Practice30Create account

A "more than" cumulative frequency table reads: more than 0: 60, more than 15: 52, more than 30: 38, more than 45: 20, more than 60: 9. Which class is the median class?

Class 10StatisticsStatistics and Probability
  • A15–30
  • B45–60
  • C0–15
  • D30–45

Step-by-Step Solution

The class frequencies are 8, 14, 18, 11, 9, so the "less than" cumulative frequencies are 8, 22, 40, 51, 60. With n = 60, n/2 = 30 and the first cf ≥ 30 is 40, which belongs to the class 30–45.
Answer: D) 30–45

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

Which statement about a "less than" cumulative frequency table is FALSE?For a distribution the median is 27.5 and the mode is 26. Using the empirical relation,…A student reports mean = 30, median = 32 and mode = 40 for one and the same…Which set of values for one distribution fits the empirical relation Mode = 3 Median − 2…The empirical relation Mode = 3 Median − 2 Mean is best described as ____.