Maths · Measures of dispersion; calculation of mean, median, mode of grouped and ungrouped data
Class 12 interval frequency 10 5 What is the mode for the grouped data?
Class \( \begin{array}{cccc}2- & 4- & 6- & 8- \\ 4 & 6 & 8 & 10\end{array} \) \( 10- \) 12 interval frequency \( 2 \quad 4 \quad 6 \) 10 5 What is the mode for the grouped data?
- A. 10 .5
- B. 12.5
- C. 13.7
- D. 9.1
Step-by-step solution
The modal class is 8-10 with frequency 10. Using the formula for mode of grouped data: Mode = L + ((f1 - f0) / (2f1 - f0 - f2)) * h, where L = 8 (lower limit of modal class), h = 2 (class width), f1 = 10, f0 = 6, f2 = 5. Calculation: Mode = 8 + ((10 - 6) / (2*10 - 6 - 5)) * 2 = 8 + (4 / 9) * 2 = 8 + 8/9 ≈ 8.89. Rounded to one decimal gives 9.1, which matches option D.
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