In a survey of 200 students, the following frequencies of marks in class 10 are recorded: 0-10: 4, 10-20: 8, 20-30: 5, 30-40: 7. Find the class marks for each interval and calculate the mean using the class marks.

medium 3 marks Class 6 · Mathematics · Data Handling

Answer

21.25

The correct answer is 21.25 — Divide the weighted sum by total frequency: $510 \div 24 = 21.25$

Step-by-step solution

Compute the class mark (midpoint) for each interval: \begin{align*}0-10&:\frac{0+10}{2}=5\\10-20&:\frac{10+20}{2}=15\\20-30&:\frac{20+30}{2}=25\\30-40&:\frac{30+40}{2}=35\end{align*}
Multiply each class mark by its frequency: \begin{align*}5\times4=20\\15\times8=120\\25\times5=125\\35\times7=245\end{align*}
Sum these products: $20 + 120 + 125 + 245 = 510$
Sum the frequencies: $4 + 8 + 5 + 7 = 24$
Divide the weighted sum by total frequency: $510 \div 24 = 21.25$

Common mistake: Using incorrect class marks or miscounting total frequencies

Concept tested: Mean from frequency distribution using class marks