a group of numbers consists of three 4's, four 5's, seven 9's. what is the median?

Question

1. (3 x 4)+(4 x 5)+(7 x 9)
2. (5 + 9) divide 2
3. (5 - 9) divide 2
4. (5 + 9) x 2
5. (3 x 4) + (4 x 5) / (7 + 9)

Answer 1

the median has nothing to do with the numbered thing you have up there. the median is the middle number when the numbers are lined up from lowest to highest.

4, 4, 4, 5, 5, 5, 5, 9, 9, 9, 9, 9, 9, 9

how many numbers are there? an even amount, so there are two middle numbers, 9 and 5. when this happens, you add the two numbers together:

9+5=14

and then you divide by 2

14 / 2 =7

so therefor, your median is 7

Answer 2

mean --- is defined as the simple arithmetic average of a set of observations

mode --- is defined as the most frequent observation

median -- is defined as that observation which is, counting-wise, exactly 1/2 way from one extreme observation to the other extreme observation

***
the way this set was constructed, there is no single definable median. exactly 1/2 the observations consist of 4s and 5s and 1/2 consist entirely of 9s. Any value of a possible observation between 5 and 9 would be the median observation.

however, you do not know that any observations other than 4, 5, and 9 are possible. It follows that claiming that (5 + 9) divided by 2 = 7 is the median can not be proved.

The weighted (or geometric) mean of [(3 x 4) + (4 x 5) + (7 x 9)] = 95 divided by the number of observations (14) = 6.7857+ would serve just as well. So would 6 or 8 -- if either of them is a possible observation.

Median is simply that point (observation) such that 1/2 the observations are less than this value and 1/2 are greater than this value.

***
And, I'll hazard a guess that if this is for some maths exam in one of the lower grades, this discussion will be far beyond what the teacher understands of math.

:-)

Answer 3

1. 95
2. 7
3. 2
4. 28
5. 2