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The mean (arithmetic mean) of three consecutive even integer
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Updated on: 16 Feb 2020, 08:33
Updated on: 16 Feb 2020, 08:33
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The mean (arithmetic mean) of three consecutive even integers is 24. What is the value of highest number among the three?
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The mean (arithmetic mean) of three consecutive even integer
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15 Feb 2020, 16:26
15 Feb 2020, 16:26
Asif123 wrote:
the mean (arithmetic mean) of three consecutive even integers is 24. What is the value of highest number among the three?
Approach #1
If the numbers in a set of values are equally spaced, then the median and mean of that set are equal
Since three consecutive even integers are equally spaced, we know that the median and mean are both 24
If the median is 24, then the middle number is 24, which means the biggest even integer in the set is 26
Answer: 26
Approach #2
Let x = the smallest integer
So, x + 2 = the next consecutive EVEN integer
And x + 4 = the next consecutive EVEN integer
If the average is 24 we can write: \(\frac{x + (x+2) + (x+4)}{3 }= 24\)
Multiply both sides by 3 to get: \(x + (x+2) + (x+4) = 72\)
Simplify: \(3x + 6 = 72\)
Solve: x = 22
This means the smallest number is 22, the next number is 24, and the last (greatest) number is 26
Answer: 26
Cheers,
Brent
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The mean (arithmetic mean) of three consecutive even integer
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16 Sep 2022, 22:10
16 Sep 2022, 22:10
Given that The mean (arithmetic mean) of three consecutive even integers is 24 and we need to find the value of highest number among the three
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Theory
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Let the three consecutive even numbers be x - 2 , x, x + 2
=> Mean = \(\frac{Sum}{3}\) = \(\frac{(x - 2) + x + (x + 2) }{ 3}\) = 24 (Given)
=> \(\frac{3x}{3}\) = x = 24
=> Highest number = x + 2 = 24 + 2 = 26
So, Answer will be 26.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
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Theory
- ‣‣‣ Mean or Average = (Sum Of All The Numbers) / (Total Number Of Numbers)
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Let the three consecutive even numbers be x - 2 , x, x + 2
=> Mean = \(\frac{Sum}{3}\) = \(\frac{(x - 2) + x + (x + 2) }{ 3}\) = 24 (Given)
=> \(\frac{3x}{3}\) = x = 24
=> Highest number = x + 2 = 24 + 2 = 26
So, Answer will be 26.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
