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The average of 13 numbers is 77. If a 14th number is included, then the average becomes 83. What is the 14th number?
1. 163
2. 164
3. 166
4. 161

1 Answer

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Correct Answer - Option 4 : 161

Given:

Average of 13 numbers = 77

Average after 14th number is included = 83

Formula used:

Sum of observations = Average × Number of observations

Calculation:

Sum of 13 numbers = 13 × 77 = 1001

Sum of 14 numbers = 14 × 83 = 1162

14th number = 1162 – 1001

⇒ 161

∴ The 14th number is 161

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