Practice30Create account

Find the median. The table gives the weights (kg) of 40 boxes. Class 20–30: 3, 30–40: 8, 40–50: 12, 50–60: 10, 60–70: 7.

Class 10StatisticsStatistics and Probability
  • A37.5
  • B45.0
  • C47.5
  • D50.0

Step-by-Step Solution

Cumulative frequencies: 3, 11, 23, 33, 40. n/2 = 20 and the first cf ≥ 20 is 23, so the median class is 40–50 with l = 40, cf = 11, f = 12, h = 10. Median = 40 + 10(20 − 11)/12 = 40 + 7.5 = 47.5 kg. (37.5 comes from using the cf of the median class, 23, instead of the cf before it.)
Answer: C) 47.5

Key idea: Median for grouped data

**Step 1**: build cumulative frequency (cf) column.
**Step 2**: find n/2 (half the total frequency).
**Step 3**: locate the **median class** — the FIRST class whose cumulative frequency ≥ n/2.
**Step 4**: Apply formula.

**Median formula**:
**Median = l + h × (n/2 − cf) / f**

Where:
- l = lower limit of median class
- h = class width
- n = total frequency
- cf = cumulative frequency of class BEFORE median class
- f = frequency of median class

The formula uses linear interpolation within the median class to find where the n/2-th item falls.

Master this chapter in 30 minutes a day.

Don't just memorise the answer — build a daily practice habit.

Practice 5 Similar Questions Free →

All Statistics practice questions

More Class 10 Statistics practice

Identify the median class. Class 0–5: 2, 5–10: 12, 10–15: 6, 15–20: 5, 20–25: 5.For the data 0–10: 8, 10–20: 12, 20–30: 20, 30–40: 10 a student wrote Median = 20 + 10 ×…A distribution has classes 0–5, 5–10, 10–15, 15–20, 20–25 with cumulative frequencies 4,…For a grouped distribution, n = 35 and the median class is 10–15 with l = 10, cf = 10, f…Find the mode of the daily pocket money (₹) of 64 children. Class 11–13: 7, 13–15: 6,…