The mean median and mode for a set of data are equal: 30,40,80,50,x. What is X?
My doubt is that the Mode cannot be more than 2 and how can the median be 2?Am I reading the question correctly?
Mean median and mode
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- neelgandham
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Swati,
The mode is the number that is repeated more often than any other number in the list and not the number of times that number is repeated.So, in this case mode can't be 2. Let me try and solve the question.
If x = 30, Mode = 30 and Mean = (30+30+40+50+80)/5 = 46. Since Mode != Mean, x !=30
If x = 40, Mode = 40 and Mean = (30+40+40+50+80)/5 = 48. Since Mode != Mean, x !=40
If x = 50, Mode = 50 and Mean = (30+40+50+50+80)/5 = 50, Median = 5-0 Since Mode = Mean = Median, x =50
The mode is the number that is repeated more often than any other number in the list and not the number of times that number is repeated.So, in this case mode can't be 2. Let me try and solve the question.
Since we know that we have only one mode, we are sure than x is one among 30,40,50,80.The mean,median and mode for a set of data are equal: 30,40,80,50,x. What is x?
If x = 30, Mode = 30 and Mean = (30+30+40+50+80)/5 = 46. Since Mode != Mean, x !=30
If x = 40, Mode = 40 and Mean = (30+40+40+50+80)/5 = 48. Since Mode != Mean, x !=40
If x = 50, Mode = 50 and Mean = (30+40+50+50+80)/5 = 50, Median = 5-0 Since Mode = Mean = Median, x =50
Anil Gandham
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- LalaB
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our set is
30,40,50,80,x
lets assume that x>50
then median =50
mean =median
(30+40+50+80+x)/5= 50
x=50
then mode=50
30,40,50,80,x
lets assume that x>50
then median =50
mean =median
(30+40+50+80+x)/5= 50
x=50
then mode=50
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Intuitive approach-
Arrange serially- 30, 40, 50 & 80
Current mean= 50
Going by the options adding 50 to set will not displace mean and will become new median
Mathematical approach-
Put X in set- 30, 40, x, 50 & 80 (as x is new meadian)
Since x is mean also, we have-
(30 + 40 + x + 50 + 80)/5 = x => x =50.
Hope it helps!!
Arrange serially- 30, 40, 50 & 80
Current mean= 50
Going by the options adding 50 to set will not displace mean and will become new median
Mathematical approach-
Put X in set- 30, 40, x, 50 & 80 (as x is new meadian)
Since x is mean also, we have-
(30 + 40 + x + 50 + 80)/5 = x => x =50.
Hope it helps!!
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Well What neelgandham said was perfectly alright... The hint or the clue to break this question was the 'mode' was a part of this question. That is what the clue is. If mode is present so far in the data i.e 30,40,80,50,x.
Therefore the x has to repeat itself and it cannot be any different term. And then the trial and error would help you get to the answer 50...
Cheeky question...
Therefore the x has to repeat itself and it cannot be any different term. And then the trial and error would help you get to the answer 50...
Cheeky question...
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