In a class of 25 students, the following frequency distribution for marks (intervals of 10) is recorded: 40–49: 3, 50–59: 7, 60–69: 10, 70–79: 4, 80–89: 1. Find the approximate mean using class marks.
Answer
61.7
The correct answer is 61.7 — Thus the approximate mean is 61.7.
Step-by-step solution
- Calculate the class mark for each interval: (40+49)/2=44.5, (50+59)/2=54.5, (60+69)/2=64.5, (70+79)/2=74.5, (80+89)/2=84.5.
- Multiply each class mark by its frequency: 3×44.5=133.5, 7×54.5=381.5, 10×64.5=645, 4×74.5=298, 1×84.5=84.5.
- Sum these products: 133.5+381.5=515, 515+645=1160, 1160+298=1458, 1458+84.5=1542.5.
- Divide by the total number of students (25): 1542.5÷25=61.7.
- Thus the approximate mean is 61.7.
Common mistake: Using the lower or upper bound of intervals instead of class marks
Concept tested: Mean using class marks
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