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NTPC Graduate Tier 1 2025 Shift-2 📅 05 Jun, 2025

If the mode of the following data is 140, then what is the value of x?
Class125-130130-135135-140140-145145-150
Frequency303033x31

A
34
B
33
C
47
D
46
Result Summary
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NTPC Graduate Tier 1
2025 • 05 Jun, 2025 • Shift-2
If the mode of the following data is 140, then what is the value of x?
Class125-130130-135135-140140-145145-150
Frequency303033x31
Correct Answer
33
Modal Class Identification: The definitive mode is given as precisely 140. This value falls perfectly on the boundary of the class interval 140-145, effectively......
Ref/Book : NTPC Graduate Tier 1 2025
Ref. Subject Mathematics
Chapter -
Ref. Topic Statistics
Pg. No -
💡 Analysis & Explanation
Modal Class Identification ▼
The definitive mode is given as precisely 140. This value falls perfectly on the boundary of the class interval 140-145, effectively establishing it as the active modal class. Thus, lower limit (L) = 140.
Formula Structuring ▼
The statistical formula is Mode = L + [(f₁ - f₀) / (2f₁ - f₀ - f₂)] * h. Here, L=140, f₁=x, f₀=33 (previous frequency), f₂=31 (subsequent frequency), and class width (h)=5.
Algebraic Simplification ▼
Substitute the known values into the equation: 140 = 140 + [(x - 33) / (2x - 33 - 31)] * 5.
Zero Condition Check ▼
Moving 140 to the left side results in 0 = [(x - 33) / (2x - 64)] * 5. For this fractional equation to equal zero, the numerator itself must exclusively be zero.
Conclusion ▼
Therefore, x - 33 = 0, which directly resolves to x = 33.
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