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# the average of 11 numbers is 11.9. if the average of first six is 10.5 and that of the last six is 9.4 the sixth number is?

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## The average of 11 numbers is 10.9 . If the average of the first six is 10.5 and the average of last six is 11.4 , find the middle (sixth) number.

Click here👆to get an answer to your question ✍️ The average of 11 numbers is 10.9 . If the average of the first six is 10.5 and the average of last six is 11.4 , find the middle (sixth) number.

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## 10.45

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## The average of 11 numbers is 10.9. If the average

Average Questions & Answers : The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is

148 Q:

The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is :

A) 10.5 B) 11.5 C) 12.5 D) 13.5 Answer:   B) 11.5 Explanation:

Middle numbers  =  [(10.5 x 6 + 11.4 x 6) - 10.9 x 11] = (131.4 - 119-9) = 11.5.

Subject: Average - Quantitative Aptitude - Arithmetic Ability

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## The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is?

Answer (1 of 2): Not certain if it is my calculation or the information given that gives me an answer that cannot be correct! Let middle number be M. All eleven set of numbers ( S) add up to 119.9 (11×10.9) First six (F6) add up to 63.0 (6×10.5) Last six (L6) add up to 68.4 (6×11.4) F6 + L6 ...

The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is?

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Not certain if it is my calculation or the information given that gives me an answer that cannot be correct!

Let middle number be M.

All eleven set of numbers ( S) add up to 119.9 (11×10.9)

First six (F6) add up to 63.0 (6×10.5)

Last six (L6) add up to 68.4 (6×11.4)

F6 + L6 = 131.4

The middle number has been added twice in the sum of F6 + L6.

So S = F6+L6-M M = F6+L6-S

M = 131.4 - 119.9 = 11.5

But if the average of the last 6 is 11.4 the middle number of the full set cannot be 11.5 as this would need to be the lowest number in this set and an average of 11.4 means that there must be numbers in that set

Related questions

The average of 17 numbers is 10.9, the first 9 numbers have an average of 11.4, what is the middle number?

The average of 17 numbers is 10.9. If the average of the first nine numbers are 10.5 and that of the last nine numbers is 11.4, what is the middle number?

The average of 11 numbers is 15. If the average of the first six numbers is 10.5 and that of the last 6 numbers is 11.4, then what is the middle number?

Average of 11 numbers is 20. If the average of six first numbers is 20. And average of last six numbers is 19 then what is the middle number?

The average of 11 numbers is 30. If the average of the first six numbers is 17.5 and that of the last six is 42.5, then what is the sixth number?

The average of 11 11 numbers is 10.9 10.9 . Total of 11=10.9×11=119.9 11=10.9×11=119.9 .

The average of first the first six number is

10.5 10.5 . Total =10.5×6=63 =10.5×6=63 .

The average of the last six number is

11.4 11.4 . Total =11.4×6=68.4 =11.4×6=68.4 .

so, the middle number is

119.9−(63+68.4)=119.9–131.4=11.5

119.9−(63+68.4)=119.9–131.4=11.5

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Priyanshi Agarwal

Studied Earth ScienceUpvoted by

Balázs Iván József

, Master Mathematics, Eötvös Loránd University (1983)2y

Related

The average of two numbers is x+y. If one number is x, what is the other number?

Let the unknown number be z.

(x+z)/2=x+y Therefore, z=x+2y. Yash Londhe

Former Lead Software Engineer at Indiabulls Consumer Finance Ltd (2019–2020)2y

Related

The average of 40 numbers is 36. The average of first 25 numbers is 19 and the average of the next 14 numbers is 41. What is the last number?

Sum of “n” numbers whose average is “a” = n * a (* denotes multiplication).

Using the above trick:

Sum of 40 numbers = 40 * 36 = 1440

Sum of first 25 numbers = 25 * 19 = 475

Sum of next 14 numbers = 14 * 41 = 574

Sum of 40 numbers = Sum of first 25 numbers + Sum of next 14 numbers + “unknown/last number” (say x)

1440 = 475 + 574 + x

so x = 391

So last number is 391.

Hope it helps!! Arjun Gupta

Lives in Mumbai, Maharashtra, India (2019–present)Author has 354 answers and 13.4M answer views5y

Related

The average of 17 numbers is 10.9, the first 9 numbers have an average of 11.4, what is the middle number?

Hey there! If we know the average of the last 9 numbers, then we can find the middle number (index 9).

Think it this way:

-You know the sum of all the 17 numbers, because you know the average. Let this sum be ‘A’

-You know the sum of first 9 numbers, again because you know the average. Let this sum be ‘B’

If you have sum of the last 9 numbers, let's call it C, then (B + C - A) will give you the middle number since this number has been added twice (once in B, and once in C) and haas been subtracted only once (in A).

Hence, the data is insufficient.

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Prasenjit Wakode

B.E. in Electrical Engineering & M.Tech in Power Electronics and Electrical Drives, Indian Institute of Technology, Kharagpur (IIT KGP) (Graduated 2011)Author has 677 answers and 1.1M answer views4y

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The average of 17 numbers is 45. The average of the first 9 of these numbers is 51, and the last 9 of these numbers is 36. What is the ninth number?

Let, sum of first 8 numbers be ‘x’ and sum of last 8 numbers be ‘y’ . Let the 9th number be ‘a’ .

As per 1st condition,

x+a+y 17 =45 x+a+y17=45

As per second condition,

x+a 9 =51 x+a9=51

As per third condition,

a+y 9

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Mohammed 8 day ago

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