Sum of Sets

[john_80a]

Hi,

I would like to additional clarification on these rules which were given in the answer to the Sum of Sets question in the Word Translations Question Bank.

1) When two sets are combined to form a composite set, the mean of the composite set must either be between the means of the individual sets or be equal to the mean of both of the individual sets.

2) when two sets are combined to form a composite set, the median of the composite set must either be between the medians of the individual sets or be equal to the median of one or both of the individual sets.

>> Basically mean of composite set should be between the means of the individual sets or equal to the mean of one of the individual sets . And the same theory applies to the statement about medians of composite sets.

Correct? The difference in the words for both statements is throwing me off.

[jeromecukier]

No, it's not the same theory!
the mean of the combination of 2 sets is between the 2 means, or equal to both means. the median of the combination of 2 sets can be equal to one median and not to the other.

this is because adding any number not equal to the mean to a set will necessarily change the mean, which is not true for the median.

here's an example of 2 sets where the combined set has the same median than one of the set but not the other:

1, 2, 9, 10. - median: 5.5
3, 4, 5. - median: 4

1, 2, 3, 4, 5, 9, 10 - median: 4.

of course, if 2 sets have the same median, the combined set will have the same median too.

[esledge]

Great reply, Jerome, thanks.

John, a visual approach to median questions really helps me. Draw a number line, and draw dots for your set elements. To investigate what can happen when two sets are combined, draw two number lines, one above the other. Median is just the vertical line where there are as many dots on the left as on the right. I've found this to be a good way to play with the concept.