Distributions in Data Science Notes – Class 10 Data Science (419)

Disitribution in Data Science Notes curated for Class 10 DS includes Uniform Distribution, Types of Distribution, Statistical Problem Solving Process and its components for quick learning and high score.

Distribution in Data Science

• Distribution is a method that shows the possible values of a variable and how often (with what probability) they occur.
• Probability tells us the mathematical chance of an event occurring.
• Distribution helps us visualize how these probabilities are spread across all possible outcomes.
• A probability distribution includes all possible outcomes of an event along with their probabilities.
• The sum of probabilities of all possible outcomes is always 1 (or 100%).
• Any outcome that is impossible has a probability of 0.

Example 1: Tossing One Coin

• A coin has two sides: Head (H) and Tail (T).
• Possible outcomes: Head, Tail
• Probability of getting Head = 1/2 = 0.5
• Probability of getting Tail = 1/2 = 0.5
• Probability of getting a third side = 0 (Impossible)

Outcome	Probability
Head (H)	0.5
Tail (T)	0.5

• Total Probability = 0.5 + 0.5 = 1
• Since both outcomes are equally likely, this is called a Uniform Distribution.

Uniform Distribution

• In a Uniform Distribution, all possible outcomes have equal probability.
• The graph of a uniform distribution shows equal-height bars for all outcomes.
• The graph is only a visual representation of the distribution.
• The actual distribution is defined by the probability values, not by the graph.

Example 2: Tossing Two Coins

• When two coins are tossed together, there are four possible outcomes:
  • Head–Head (HH)
  • Head–Tail (HT)
  • Tail–Head (TH)
  • Tail–Tail (TT)

Outcome	Probability
HH	0.25
HT	0.25
TH	0.25
TT	0.25

• Total Probability = 0.25 + 0.25 + 0.25 + 0.25 = 1
• Each outcome has an equal probability (0.25).
• The probability distribution graph contains four bars of equal height, representing a Uniform Distribution.

Types of Distributions

• The types of distributions in data science depend on the type of data encountered while solving problems.
• Data is classified into two types:
  • Discrete Data
  • Continuous Data

Discrete Data

• Discrete data takes only specified values.
• It has fixed outcomes.
• Example: In a test, a student can either Pass or Fail.

Continuous Data

• Continuous data can take any value within a given range.
• The range can be finite or infinite.
• Examples:
  • Depth of an ocean
  • Weight of a person
  • Length of a road

Statistical Problem-Solving Process

• The Statistical Problem-Solving Process is used to collect and analyze data.
• Its main purpose is to answer statistical investigative questions.
• The process consists of four components.
• Each component involves exploring and addressing variability.

Components of Statistical Problem-Solving Process

1. Formulate Statistical Investigative Questions
2. Collect/Consider the Data
3. Analyze the Data
4. Interpret the Data

Formulate Statistical Investigative Questions

• This step is also called anticipating variability at the beginning of the statistical problem-solving process.
• Statistical investigative questions are questions that anticipate variability in the data.

Examples of Statistical Investigative Questions

• How fast can my plant grow?
• Do plants exposed to more sunlight grow faster?
• How does sunlight affect the growth of a plant?

Non-Statistical Investigative Question

• How tall is the plant?
• This is not a statistical investigative question because it is answered with a single height and does not involve variability.

Features of a Good Statistical Investigative Question

• The variables of interest should be clearly defined.
• The group or population being studied should be clearly identified.
• The purpose of the question should be clear.
• It should focus on the whole group, not on an individual.

Collect/Consider the Data

• This step is also called acknowledging variability while designing for differences.
• Data collection designs must acknowledge variability in data.
• Some methods are used to reduce and detect variability, such as:
  • Statistical Process Control (SPC)
  • Random Sampling
• Other methods are used to induce variability to test treatments, such as Design of Experiments (DOE).
• In experimental designs, different groups are subjected to different treatments.
• Random assignment to groups helps reduce differences caused by factors that are not manipulated or controlled in the experiment.
• The main statistical focus is to:
  • Look for variability.
  • Account for variability.
  • Explain variability.
• Data may be collected first-hand or acquired from another source.
• After the data is available, it needs to be examined (interrogated).

Analyze the Data

• This step is also called accounting for variability while analyzing distributions.
• During data analysis, we try to understand the variability in the data.
• Graphical displays and numerical summaries are used to:
  • Explore variability.
  • Describe variability.
  • Compare variability in distributions.
• Variability can be studied by observing the:
  • Overlap of the distributions.
  • Separation of the distributions.

Interpret the Results

• This step is also called allowing for variability while looking beyond the data.
• Statistical interpretations are made in the presence of variability.
• Variability must be considered while interpreting results.
• In a randomized comparative medical experiment, there are two important sources of variability:
  • Randomization to the treatment group.
  • Variability from one individual to another.
• When generalizing the results beyond the collected data, these sources of variability must be taken into account.