Central Tendency & DispersionPYQ Nov. 19Question 2990 of 473
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Find the mode of the following data:Class | 3-6 | 6-9 | 9-12 | 12-15 | 15-18 | 18-21Freq. | 2 | 5 | 10 | 23 | 21 | 12

Options

A25\displaystyle 25
B4.6\displaystyle 4.6
C14.6\displaystyle 14.6
D13.5\displaystyle 13.5
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Correct Answer

✅ Option c — 14.6\displaystyle 14.6

All Options:

  • A25\displaystyle 25
  • B4.6\displaystyle 4.6
  • C14.6\displaystyle 14.6
  • D13.5\displaystyle 13.5

Detailed Solution & Explanation

**Step 1: Identify the modal class.** Frequencies: 3-6: 2, 6-9: 5, 9-12: 10, 12-15: 23, 15-18: 21, 18-21: 12. The highest frequency is 23, so the modal class is **12-15**. **Step 2: Identify values for the mode formula.** - L\displaystyle L = lower boundary of modal class = 12\displaystyle 12 - f1\displaystyle f_1 = frequency of modal class = 23\displaystyle 23 - f0\displaystyle f_0 = frequency of pre-modal class = 10\displaystyle 10 - f2\displaystyle f_2 = frequency of post-modal class = 21\displaystyle 21 - h\displaystyle h = class width = 3\displaystyle 3 **Step 3: Apply the formula.** Mode=L+f1−f02f1−f0−f2×h\text{Mode} = L + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h =12+23−102(23)−10−21×3= 12 + \frac{23 - 10}{2(23) - 10 - 21} \times 3 =12+1346−31×3= 12 + \frac{13}{46 - 31} \times 3 =12+1315×3= 12 + \frac{13}{15} \times 3 =12+3915=12+2.6=14.6= 12 + \frac{39}{15} = 12 + 2.6 = 14.6 Hence, **Option C** is the correct answer.

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