Temperature of patients in a hospital
(b) Religion of citizens
(c) Number of books in a library
(d) Education level: High School, Bachelor's, Master's, PhD
(e) Weight of newborn babies
(f) Marital status: Single, Married, Divorced
4. You want to find out the favourite food of students in your college. Would you use primary or secondary data? Explain why. What method would you use to collect it?
5. List three advantages and three disadvantages of using secondary data for research.
6. BONUS: Visit the Census of India website (censusindia.gov.in). Find the total population of India from the most recent census. Is this a parameter or a statistic? Explain.
Questions? Let's discuss!
Lecture 4โ5: Organisation of Data โ Classification & Frequency Distribution, Cumulative Frequency Distribution
Lecture 6โ7: Representation of Data โ Tabular, Graphical & Diagrammatic
Lecture 8: Review & Problem-Solving
Unit I ยท Lectures 1โ3 ยท BDS113 Introduction to Statistics ยท B.Sc. Data Science, Semester II