Q.Using the same daily-wages data as Example 3 (0–20: 6, 20–40: 10, 40–60: 18, 60–80: 15, 80–100: 11 workers), find P25 and confirm it equals Q1 = ₹38 from Example 3.

P25 and Q1 both locate the identical 25% point of a distribution, so computing P25 independently must reproduce Q1 exactly. …

Step 1 — Locate the percentile class. $k = \frac{25N}{100} = \frac{25(60)}{100} = 15$. From the cumulative frequencies (6, 16, 34, 49, 60), the first cf ≥ 15 is 16, in class 20–40 (L = 20, cf before = 6, f = 10, h = 20).

Step 2 — Interpolate.

$P_{25} = 20 + \frac{15-6}{10}\times20 = 20+\frac{9}{10}\times20 = 20+18 = 38$ …

Treating a successful match between P25 and Q1 as 'automatic' and therefore skipping the actual interpolation — the relationship guarantees the two values MUST agree if both are computed correctly, but it does not exempt a student fr …