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Five numbers in a set are arranged from least to greatest. I [#permalink]
09 Dec 2017, 18:18

Expert's post

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Question Stats:

100% (01:08) correct
0% (00:00) wrong based on 11 sessions

Five numbers in a set are arranged from least to greatest. If the median of the first two numbers is 13 and the average (arithmetic mean) of the remaining numbers is 23, what is the average (arithmetic mean) of the entire set?

Re: Five numbers in a set are arranged from least to greatest. I [#permalink]
29 Dec 2017, 13:19

Expert's post

Explanation

Take the problem a piece at a time. If a set has only two numbers, the median is the average of those two numbers. Set up average wheels for each of the first two averages.

For the first one, two numbers that average 13 total to 26. For the second average, three numbers that average 23, so the must have a total of 69. Set up one final average wheel for all five numbers: 5 numbers total 95. Solve for the average, and you should get 19 from \(95 \div 5\).
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Re: Five numbers in a set are arranged from least to greatest. I [#permalink]
09 Jan 2018, 13:06

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Expert's post

sandy wrote:

Five numbers in a set are arranged from least to greatest. If the median of the first two numbers is 13 and the average (arithmetic mean) of the remaining numbers is 23, what is the average (arithmetic mean) of the entire set?

Five numbers in a set are arranged from least to greatest. Let the number be a, b, c, d, and e (where a < b < c < d < e)

The median of the first two numbers is 13 So, (a + b)/2 = 13 Multiply both sides by 2 to get: a + b = 26

The average (arithmetic mean) of the remaining numbers is 23 So, (c + d + e)/3 = 23 Multiply both sides by 3 to get: c + d + e = 69

What is the average (arithmetic mean) of the entire set? Average of entire set = (a + b + c + d + e)/5 = (26 + 69)/5 = 95/5 = 19

Answer: 19

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