Q.The marks of 11 students, arranged in ascending order, are: 12, 15, 18, 20, 22, 25, 28, 30, 33, 38, 45. Compute Bowley's coefficient of skewness.

With 11 already-ordered values, the quartiles are simply the 3rd, 6th and 9th values by position — no interpolation is needed for an individual series.

Data (already sorted, $N=11$): 12, 15, 18, 20, 22, 25, 28, 30, 33, 38, 45.

For an individual series, quartiles are located by rank position: $Q_1$ at $\frac{N+1}{4}$, Median at $\frac{N+1}{2}$, $Q_3$ at $\frac{3(N+1)}{4}$.

Step 1 — $Q_1$ position $=\frac{11+1}{4}=3$rd value $= 18$.

Step 2 — Median position $=\frac{11+1}{2}=6$th value $=25$.

Step 3 — $Q_3$ position $=\frac{3(11+1)}{4}=9$th value $=33$.

Step 4 — Bowley's coefficient.

Independent check. $(Q_3-\text{Median})=33-25=8$ and $(\text{Median}-Q_1)=25-18=7$; the two half-ranges (8 and 7) are nearly equal, so a coefficient very close to zero is exactly what should be expected — 0.067 is consistent with this near-balance.

Comment. The coefficient is small and positive, so this set of marks is very close to symmetric, with only a very slight positive skew (the upper half of the data is marginally more spread out than the lower half).

For an individual series, do not apply the continuous-series interpolation formula (L plus a fraction times h) — with individual/ungrouped data there are no class intervals, so quartiles are found directly by rank position. Also, always use N plus 1 (not N) in the position formula for an individual/discrete series.