Mode Median

[agganitk]

Set X is composed of the total daily rainfall for a 5 day period.Is the mode of set X greater than the median?
1. mean and median od set X is equal to 5
2. If the median was removed from set X,the mean and mode would remain unchanged,but the median would decrease.

[mehravikas]

Stumped on this one

[sanjana]

I'll take a shot at this one.
Statement 1
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For mean to equal the median of a set,the numbers have to be equally spaced.
Now mean = median = 5
The set can be {5,5,5,5,5},here mean = median = 5 and mode also is 5
Also the set can be
{3,4,5,6,7},mean=median=5 but mode is 7
Hence,mode may or may not be greater than the median.
Insufficient.

Statement 2
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From the given statment.

{5,5,5,5,5} if we remove the median : 5,
the set becomes
{5,5,5,5}
Mean = median = mode = 5
But violates the statement so not a valid set.

I am unable to find a set with different numbers for which the second statment is true.

I would go for E,whats the OA?

[mehravikas]

Agree with @sanjana - Not able to find a set, which makes statement 2 valid.