1. What is a 5 Number Summary?

The 5 number summary is a descriptive statistics tool that provides a quick overview of a dataset's distribution. It consists of five values: minimum, first quartile (Q1), median, third quartile (Q3), and maximum.

2. How Does the Calculator Work?

The calculator computes the following values:

Where:

• Minimum — The smallest value in the dataset
• Q1 — The 25th percentile (value below which 25% of the data falls)
• Median — The 50th percentile (middle value of the dataset)
• Q3 — The 75th percentile (value below which 75% of the data falls)
• Maximum — The largest value in the dataset

Explanation: The calculator first sorts the data, then calculates each of these five values using standard statistical methods.

3. Importance of 5 Number Summary

Details: The 5 number summary is crucial for understanding data distribution, identifying outliers, and creating box plots. It provides more information than just the mean and standard deviation.

4. Using the Calculator

Tips: Enter your numerical data separated by commas (e.g., 12, 15, 18, 22, 25, 30). The calculator will ignore any non-numeric values in your input.

5. Frequently Asked Questions (FAQ)

Q1: How is Q1 different from the median?
A: Q1 represents the 25th percentile while the median represents the 50th percentile. Q1 shows where the first quarter of data ends.

Q2: What can I learn from a 5 number summary?
A: You can understand the data's spread, central tendency, and skewness. The distance between Q1 and Q3 (IQR) shows where the middle 50% of data lies.

Q3: How does this help identify outliers?
A: Values more than 1.5×IQR below Q1 or above Q3 are typically considered outliers.

Q4: What's the difference between quartiles and percentiles?
A: Quartiles are specific percentiles - Q1 is the 25th percentile, median is 50th, Q3 is 75th.

Q5: Can I use this for non-numeric data?
A: No, the 5 number summary only makes sense for numerical (quantitative) data.