Identifying Patterns Notes – Class 10 Data Science (419)

Identifying Patterns Notes for Class 10 DS covering Bias, Identifying Bias, Types of Bias, Probability for Statistics, and the Central Limit Theorem with clear concepts and practical examples.

What is Partiality, Preference and Prejudice (Bias)?

• Sometimes, we have a special fondness for a particular thing which can make us partial or biased towards it.
• Such partiality may affect or deviate the outcome in favour of a particular thing.
• This is not the correct way of dealing with data on a large scale.

What is Bias?

• Partiality, preference, and prejudice towards a set of data is called Bias.
• In Data Science, bias is a deviation from the expected outcome in the data.

Why Does Bias Occur?

• Bias mainly occurs because of:
  • Sampling
  • Estimation
• In Data Science, data is often collected from found data (data collected for a purpose other than modelling). Such data is more likely to contain biases.

Why Does Bias Matter?

• Predictive models learn only from the data used for training.
• If the training data is biased, the model’s:
  • Accuracy is reduced.
  • Fidelity (reliability) is compromised.
• Biased models may also discriminate against certain groups of people.

How to Identify Partiality, Preference and Prejudice (Bias)?

• Common statistical and cognitive biases are categorized into the following types:
  1. Selection Bias
  2. Linearity Bias
  3. Confirmation Bias
  4. Recall Bias
  5. Survivor Bias

Selection Bias

• Occurs when the model itself influences the creation of training data.
• Happens when the sample data is not representative of the actual future population.
• Common in:
  • Recommendation systems
  • Polls
  • Personalized advertisements

 Linearity Bias

• Assumes that a change in one quantity causes an equal and proportional change in another quantity.
• It is a cognitive bias, not a statistical bias.
• Occurs because of incorrect human perception, not because of data collection or analysis.

Confirmation Bias

• Also known as Observer Bias. Occurs when people see what they expect or want to see in the data.
• Researchers may begin a study with subjective opinions, either consciously or unconsciously.
• It can also occur when data labelers allow personal opinions to influence labeling, resulting in inaccurate data.

Recall Bias

• It is a type of measurement bias. Commonly occurs during the data labeling stage.
• Happens when similar data is labeled inconsistently.
• Inconsistent labeling reduces the accuracy of the dataset.

Survivor Bias

• Occurs when we focus only on successful examples and ignore failures.
• This leads to a distorted understanding of the data.
• Survivor bias can be reduced by:
  • Collecting as many inputs as possible.
  • Studying failures as well as average performers, not just successful cases.

Probability for Statistics

• Probability is the study of randomness. It is the foundation of making predictions in statistics.
• Probability helps us predict how likely or unlikely an event is to occur.
• It can also be used to make informal predictions beyond the available data.
• Probability is an essential tool in statistics.

Problem 1: Mathematical Probability

• Assumption: The coin is fair.
• Question: If a fair coin is tossed 10 times, how many times will Tail appear?
• This is a mathematical probability problem.
• The solution starts with the assumption that the coin is fair.
• The possible number of tails can be 0, 1, 2, …, 10.
• The answer is obtained through logical deductions using probability.

Problem 2: Statistics Problem

• Situation: You pick up an unknown coin.
• Question: Is the coin fair or biased?
• This is a statistics problem.
• It uses the mathematical probability model from Problem 1 as a tool.
• The answer is found through experimentation, not assumptions.

Difference Between the Two Problems

Problem 1	Problem 2
Assumes the coin is fair.	Does not know whether the coin is fair or biased.
Based on mathematical probability.	Based on statistical experimentation.
Uses logical deductions.	Uses observed experimental results.
Predicts possible outcomes.	Determines whether the coin is fair by analyzing collected data.

The Central Limit Theorem (CLT)

What is the Central Limit Theorem?

• The Central Limit Theorem (CLT) states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
• It applies when the population has a finite variance and the sample size is sufficiently large.
• The mean of all sample means is approximately equal to the population mean.

Key Points of the Central Limit Theorem

• As the sample size increases, the distribution of sample means becomes nearly normal.
• A sample size of 30 or more is generally considered sufficient for the Central Limit Theorem to hold.
• The sample mean is equal to the population mean.

Example of Central Limit Theorem

• Suppose there are 50 houses, each having 5 people.
• The objective is to find the average weight of people in the area.

Traditional Approach

1. Measure the weight of every person.
2. Add all the weights.
3. Divide by the total number of people to find the average.
4. This approach becomes time-consuming when the population is very large.

Alternative Approach Using CLT

1. Randomly select multiple samples, each containing 30 people.
2. Calculate the mean of each sample.
3. Calculate the mean of all sample means.
4. The histogram of sample means will resemble a normal distribution.

Central Limit Theorem Formula

• Sample Mean:
  
• Sample Standard Deviation:
  

Where:

• μ = Population Mean
• σ = Population Standard Deviation
• μx̄ = Sample Mean
• σx̄ = Sample Standard Deviation
• n = Sample Size

Solved Example (Case Study):

In India, the recorded weights of the male population are following a normal distribution. The mean and the standard deviations are 68 kgs and 10 kgs, respectively. If a person is eager to find the record of 50 males in the population, then what would mean and the standard deviation of the chosen sample?

Given:

• Population Mean (μ) = 68 kg
• Population Standard Deviation (σ) = 10 kg
• Sample Size (n) = 50

Solution:

• Since n > 30, the Sample Mean = Population Mean = 68 kg.
• Sample Standard Deviation: σx= σ/√n
• Thus, Standard Deviation = 10/√50 = 1.41kg

Why is the Central Limit Theorem Important?

• The Central Limit Theorem (CLT) states that regardless of the population distribution, the sampling distribution approaches a normal distribution as the sample size increases.
• Researchers usually do not know the exact population mean.
• By selecting many random samples from the population, the sample means cluster around the population mean.
• This helps researchers make a good estimate of the population mean.
• As the sample size increases, the sampling error decreases, making the estimate more accurate.

Applications of the Central Limit Theorem

1. Voting Polls
   • Used to estimate the number of people supporting a particular election candidate.
   • Confidence intervals reported in election polls are calculated using the Central Limit Theorem.
2. Family Income Estimation
   • Used to estimate the average (mean) family income of a specific region using sample data.