Types of Sampling and Sampling Distribution

What is Sampling?

Random Sampling

• In random sampling, everyone in the universe has an equal chance of being selected..
• For instance, if you want to study the heights of students in a school, you could randomly select a certain number of students from each grade.

Stratified Sampling

• In stratified sampling, the population is divided into several groups or strata and a sample is selected from each stratum.
• For example, if you want to survey people's opinions on a product,
• you might divide the population into age groups and then randomly select individuals from each group.

Convenience Sampling

• Simple criteria include selecting people who are easy to find or contact.
• For instance, conducting a survey by asking people passing by on the street.
• Example: In data visualization, suppose you are analyzing customer satisfaction ratings for a product.
• You might randomly sample a certain number of customers from your entire customer base and visualize their feedback using charts or graphs.

Systematic Sampling

• Good sampling consists of selecting every nth element from a list or population, starting from a matching point.
• It provides a structured way of sampling.
• Example: In a manufacturing plant, if you want to check the quality of products,
• you might use systematic sampling by selecting every 10th product from the production line for inspection.

Cluster Sampling

• Cluster sampling involves dividing the population into clusters or groups based on geographical or other characteristics,
• The entire group is then randomly selected for the sample.
• In a survey about city demographics, you might use cluster sampling by dividing the city into
• neighborhoods (clusters) and then randomly selecting a few neighborhoods to survey residents.

Sampling Distribution

Central Limit Theorem

• The central limit theorem says it doesn't matter what the population distribution is.
• The sampling distribution of the sample mean tends to approximate a normal distribution when the sample size is large.
• For example, even if you have a very skewed population of ages, averaging the ages from large random samples will result in a bell curve.

Standard Error

• The standard error measures the variability of sample means in a sampling distribution.
• It is calculated as the standard deviation of sample means.
• Example: Let's say you want to estimate the average income of a family in a city.,
• calculate the mean income for each sample, and create a sampling distribution of these sample means.
• Using data visualization techniques like histograms or box plots,
• you can visualize the distribution of sample means and estimate the population mean income.

Confidence Intervals

• Sampling distributions are also used to calculate confidence intervals
• which represent the range of values within which the true population parameter (like mean or proportion) is likely to fall.

Types of data elements

Numeric Data

• Numeric data consists of numerical values that can be measured and quantified.
• Examples include temperature readings, sales figures, and population counts.
• A bar chart showing monthly sales revenue for a company, with each bar representing the sales amount in dollars.

Categorical Data

• Categorical data represents qualitative characteristics and is divided into distinct categories or groups.
• Examples include product categories, customer segments, and survey responses (e.g., Yes/No).
• A pie chart showing the distribution of product sales by category, where each slice represents a different product category.

Ordinal Data

• Ordinal data is a type of categorical data that has a defined order or ranking.
• Examples include survey ratings (e.g., satisfaction levels from "Very Satisfied" to "Very Dissatisfied")
• and educational levels (e.g., High School, Bachelor's, Master's, etc.).
• A horizontal bar chart showing the average customer satisfaction ratings for different products, ranked from highest to lowest.

Time-Series Data

• Time-series data represents values measured over time intervals.
• Examples include stock prices, temperature trends over months, and website traffic by hour/day.
• A line chart depicting the monthly average temperature in a city over the past year,
• with each point representing the temperature for a specific month.

Text Data

• Text data includes unstructured textual information such as customer reviews, social media posts, and email content.
• Word clouds or sentiment analysis charts showing the most frequently used words or sentiments in customer reviews for a product or service.

Conclusion