Five Number Summary Calculator

Five Number Summary is evaluated from Number 1, Number 2 and Number 3. The calculation reports Minimum, Q1 and Median.

Results

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About the Five Number Summary Calculator

Five Number Summary is treated here as a quantitative relation between Number 1, Number 2, Number 3 and Number 4 and Minimum, Q1, Median and Q3.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Sort data. Q1 = 25th percentile value, Q3 = 75th percentile value (linear interpolation). IQR = Q3 - Q1. Fences = Q1 ± 1.5 x IQR.

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Sort data. Q1 = 25th percentile value, Q3 = 75th percentile value (linear interpolation). IQR = Q3 - Q1. Fences = Q1 ± 1.5 x IQR.

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Home sale prices ($K): 220, 285, 315, 350, 390, 420, 480, 510, 620, 890

Inputs

n1: 220 n2: 285 n3: 315 n4: 350 n5: 390 n6: 420 n7: 480 n8: 510 n9: 620 n10: 890
Minimum: 220. Q1: 323.75. Median: 405. Q3: 502.5. Maximum: 890. IQR: 178.75. Lower Fence: 55.625. Upper Fence: 770.625

With Number 1 = 220, Number 2 = 285, Number 3 = 315 and Number 4 = 350 as the stated inputs, the result is Minimum = 220, Q1 = 323.75 and Median = 405. Each value corresponds to the declared output fields.

Example 2: Student test scores: 52, 65, 71, 78, 82, 85, 87, 91, 94, 99

Inputs

n1: 52 n2: 65 n3: 71 n4: 78 n5: 82 n6: 85 n7: 87 n8: 91 n9: 94 n10: 99
Minimum: 52. Q1: 72.75. Median: 83.5. Q3: 90. Maximum: 99. IQR: 17.25. Lower Fence: 46.875. Upper Fence: 115.875

With Number 1 = 52, Number 2 = 65, Number 3 = 71 and Number 4 = 78 as the stated inputs, the result is Minimum = 52, Q1 = 72.75 and Median = 83.5. Each value corresponds to the declared output fields.

Example 3: Daily step counts: 4200, 6800, 7500, 8100, 9200, 9800, 10500, 11200, 12400, 18700

Inputs

n1: 4200 n2: 6800 n3: 7500 n4: 8100 n5: 9200 n6: 9800 n7: 10500 n8: 11200 n9: 12400 n10: 18700
Minimum: 4,200. Q1: 7,650. Median: 9,500. Q3: 11,025. Maximum: 18,700. IQR: 3,375. Lower Fence: 2,587.5. Upper Fence: 16,087.5

With Number 1 = 4,200, Number 2 = 6,800, Number 3 = 7,500 and Number 4 = 8,100 as the stated inputs, the result is Minimum = 4,200, Q1 = 7,650 and Median = 9,500. Each value corresponds to the declared output fields.

Example 4: Employee salaries ($K): 45, 52, 58, 62, 65, 68, 72, 78, 88, 145

Inputs

n1: 45 n2: 52 n3: 58 n4: 62 n5: 65 n6: 68 n7: 72 n8: 78 n9: 88 n10: 145
Minimum: 45. Q1: 59. Median: 66.5. Q3: 76.5. Maximum: 145. IQR: 17.5. Lower Fence: 32.75. Upper Fence: 102.75

With Number 1 = 45, Number 2 = 52, Number 3 = 58 and Number 4 = 62 as the stated inputs, the result is Minimum = 45, Q1 = 59 and Median = 66.5. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate the five-number summary for box plots
  • Identify quartiles and IQR
  • Detect statistical outliers in a dataset