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Question
For which set of numbers do the mean, median and mode all have the same value?
Options
2, 2, 2, 2, 4
1, 3, 3, 3, 5
1, 1, 2, 5, 6
1, 1, 1, 2, 5
Solution
For the data 2, 2, 2, 2, 4 of 5 numbers, we have
MEAN = `(2+2+2+2+4)/5`
`=12/5`
=2.4
`MEDIAN = ((5+1)/2)^(th) value`
=3nd value
=2
Since, 2 occurs maximum number of times,MODE= 2
MEAN≠ MEDIAN
For the data 1, 3, 3, 3, 5 of 5 numbers, we have
`MEAN = (1+3+3+3+5)/5`
=`15/5`
=3
`MEDIAN = ((5+1)/2)^(th)` value
= 3nd value
= 3
Since, 3 occurs maximum number of times,MODE = 3
MEAN = MEDIAN =MODE
Hence, the correct choice is (b).
Note that if it happens that the result is not true for the second data then we must follow the same procedure for the other data’s.
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