Home > Topics > Business Statistics – I > Bowley's Coefficient of Skewness

Bowley's Coefficient of Skewness – Formula, Calculation & Interpretation

Bowley's Coefficient of Skewness is a quartile-based measure of skewness. It is useful when the median is a better central value than the mean — especially for open-ended, ordinal, or highly skewed data.

Concept

Bowley's measure studies asymmetry using Q1 (lower quartile), Median and Q3 (upper quartile). A symmetric distribution satisfies: Q3 − Median = Median − Q1. If one side is longer, the distribution becomes skewed.

Formula & Components

Bowley's Coefficient of Skewness is defined as:

Bowley's Skewness = (Q3 + Q1 - 2*M) / (Q3 - Q1)

Where:

  • Q1 = first quartile
  • M = median
  • Q3 = third quartile

Steps to Calculate

  1. Arrange data in ascending order (if ungrouped) or compute cumulative frequencies (if grouped).
  2. Find positions: Q1 at N/4, Median at N/2, Q3 at 3N/4.
  3. If grouped, use interpolation to compute Q1, Median and Q3.
  4. Substitute values into the formula and interpret the sign and magnitude.

Solved Example (Ungrouped Data)

Data: 5, 7, 9, 12, 13, 15, 18, 20, 25

  • Median = 13
  • Q1 = 9
  • Q3 = 18

Apply formula:

Sk = (18 + 9 - 2*13) / (18 - 9) = 1 / 9 ≈ 0.11

Interpretation: 0.11 indicates a slight positive skew.

Solved Example (Grouped Data)

Class IntervalFrequency
0-105
10-207
20-308
30-4010
40-505

Total N = 35. Compute cumulative frequencies and locate positions: Q1 (N/4 = 8.75), Median (N/2 = 17.5), Q3 (3N/4 = 26.25). Use interpolation to compute quartile values as follows.

Q1 (class 10-20): L=10, h=10, CF_before=5, f=7

Q1 = 10 + ((8.75 - 5)/7) * 10 = 15.36

Median (class 20-30): L=20, CF_before=12, f=8

M = 20 + ((17.5 - 12)/8) * 10 = 26.88

Q3 (class 30-40): L=30, CF_before=20, f=10

Q3 = 30 + ((26.25 - 20)/10) * 10 = 36.25

Apply Bowley's formula:

Sk = (36.25 + 15.36 - 2*26.88) / (36.25 - 15.36) = -2.15 / 20.89 ≈ -0.10

Interpretation: slight negative skew.

Interpretation of Results

  • Positive value → right tail longer
  • Negative value → left tail longer
  • Value near 0 → near symmetry

Important Notes

Bowley's coefficient is based on the middle 50% and is therefore robust to outliers. It is most suitable for ordinal or open-ended distributions and lies between -1 and +1.

Quiz Time! 🎯

Test Your Knowledge

Question 1 of 5

1. Bowley’s skewness is based on:

Mean
Quartiles
Mode
Range
← PreviousNext →