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The arithmetic mean of 1, 5, 9, 2, 2, 3, x, a, 9 is 5. Find the arithmetic mean of a and x.
1. 14
2. 7
3. 11
4. 10

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Correct Answer - Option 2 : 7

Given:

Data = (1, 5, 9, 2, 2, 3, x, a, 9)

Arithmetic mean = 5

Formula Used:

Arithmetic mean = Sum of terms/Number of terms

Calculations:

Number of terms = 9

Sum of terms = 1 + 5 + 9 + 2 + 2 + 3 + x + a + 9

⇒ Sum of terms = 31 + a + x

Arithmetic mean = Sum of terms/Number of terms

⇒ 5 = (31 + a + x)/9

⇒ (31 + a + x) = 5 × 9

⇒ (31 + a + x) = 45

⇒ a + x = 45 - 31 = 14

Arithmetic mean of a and x = (a + x)/2

⇒ Arithmetic mean of a and x = 14/2

⇒ Arithmetic mean of a and x = 7

∴ The arithmetic mean of a and x is 7.

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