Q.Using the same daily-wages data (0–20: 6, 20–40: 10, 40–60: 18, 60–80: 15, 80–100: 11 workers), calculate P70.

A percentile in a continuous series is located exactly like a quartile or decile, using position iN/100. …

Step 1 — Locate the percentile class. $k = \frac{70N}{100} = \frac{70(60)}{100} = 42$. From the cumulative frequencies (6, 16, 34, 49, 60), the first cf ≥ 42 is 49, in class 60–80 (L = 60, cf before = 34, f = 15, h = 20).

Step 2 — Interpolate. …

Cross-check against Q3 and D7 from the same distribution. P70 (₹70.67) lies, as it must, below Q3 = ₹74.67 (the 75% point, Example 3) and above D6 = ₹62.67 (the 60% point, Example 4) — exactly the ordering a higher-percentage partitio …

Confusing P70 with D7 — they are NOT the same value in general; D7 = P70 only because 7/10 and 70/100 are the same fraction, which is true here, but a student must still compute using i=70 wi …