- A40
- B48
- C44
- D88
Step-by-Step Solution
Median = l + h(n/2 − cf)/f → 50 = 40 + 20(60 − cf)/32 → 10 = 20(60 − cf)/32 → 16 = 60 − cf → cf = 44. So 17 + f₁ = 44.
Answer: C) 44
For data 0–20:17, 20–40:f₁, 40–60:32, 60–80:f₂, 80–100:19 with total frequency 120 and median 50, the median class is 40–60. Given cf before median class = 17 + f₁ and f = 32, l = 40, h = 20, and median = 50, find (17 + f₁).
Class 10StatisticsStatistics and Probability
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.
**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
A distribution is written in inclusive form as 10–19, 20–29, 30–39, 40–49. The true…The inclusive classes 1–10, 11–20, 21–30 are converted to the exclusive (continuous)…The table shows the marks of 50 students. Class 0–20: 8, 20–40: 12, 40–60: 15, 60–80:…Use the assumed mean method with a = 40. The table gives the ages of 30 people. Class…Use the step-deviation method with a = 125 and h = 50. Class 0–50: 4, 50–100: 8,…