Practice30Create account

The table shows the marks of 50 students. Class 0–20: 8, 20–40: 12, 40–60: 15, 60–80: 10, 80–100: 5. Find the mean by the direct method.

Class 10StatisticsStatistics and Probability
  • A36.8
  • B46.8
  • C45.0
  • D50.0

Step-by-Step Solution

Class marks are 10, 30, 50, 70, 90. Σfx = 80 + 360 + 750 + 700 + 450 = 2340 and Σf = 50, so mean = 2340/50 = 46.8. (36.8 is what you get by multiplying the frequencies by the lower limits instead of the class marks.)
Answer: B) 46.8

Key idea: Mean by direct method

**Setup**: data given as class intervals with frequencies. Compute class marks ᵢ.

**Formula**: **̄ = Σᵢᵢ) / Σᵢ**

Multiply each class mark by its frequency, sum, divide by total frequency.

**Example**:
| Class | (mark) | |
|---|---|---|---|
| 0–10 | 5 | 5 | 25 |
| 10–20 | 8 | 15 | 120 |
| 20–30 | 7 | 25 | 175 |

Σ, Σ. Mean = 320/20 = 16.

**When to use**: small class marks; arithmetic stays manageable.

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

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,…A distribution has the equal-width classes 500–520, 520–540, 540–560, 560–580, 580–600…For the distribution 0–10: 5, 10–30: 12, 30–35: 9, 35–60: 4 the class widths are 10, 20,…The mean of the following data is 46. Class 0–20: 7, 20–40: f, 40–60: 12, 60–80: 8,…