A set of 12 numbers has an arithmetic mean of 20. if the numbers 10 and 14 are removed from the set, what is the arithmetic mean of the 10 numbers remaining in the set?

A set of 12 numbers has an arithmetic mean of 20. if the numbers 10 and 14 are removed from the set, what is the arithmetic mean of the 10 numbers remaining in the set?

Question
Polynomial arithmetic
asked 2020-10-18
A set of 12 numbers has an arithmetic mean of 20. if the numbers 10 and 14 are removed from the set, what is the arithmetic mean of the 10 numbers remaining in the set?

Answers (1)

2020-10-19
For a set of positive numbers \(x_{1},\ x_{2},\ \cdots,\ X_{n}\), the arithmetic mean is given as \(\text{Arithmetic Mean}=\ \frac{x_{1}\ +\ x_{2}\ +\ \cdots\ +\ x_{n}}{n}\) Now, set of 12 numbers which includes 10 and 14 has an arithmetic mean of 20. Let x be the sum of the remaining 10 numbers. \(AM =\ \frac{x\ +\ 10\ +\ 14}{12} = 20\)
\(\frac{x\ +\ 24}{12}=20\)
\(x=240\ -\ 24=216\) Now, we find the arithmetic mean of the remaining 10 numbers whose sum is 216. \(\therefore\ \frac{x}{10}=\ \frac{216}{10}=21.6\)
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