Fundamentals of Numerical Summary Measures.pptx

This document explain about mean, variability, sd and se

1. Fundamentals of Numerical Summary Measures Mean, Variability, Standard Deviation, and Error with Examples and Exercises

2. Overview Numerical summary measures help describe and interpret data. Key concepts: • Mean (average) • Variability (spread) • Standard Deviation (SD) • Error and Margin of Error These measures are essential for understanding data patterns, reliability, and comparisons.

3. Mean (Average) The mean is the sum of all values divided by the number of values. Formula: mean = (Σx) / n Example in daily life: • Average score of students in a class • Average daily temperature • Average monthly expenses Interpretation: represents the 'center' of the data distribution.

4. Variability (Spread) Variability tells us how spread out or consistent the data are. Common measures: • Range = Max - Min • Variance = Average of squared differences from the mean Example: Two students have the same average score (85), but one’s scores vary from 60–100, the other’s from 80–90. → The second student has lower variability, meaning more consistent performance.

5. Standard Deviation (SD) Standard Deviation is the square root of variance. It shows how far data points tend to deviate from the mean. Formula: SD = √[ Σ(x - mean)² / n ] Daily life example: • Consistency of delivery times for an online store. • Variation in daily step counts recorded by a smartwatch. A small SD → data are close to the mean. A large SD → data are widely spread.

6. Error and Margin of Error Error measures how far an estimate is from the true value. It represents uncertainty or inaccuracy in data or measurement. Margin of Error (MoE) = z × (SD / √n) • z depends on confidence level (e.g., 1.96 for 95%) Example: • A survey says 60% ± 3% of people prefer coffee → true preference likely between 57% and 63%.

7. Graphical Illustration Graph illustration ideas: • Bar chart showing two groups with different means. • Line graph showing consistency (low SD) vs high fluctuation (high SD). • Bell curve representing normal distribution around mean.

8. Exercises 1. Compute the mean of: 5, 7, 8, 10, 12. 2. Find the range and standard deviation of: 10, 10, 12, 18, 20. 3. A survey shows 70% ± 4% of students prefer online classes. What is the confidence interval? 4. In your own words, explain why variability is important in research data.

9. Summary • Mean shows the center of data. • Variability shows the spread or consistency. • SD measures typical deviation from the mean. • Error and MoE show uncertainty of estimates. Together, these measures provide a complete understanding of your data.