The marks obtained by 30 students of tenth class in a school in mathematics paper consisting of 100 marks are

Question

The marks obtained by 30 students of tenth class in a school in mathematics paper consisting of 100 marks are presented in the following table. Find the arithmetic mean of the data. Class interval No. of students 10 – 25 2 25 – 40 3 40 – 55 7 55 – 70 6 70 – 85 6 85 - 100 6

Examoogle · Accepted Answer

The correct answer is Option B: 62. Use the Assumed Mean Method. Pick a middle class mark as 'a' (say 62.5), calculate deviations $d_i = x_i - a$, find $\sum f_i d_i$, and use $\bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}$.

Step-by-Step Solution & Concepts:
Shortcut Trick: Use the Assumed Mean Method. Pick a middle class mark as 'a' (say 62.5), calculate deviations $d_i = x_i - a$, find $\sum f_i d_i$, and use $\bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}$.

Formula Used: $$\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$$

Given: Class intervals: 10-25, 25-40, 40-55, 55-70, 70-85, 85-100. Frequencies: 2, 3, 7, 6, 6, 6. Total students N = 30.

Steps: Calculate class marks (mid-points): Calculate the mid-point $x_i = \frac{	ext{lower limit} + 	ext{upper limit}}{2}$ for each interval.. Calculate product $f_i x_i$: Multiply each frequency $f_i$ by its respective class mark $x_i$.. Sum the values: Find the sum of products $\sum f_i x_i = 35 + 97.5 + 332.5 + 375 + 465 + 555 = 1860$.. Calculate mean: Divide the total sum by the total number of students ($N=30$).

Answer: B is correct because the calculated arithmetic mean of the provided frequency distribution is 62.

Exam Tip: This is the foundation for calculating Median and Mode for grouped data, where identifying the correct class intervals is essential.

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Option A: 72

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Option C: 65

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Option D: 76 Question ID : 441009340510 Option 1 ID : 4410091328064 Option 2 ID : 4410091328063 Option 3 ID : 4410091328062 Option 4 ID : 4410091328065 Status : Not Attempted and Marked For Review Chosen Option : --

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