Question 12

Mathematics Statistics Medium

Consider the following grouped data: $$ \begin{array}{|c|c|} \hline \text{Class Interval} & \text{Number of Students} \\ \hline 20-25 & 8 \\ 25-30 & 14 \\ 30-35 & 20 \\ 35-40 & 18 \\ 40-45 & 10 \\ 45-50 & 6 \\ \hline \end{array} $$

(A) 32.14
(B) 31.67
(C) 33.75
(D) 34.12
✓ Correct Answer: Option C Verified Solution

📘 Step-by-Step Solution & Detailed Explanation:

The modal class is the class interval with the highest frequency. Here, the highest frequency is 20, which corresponds to the class interval 30-35. For the modal class 30-35: Lower limit (\( L \)) = 30 Frequency of the modal class (\( f_1 \)) = 20 Frequency of the preceding class (\( f_0 \)) = 14 Frequency of the succeeding class (\( f_2 \)) = 18 Class width (\( h \)) = 5 The formula for calculating Mode is: \[ Mode = L + \left( \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \right) \times h \] Substitute the values: \[ Mode = 30 + \left( \frac{20 - 14}{2(20) - 14 - 18} \right) \times 5 \] \[ Mode = 30 + \left( \frac{6}{40 - 32} \right) \times 5 \] \[ Mode = 30 + \left( \frac{6}{8} \right) \times 5 \] \[ Mode = 30 + 3.75 = 33.75 \]

Practice Similar Statistics Questions

Reinforce your conceptual grasp with related questions from MAH MCA CET 2026:

Q11 The distances (in meters) for seven throws of a shotputter are: 14.5,...
Solve →
Q13 An investigator has missed a value while collecting data in an experiment....
Solve →
Q15 For a given sample, the computed values of the variance and fourth central...
Solve →
Q1 The set \( (A B)∩ C \) is not equal to
Solve →
Q2 Define a relation \( \) on the set \( \ 1,2,3,4,5,6,7,8,9,10\ \) by \( a b...
Solve →
Full-Length Test Series

Prepare for MAH MCA CET Under Real Exam Conditions

Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.

Start Free Mock Test Series →