Central Tendency & DispersionPYQ Jun 23Question 3004 of 473
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Find the mode of the following data:X | F(x)25-30 | 2030-35 | 5335-40 | 4240-45 | 4245-50 | 4150-55 | 43

Options

A31.75\displaystyle 31.75
B30.75\displaystyle 30.75
C33.75\displaystyle 33.75
D35.75\displaystyle 35.75
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Correct Answer

✅ Option c — 33.75\displaystyle 33.75

All Options:

  • A31.75\displaystyle 31.75
  • B30.75\displaystyle 30.75
  • C33.75\displaystyle 33.75
  • D35.75\displaystyle 35.75

Detailed Solution & Explanation

**Step 1: Identify the modal class.** Frequencies: 25-30: 20, 30-35: 53, 35-40: 42, 40-45: 42, 45-50: 41, 50-55: 43. Highest frequency = 53, so modal class is **30-35**. **Step 2: Identify values for the mode formula.** - L=30\displaystyle L = 30 - f1=53\displaystyle f_1 = 53 - f0=20\displaystyle f_0 = 20 (pre-modal class frequency) - f2=42\displaystyle f_2 = 42 (post-modal class frequency) - h=5\displaystyle h = 5 **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 =30+53−202(53)−20−42×5= 30 + \frac{53 - 20}{2(53) - 20 - 42} \times 5 =30+33106−62×5= 30 + \frac{33}{106 - 62} \times 5 =30+3344×5= 30 + \frac{33}{44} \times 5 =30+16544=30+3.75=33.75= 30 + \frac{165}{44} = 30 + 3.75 = 33.75 This matches **Option C** (33.75\displaystyle 33.75), not Option B. The computed answer is 33.75\displaystyle 33.75. Hence, **Option C** is the correct answer.

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