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Ubify Financial Advisory Board
FINANCIAL ANALYSTS & CPA REVIEWERS
About This Tool
This statistical five-number summary calculator computes exploratory data distributions and detects mild and extreme mathematical outliers using the standard Tukey Interquartile Range (IQR) fence rule. Data analysts, biostatisticians, and quality control engineers can evaluate dataset spread, skewness, and quartile boundaries from raw comma-separated values.
### Five-Number Summary and Tukey Outlier Formulation The statistical engine sorts numerical inputs and evaluates partition percentiles:
- **Quartile Partitions:** - *Minimum:* Smallest observation within non-outlier boundaries. - *First Quartile ($Q_1$):* 25th percentile midpoint of the lower half of the dataset. - *Median ($Q_2$):* 50th percentile central observation. - *Third Quartile ($Q_3$):* 75th percentile midpoint of the upper half of the dataset. - *Maximum:* Largest observation within non-outlier boundaries. - **Interquartile Range (IQR):** $$\text{IQR} = Q_3 - Q_1$$ - **Tukey Outlier Fences:** - *Lower Fence:* $Q_1 - 1.5 \times \text{IQR}$ - *Upper Fence:* $Q_3 + 1.5 \times \text{IQR}$ - *Outlier Detection:* Any data point strictly below the lower fence or above the upper fence is flagged as an outlier.
### Worked Numeric Example Analyzing a sample dataset of 13 measurements: - **Sorted Dataset:** `[12, 15, 18, 22, 24, 25, 26, 28, 30, 31, 35, 42, 68]`
**Calculation Steps:** 1. **Median ($Q_2$):** 7th value = **26**. 2. **First Quartile ($Q_1$):** Median of lower 6 values `[12, 15, 18, 22, 24, 25]` = $(18 + 22) / 2 = \mathbf{20}$. 3. **Third Quartile ($Q_3$):** Median of upper 6 values `[28, 30, 31, 35, 42, 68]` = $(31 + 35) / 2 = \mathbf{33}$. 4. **Interquartile Range:** $\text{IQR} = 33 - 20 = \mathbf{13}$. 5. **Outlier Boundaries:** - Lower Fence: $20 - (1.5 \times 13) = 20 - 19.5 = \mathbf{0.50}$. - Upper Fence: $33 + (1.5 \times 13) = 33 + 19.5 = \mathbf{52.50}$. 6. **Outlier Identification:** Value **68** exceeds 52.50 and is classified as a statistical outlier.
### Client-Side Computation Guarantee All sorting, quartile evaluations, and Tukey fence tests execute 100% locally in your client web browser. Datasets are never transmitted to external servers.
How to Use
- 1
Enter your dataset as comma-separated or space-separated numbers (minimum 4 values).
- 2
Inspect the computed five-number summary: Min, Q1, Median, Q3, and Max.
- 3
Check the Interquartile Range (IQR) and upper/lower Tukey outlier fence thresholds.
- 4
Review the outlier detection card listing any numbers that exceed the inner fences.
Frequently Asked Questions
How does Tukey define an outlier in a box plot?
Tukey defines an outlier as any point falling more than 1.5 times the Interquartile Range (IQR) below Q1 or above Q3.
Why are at least 4 numbers required for calculation?
Calculating quartiles requires partitioning the dataset into lower and upper halves; datasets with fewer than 4 items cannot produce meaningful quartile boundaries.
Are entered numerical datasets sent to a server?
No. All parsing, sorting, and statistical evaluations run locally in your client browser memory.