Enter up to 10 values to compute the five-number summary used to construct a box plot: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.
Box plots (also called box-and-whisker plots) are visualizations that compactly display the distribution of a dataset through a "five-number summary": minimum, first quartile (Q1), median, third quartile (Q3), and maximum. The box represents the middle 50% of data (IQR = Q3 − Q1); whiskers extend to min and max (or 1.5×IQR if there are outliers). The median is marked as a line inside the box.
This calculator returns the five-number summary for any dataset. Box plots are excellent for comparing distributions, spotting skewness, and identifying outliers. They're widely used in exploratory data analysis, scientific research, business analytics, and quality control. Unlike histograms, box plots work well for small samples and don't require choosing bin sizes.
Box plots reveal distribution shape: - **Symmetric distribution**: median in center of box; whiskers similar length. - **Right-skewed**: median closer to bottom of box; longer upper whisker. - **Left-skewed**: median closer to top; longer lower whisker. - **With outliers**: individual points beyond 1.5×IQR from box.
Common applications: comparing student test scores across schools, comparing salaries across departments, analyzing manufacturing defect rates across shifts, and exploring any continuous distribution.
**Scenario:** Student scores: 65, 70, 72, 75, 78, 80, 82, 85, 88, 95. **Calculation:** Min: 65. Q1: 72. Median: 79. Q3: 85. Max: 95. IQR: 13. **Result:** Median 79 is centered in box (72-85), suggesting near-symmetric distribution. Range 30. Whiskers extend from 65 to 95.
**Scenario:** Department A salaries (thousands): 40, 42, 45, 50, 55, 60, 62, 65, 70, 75. Department B: 30, 35, 40, 50, 55, 60, 65, 70, 90, 120. **Calculation:** A: Median=57.5, Q1=46.25, Q3=63.75, IQR=17.5. B: Median=55, Q1=37.5, Q3=67.5, IQR=30 (wider spread). B has outliers (90, 120 beyond Q3+1.5IQR=112.5). **Result:** Department B has wider salary range and includes outliers (high earners). Department A more consistent. Median salaries similar but distributions different.
**Scenario:** Sample data: 5, 10, 12, 15, 18, 20, 22, 25, 28, 100. **Calculation:** Q1=11.5, Median=19, Q3=26.5, IQR=15. Outlier: 100 (> 26.5+22.5=49). **Result:** Strongly right-skewed with outlier 100. Median 19 closer to Q1 than Q3. Distribution suggests one or two extreme values pulling mean upward. Investigate 100: data error or legitimate extreme value.
**Use box plots for:**
- **Comparing distributions** across groups or time periods. - **Outlier detection**: 1.5×IQR rule. - **Identifying skewness**: position of median in box. - **Sample comparison**: useful even for small samples. - **Quality control**: monitoring process consistency.
**Box plot vs histogram:**
- **Box plot**: better for comparing multiple groups, compact. - **Histogram**: better for detailed shape, larger samples.
**Reading a box plot:**
1. **Box position**: where typical values are. 2. **Box width (IQR)**: spread of middle 50%. 3. **Whisker length**: range excluding outliers. 4. **Median line position**: skewness indicator. 5. **Outlier points**: extreme values needing investigation.
**Comparing groups:**
- **Box overlap**: substantial overlap suggests similar groups. - **Non-overlapping boxes**: clear distribution differences. - **Different medians**: locations differ. - **Different IQRs**: variability differs.
**Common variations:**
- **Tukey style**: standard whiskers to 1.5×IQR limit. - **Min-max whiskers**: whiskers to actual min/max. - **Percentile whiskers**: extending to 5th and 95th. - **Custom**: software allows customization.
**Software:**
- **Excel**: Insert → Charts → Box & Whisker. - **R**: boxplot() function; ggplot2 geom_boxplot. - **Python**: matplotlib boxplot(), seaborn boxplot. - **SPSS**: Graphs → Boxplot.
**Limitations:**
- Doesn't show bimodal distributions clearly. - Hides distribution shape details. - Sample size not visible. - Outlier definition can vary.
**Modern alternatives:**
- **Violin plot**: shows density on box plot. - **Strip plot**: shows individual data. - **Beeswarm plot**: avoids overlap. - **Letter-value plot**: additional quartiles.
**Best practices:**
- Always include axis labels and units. - Show sample size (n) next to each box. - Use consistent y-axis scale for comparison. - Annotate outliers when meaningful. - Consider showing means alongside medians.
Calculate the interquartile range (IQR) from a data set of up to 10 values.
Detect outliers in a data set using the IQR method.
Calculate mean, median, and mode from a dataset of up to 10 values.
Generate frequency distribution from data with configurable number of bins.
Calculate population and sample standard deviation from a data set.
Calculate basic probability from favorable outcomes divided by total outcomes.
Minimum
5
Q1 (25th Percentile)
12.5
Median (Q2)
20
Q3 (75th Percentile)
27.5
Maximum
35
IQR
15
Range
30
Data Points
7