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

Answer 1

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`  

=3^nd 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

= 3^nd 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.