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The average (arithmetic mean) of y numbers is x. If 30 is ad
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30 Jun 2018, 09:52
30 Jun 2018, 09:52
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The average (arithmetic mean) of y numbers is x. If 30 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?
A x/7 - 5
B x/6 - 6
C x/6 - 5
D x/5 - 7
E x/5 - 6
A x/7 - 5
B x/6 - 6
C x/6 - 5
D x/5 - 7
E x/5 - 6
Re: The average (arithmetic mean) of y numbers is x. If 30 is ad
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01 Jul 2018, 12:50
01 Jul 2018, 12:50
1st condition states that
(Sum of numbers) / Total numbers (y) = x ---> Rearranging
Sum of Numbers = y * x ---> (1)
2nd Condition states that
(Sum of Numbers + 30) / Total Numbers (y + 1) = (x - 5) ----> Rearranging
Sum of Numbers + 30 = (x - 5) * (y + 1)
Substituting from (1) and solving
y = x/5 - 7.....which is D above
(Sum of numbers) / Total numbers (y) = x ---> Rearranging
Sum of Numbers = y * x ---> (1)
2nd Condition states that
(Sum of Numbers + 30) / Total Numbers (y + 1) = (x - 5) ----> Rearranging
Sum of Numbers + 30 = (x - 5) * (y + 1)
Substituting from (1) and solving
y = x/5 - 7.....which is D above
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The average (arithmetic mean) of y numbers is x. If 30 is ad
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08 Jul 2021, 08:22
08 Jul 2021, 08:22
Theory: Average = \(\frac{Sum Of All The Values}{Total Number Of Values}\)
The average (arithmetic mean) of y numbers is x
Let the Sum of y numbers is denoted by \(S_y\)
Using, Average = \(\frac{Sum Of All The Values}{Total Number Of Values}\), We get
x = \(\frac{S_y}{y}\)
=> \(S_y\) = xy
30 is added to the set of numbers, then the average will be x - 5
Now, total number of numbers become y + 1 [ 30 is the extra number added to y numbers making the total number of numbers as y + 1]
Sum of y+1 numbers = \(S_y\) + 30 = xy + 30
Using, Average = \(\frac{Sum Of All The Values}{Total Number Of Values}\), We get
x-5 = \(\frac{xy + 30}{y+1}\)
=> (x-5)*(y+1) = xy + 30
=> xy - 5y + x - 5 = xy + 30
=> x - 5 - 30 = 5y
=> 5y = x - 35
=> y = \(\frac{x-35}{5}\) = \(\frac{x}{5}\) - \(\frac{35}{5}\)
=> y = \(\frac{x}{5}\) - 7
So, answer will be D
Hope it helps!
To learn more about Statistics watch the following video
The average (arithmetic mean) of y numbers is x
Let the Sum of y numbers is denoted by \(S_y\)
Using, Average = \(\frac{Sum Of All The Values}{Total Number Of Values}\), We get
x = \(\frac{S_y}{y}\)
=> \(S_y\) = xy
30 is added to the set of numbers, then the average will be x - 5
Now, total number of numbers become y + 1 [ 30 is the extra number added to y numbers making the total number of numbers as y + 1]
Sum of y+1 numbers = \(S_y\) + 30 = xy + 30
Using, Average = \(\frac{Sum Of All The Values}{Total Number Of Values}\), We get
x-5 = \(\frac{xy + 30}{y+1}\)
=> (x-5)*(y+1) = xy + 30
=> xy - 5y + x - 5 = xy + 30
=> x - 5 - 30 = 5y
=> 5y = x - 35
=> y = \(\frac{x-35}{5}\) = \(\frac{x}{5}\) - \(\frac{35}{5}\)
=> y = \(\frac{x}{5}\) - 7
So, answer will be D
Hope it helps!
To learn more about Statistics watch the following video
