P&S project presentation ENGINEERING MATHS.pptx

P&S

1. Subject:- Probability and Statistics (1005) Topic :-Statistics Centurion University Of Technology and Management Presented By:- P.Niteesh -231801370071 B.Ramya sri -231801370073

2. Introduction to Statistics Statistics is the study of using data to understand patterns, trends, and make informed decisions. It involves collecting, organizing, analyzing, and interpreting information to gain insights and draw meaningful conclusions.

3. Random Sampling 1) Unbiased Representation :- Random sampling ensures that each member of the population has an equal chance of being selected, providing an unbiased representation. 2) Efficient Analysis :- By analyzing a random sample, researchers can make inferences about the larger population, saving time and resources. 3) Minimized Errors :- Random sampling helps to minimize the risk of systematic errors, leading to more accurate and reliable results.

4. Population and Sample Population:- The entire group of individuals or objects that are the focus of a statistical study. Sample:- A subset of the population that is selected for analysis, representing the larger group. Relationship:- Statistics allow us to draw conclusions about the population based on the analysis of a carefully selected sample.

5. Sample Mean and Variances 1) Sample Mean The average value of the data points in a sample, calculated by summing the values and dividing by the number of data points. 2) Sample Variance A measure of how spread out the data points in a sample are from the sample mean, indicating the degree of dispersion. 3) Significance The sample mean and variance are crucial in understanding the characteristics of the larger population and making statistical inferences.

6. Point and Interval Estimations Point Estimation:- A single value that serves as the best guess or estimate of an unknown population parameter. Interval Estimation:- A range of values, called a confidence interval, that is likely to contain the true population parameter. Significance:- Point and interval estimations are essential for making informed decisions and drawing meaningful conclusions from statistical data.

7. Confidence Intervals Confidence Level The probability that the true population parameter falls within the confidence interval. Interval Width The range of values that define the confidence interval, influenced by sample size and variability. Precision Confidence intervals provide a range of values that indicate the precision of the estimate.

8. Normal Distribution in Statistics Symmetry The normal distribution is a bell-shaped curve that is symmetric around the mean, with equal areas on both sides. Standardization The normal distribution can be standardized using the z-score, allowing for comparisons and probability calculations. Importance The normal distribution is a fundamental concept in statistics, used in a wide range of applications and analyses.

9. Conclusion In conclusion, statistics is a powerful tool for understanding and interpreting data, allowing us to make informed decisions and draw meaningful conclusions. By mastering the fundamental concepts, such as random sampling, population and sample, and the normal distribution, you can unlock the full potential of statistical analysis.