Central Tendency & DispersionICAI SM, MTP Nov 20Question 2890 of 473
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Two variables assume the values 1,2,…,5\displaystyle 1, 2, \dots, 5 with frequencies as 1,2,3,…,5\displaystyle 1, 2, 3, \dots, 5 then what is the AM?

Options

A113\displaystyle \frac{11}{3}
B158\displaystyle \frac{15}{8}
C4.86
D10
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Correct Answer

✅ Option a — 113\displaystyle \frac{11}{3}

All Options:

  • A113\displaystyle \frac{11}{3}
  • B158\displaystyle \frac{15}{8}
  • C4.86
  • D10

Detailed Solution & Explanation

**Step 1: Set up the frequency table.** | Value (x\displaystyle x) | Frequency (f\displaystyle f) | fx\displaystyle fx | |-------------|-----------------|------| | 1 | 1 | 1 | | 2 | 2 | 4 | | 3 | 3 | 9 | | 4 | 4 | 16 | | 5 | 5 | 25 | **Step 2: Compute totals.** ∑f=1+2+3+4+5=15\sum f = 1+2+3+4+5 = 15 ∑fx=1+4+9+16+25=55\sum fx = 1+4+9+16+25 = 55 **Step 3: Compute AM.** xˉ=∑fx∑f=5515=113\bar{x} = \frac{\sum fx}{\sum f} = \frac{55}{15} = \frac{11}{3} Hence, **Option A** is the correct answer.

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