The mean of fourteen consecutive integers is 27 1/2. If the integers a

Question

The mean of fourteen consecutive integers is  27 \frac{1}{2} . If the integers are arranged in increasing order. what is the mean of the largest seven integers?

A. 24
B. 25
C. 31
D. 34
E. 35

Lipun · Answer

Mean = 27.5
Since number of elements is even and elements are consecutive integers, the mean will the average of 7th and 8th integers => 7th element = 27
=> first element = 21
=> 4th element = 24

Edited: mean of largest 7 numbers will be the 11th integer
11th integer = 31
Ans: C

dimri10 · Answer

because they are Even numbers the mean is between 7th and 8th items so 27 an 28

28 is the smallest of the largest seven numbers and 34 is the largest, so 28+34/2= 31

rahulsinha2103 · Answer

(C). mean = 55/2. Since there are 14 consecutive numbers, mean 55/2 is also mean of 7th and 8th numbers. Therefore 7th number is 27 and 8th is 28.
So, largest 7 numbers are - 28, 29, 30, 31, 32, 33, 34. And mean of these 7 numbers would be 4th number - 31.

nkme2007 · Answer

As it is mentioned that the  integers are consecutive

Let the first integer be  a , the  14th integer will be a+13d, where d = 1

Average of the 14 integers = { }/2 = 27.5

=> a+6.5 = 27.5

=> a = 21

Finally,  8th integer = a+7d = 28 
And,  14th integer = a+13d = 34

Mean of last 7 integers = (28+34)/2 = 31

OA: C

Fdambro294 · Answer

Rule: in any Evenly Spaced Set (including Consecutive Integers), the Median = Mean

Rule: in a Set of Consecutive Integers, if there is an Even No. of Terms, the Median = Mean = will take the Form of X.5 because it will be in between the Middle 2 Terms in the Set --- when written in Ascending Order

If there are 14 Consecutive Integers written in Ascending Order and the Median = Mean = 27.5 ----

1st) there will be 7 Consecutive Integers less than the Mean and 7 Consecutive Integers greater than the Mean

and

2nd) 28 will be the 1st Integer of the 7 Consecutive Integers greater than the Mean

The Mean of these 7 Consecutive Integers from   inclusive = Median/Middle Number because there is an Odd No. of Terms. ---- therefore, the Mean = 31

illustration

28 ---- 29 ----- 30 -----31 -----32 ----33 -----34

Evenly Spaced Set, so the Median = Mean = 31

-C-

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The mean of fourteen consecutive integers is 27 1/2. If the integers a

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The mean of fourteen consecutive integers is 27 1/2. If the integers a

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