Measures of Central Tendency and DispersionMCQMTP June 2023 Series IIQuestion 2920 of 473
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The average of 6\displaystyle 6 numbers is $30$. If the average of the first four is $25$ and that of the last three is $35$, the fourth number is

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Correct Answer

✅ Option a — 25

All Options:

  • A25
  • B30
  • C35
  • D40

Detailed Solution & Explanation

**Step 1: Find the total sum of all 6 numbers.** Sum of all 6=6×30=180Sum of all 6=6\displaystyle \text{Sum of all 6} = 6 ×\displaystyle \times 30 = 180 **Step 2: Find sum of first 4 numbers.** Sum of first 4=4×25=100Sum of first 4=4\displaystyle \text{Sum of first 4} = 4 ×\displaystyle \times 25 = 100 **Step 3: Find sum of last 3 numbers.** Sum of last 3=3×35=105Sum of last 3=3\displaystyle \text{Sum of last 3} = 3 ×\displaystyle \times 35 = 105 **Step 4: Find the 4th number.** Note: The 6 numbers are n1,n2,n3,n4,n5,n6\displaystyle n_1, n_2, n_3, n_4, n_5, n_6. - First 4: n1+n2+n3+n4=100\displaystyle n_1+n_2+n_3+n_4 = 100 - Last 3: n4+n5+n6=105\displaystyle n_4+n_5+n_6 = 105 - All 6: n1+n2+n3+n4+n5+n6=180\displaystyle n_1+n_2+n_3+n_4+n_5+n_6 = 180 Adding first 4 and last 3: (n1+n2+n3+n4)+(n4+n5+n6)=100+105=205(n_1+n_2+n_3+n_4) + (n_4+n_5+n_6) = 100 + 105 = 205 But total sum =180\displaystyle = 180, so: 205−n4=180  ⟹  n4=205−180=25205 - n_4 = 180 \implies n_4 = 205 - 180 = 25 Hence, **Option A** is the correct answer.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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