Central Tendency & DispersionPYQ Nov. 19Question 2992 of 473
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Find the mode of the following:0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-607 | 14 | 22 | 34 | 20 | 19

Options

A32\displaystyle 32
B34.61\displaystyle 34.61
C25.42\displaystyle 25.42
D35\displaystyle 35
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Correct Answer

✅ Option b — 34.61\displaystyle 34.61

All Options:

  • A32\displaystyle 32
  • B34.61\displaystyle 34.61
  • C25.42\displaystyle 25.42
  • D35\displaystyle 35

Detailed Solution & Explanation

**Step 1: Identify the modal class.** Frequencies: 0-10: 7, 10-20: 14, 20-30: 22, 30-40: 34, 40-50: 20, 50-60: 19. Highest frequency = 34, so modal class is **30-40**. **Step 2: Identify values for the mode formula.** - L=30\displaystyle L = 30 - f1=34\displaystyle f_1 = 34 - f0=22\displaystyle f_0 = 22 (pre-modal class frequency) - f2=20\displaystyle f_2 = 20 (post-modal class frequency) - h=10\displaystyle h = 10 **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+34−222(34)−22−20×10= 30 + \frac{34 - 22}{2(34) - 22 - 20} \times 10 =30+1268−42×10= 30 + \frac{12}{68 - 42} \times 10 =30+1226×10= 30 + \frac{12}{26} \times 10 =30+12026=30+4.615≈34.61= 30 + \frac{120}{26} = 30 + 4.615 \approx 34.61 Hence, **Option B** is the correct answer.

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