3. Sir students from an institute took a standardized
test. The number of mistakes committed by five
of the students was 18, 14, 20, 8 and 12. If the
sixth student committed x number of mistakes,
such that the mean number of mistakes per
student for the six students is equal to the median,
x could be which of these?
Answers
Given : students from an institute took a standardized test. The number of mistakes committed by five of the students was 18, 14, 20, 8 and 12. If the sixth student committed x number of mistakes,
such that the mean number of mistakes per student for the six students is equal to the median,
To Find : Value of x
Solution:
arrange in order
8 12 14 18 20
Mean of 5 = ( 8 + 12 + 14 + 18 + 20 )/5 = 72/5 = 14.4
Median = 14
Now on adding x the median can lie between 12 and 18 only
on closer inspection between (12 + 14)/2 and ( 14 + 18)/2
= 13 and 16
so New mean can be between 13 and 16
Hence Sum can be 13* 6 = 78 to 96
Current sum = 72
Hence x can be 6 to 24
Few hit and trial
(72 + x ) /6 = new mean
x = 6
=> new mean = 13
new median = (12 + 14)/2 = 13
Satisfied :
(72 + x ) /6 = new mean
x = 12
=> new mean = 14
new median = (12 + 14)/2 = 13
x = 15
=> new mean = 14.5
new median = (14 + 12)/2 = 14.5
Hence for x = 15
Mean and median will be same 14.5
x = 18
=> new mean = 15
new median = (14 + 18)/2 = 16
x = 24
=> new mean = 16
new median = (14 + 18)/2 = 16
Satisfied
x can be between 6 to 24
and 6 , 15 and 24 are satisfying the condition
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