Quartiles math report_Ungrouped_Data.pptx

Math

1. Quartiles (Ungrouped Data) Definition, Formula, Steps, and Example

2. Introduction to Quartiles Quartiles divide a data set into four equal parts. They help in understanding data distribution and variability.

3. Quartile Formula To find quartiles: Q1 = (1/4)(n+1)th value Q2 = (Median) (n+1)/2 th value Q3 = (3/4)(n+1)th value

4. Steps to Find Quartiles 1. Arrange data in ascending order. 2. Calculate Q1 (First Quartile). 3. Calculate Q2 (Median/Second Quartile). 4. Calculate Q3 (Third Quartile). 5. Interpret the results.

5. Step 1: Arrange Data in Ascending Order Organize the dataset from smallest to largest value.

6. Step 2: Calculate Q1 (First Quartile) Q1 = (1/4)(n+1)th value Find the position of Q1 in the ordered dataset.

7. Step 3: Calculate Q2 (Median) Q2 = (n+1)/2 th value If n is odd, Q2 is the middle value. If even, Q2 is the average of two middle values.

8. Step 4: Calculate Q3 (Third Quartile) Q3 = (3/4)(n+1)th value Find the position of Q3 in the ordered dataset.

9. Step 5: Interpret the Results Q1, Q2, and Q3 help describe how data is spread and identify outliers.

10. Example Problem Find Q1, Q2, and Q3 for the dataset: 3, 7, 8, 12, 13, 14, 18, 21, 23, 27.

11. Step-by-Step Solution 1. Arrange the data (already sorted). 2. Q1 = 3rd value = 8 3. Q2 = Median = 13 4. Q3 = 8th value = 21

12. Graphical Representation A boxplot visually represents quartiles and outliers in data.

13. Real-Life Applications of Quartiles 1. Analyzing income distribution 2. Evaluating student test scores 3. Understanding weather patterns

14. Summary of Key Points • Quartiles divide data into four equal parts. • Q1 = First Quartile, Q2 = Median, Q3 = Third Quartile. • Used in statistics for data analysis and interpretation.

15. Thank You! Any questions?