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Set H contains five positive integers such that the mean, median, mod
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09 Sep 2022, 06:12
09 Sep 2022, 06:12
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Set H contains five positive integers such that the mean, median, mode, and range are all equal. The sum of the data is 25.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
the smallest possible number in set H |
6 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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Re: Set H contains five positive integers such that the mean, median, mod
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09 Sep 2022, 07:32
09 Sep 2022, 07:32
2
Set H contains five positive integers such that the mean, median, mode, and range are all equal. The sum of the data is 25.
sum=25 of 5 positive integers so we know mean = 5 that means median mode range are also all equal to 5.
mode=5 means 5 is most repeated so we have atleast 2 5's
For the median to be 5, with two 5s, there must be at least one number above 5
The sum of remaining 3 numbers would atmax be x+y+z= 15 ( 25-10, 2 5s for 5 to be the mode)
x,y,z are the remaining numbers and distinct values( if there are 2 5's only we will know that later) lets assume x>y>z
for range to be 5, x=z+5
2z+y+5=15
2z+y=10
if y=z, then y=3 (rounded off) so z<3.5 so possible values for z,y,x= {1,8,6},{2,6,7},{3,4,8}
we know x>y>z that is only possible in the 2nd and 3rd combination so we get
2,5,5,6,7 or 3,4,5,5,8
the smallest possible number is either 2 or 3 and both of them are less than quantity B so
Quantity B is greater
sum=25 of 5 positive integers so we know mean = 5 that means median mode range are also all equal to 5.
mode=5 means 5 is most repeated so we have atleast 2 5's
For the median to be 5, with two 5s, there must be at least one number above 5
The sum of remaining 3 numbers would atmax be x+y+z= 15 ( 25-10, 2 5s for 5 to be the mode)
x,y,z are the remaining numbers and distinct values( if there are 2 5's only we will know that later) lets assume x>y>z
for range to be 5, x=z+5
2z+y+5=15
2z+y=10
if y=z, then y=3 (rounded off) so z<3.5 so possible values for z,y,x= {1,8,6},{2,6,7},{3,4,8}
we know x>y>z that is only possible in the 2nd and 3rd combination so we get
2,5,5,6,7 or 3,4,5,5,8
the smallest possible number is either 2 or 3 and both of them are less than quantity B so
Quantity B is greater
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Re: Set H contains five positive integers such that the mean, median, mod
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16 Sep 2022, 21:50
16 Sep 2022, 21:50
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Given that Set H contains five positive integers such that the mean, median, mode, and range are all equal. The sum of the data is 25. And we need to find the smallest possible number in set H
=======================================================================
Theory
=======================================================================
As there are 5 numbers so Median = Middle term = Third Term
Mean = \(\frac{Sum}{5}\) = \(\frac{25}{5}\) = 5
Mean = Median = Mode = Range = Third Term = 5
So, the set is _ , _ , 5 , _ , _
Now, the mode is 5 so 5 has to occur the maximum number of times.
Let's say 5 occurs 2 times so we have two possibilities
_ , 5 , 5 , _ , _
_ , _ , 5 , 5 , _
In, _ , 5 , 5 , _ , _ case we will have two numbers bigger than 5. Lets say 6 and 7 and range is 5 so first number will become 7-5 = 2
So the set becomes 2, 5, 5, 6, 7 and it satisfies all conditions
_ , _ , 5 , 5 , _ case lets take the two smaller numbers as 3 and 4. So the largest number will become 3 + 5 = 8
So the set becomes 3, 4, 5, 5, 8 and it satisfies all conditions
Clearly Quantity B(6) > Quantity A(2 or 3)
So, Answer will be B.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
=======================================================================
Theory
- ‣‣‣ Mean = (Sum Of All The Numbers) / (Total Number Of Numbers)
‣‣‣ Mode is the number which has occurred the maximum number of times in the set.
‣‣‣ Median is the middle value of the set
‣‣‣ Range of a set is the difference between the highest and lowest value of the set.
=======================================================================
As there are 5 numbers so Median = Middle term = Third Term
Mean = \(\frac{Sum}{5}\) = \(\frac{25}{5}\) = 5
Mean = Median = Mode = Range = Third Term = 5
So, the set is _ , _ , 5 , _ , _
Now, the mode is 5 so 5 has to occur the maximum number of times.
Let's say 5 occurs 2 times so we have two possibilities
_ , 5 , 5 , _ , _
_ , _ , 5 , 5 , _
In, _ , 5 , 5 , _ , _ case we will have two numbers bigger than 5. Lets say 6 and 7 and range is 5 so first number will become 7-5 = 2
So the set becomes 2, 5, 5, 6, 7 and it satisfies all conditions
_ , _ , 5 , 5 , _ case lets take the two smaller numbers as 3 and 4. So the largest number will become 3 + 5 = 8
So the set becomes 3, 4, 5, 5, 8 and it satisfies all conditions
Clearly Quantity B(6) > Quantity A(2 or 3)
So, Answer will be B.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
