The first three books in the series have 117, 135, and 117 pages. The author finishes the series with a fourth book that has 151 pages. Which is not true?
A. The range is smaller than the mean.
B. The mean is smaller than the median.
C. The mean is larger than the mode.
D. The median is larger than the mode.

Question

The first three books in the series have 117, 135, and 117 pages. The author finishes the series with a fourth book that has 151 pages. Which is not true?
A. The range is smaller than the mean.
B. The mean is smaller than the median.
C. The mean is larger than the mode.
D. The median is larger than the mode.

solomonzelman · Answer

The range is maximum-minimum.

howard-wolowitz · Answer

Yes! Were on the same page

solomonzelman · Answer

I am sure you can tell that
max−min=151−117<100

And mean>100 since all values are greater than 100.

howard-wolowitz · Answer

ok so that means the mean is smaller then the rest

howard-wolowitz · Answer

so I think the answer is B

howard-wolowitz · Answer

the median of all the rest of the values, is ... the median

solomonzelman · Answer

Median = (117+135)/2

Mean = (117+135+117+151)/
=(117+135+117+135+positive)/4
=(117+135+117+135)/4 + positive/4
=(2•(117+135))/4 + positive
=(117+135)/2 + positive

solomonzelman · Answer

I proved that mean is larger than the median

solomonzelman · Answer

So B is wrong... see how?

howard-wolowitz · Answer

yes but thats upsetting

solomonzelman · Answer

I gave you the hint

solomonzelman · Answer

max−min=151−117<100

right ?

howard-wolowitz · Answer

yes right I tihnk

solomonzelman · Answer

good

solomonzelman · Answer

If all values are greater than 100, then their mean is also greater than 100

solomonzelman · Answer

is that reasonable?

solomonzelman · Answer

Oh, the question is not true!
I am sorry!!
Then, B is right

solomonzelman · Answer

but, let's still work other options, if you don't mind.

howard-wolowitz · Answer

ok

solomonzelman · Answer

Ok, so
Range = max - min = 151−117<100
Mean > 100  (since all values are greater than 100)

solomonzelman · Answer

Which option is true based on that?

howard-wolowitz · Answer

mode

howard-wolowitz · Answer

are you asking me whats bigger then the mean?

solomonzelman · Answer

from my post,  Range<100,  Mean>100.
So,   Range<Mean.

solomonzelman · Answer

So based on that statement A is true.

solomonzelman · Answer

117,  135,  117,  151

solomonzelman · Answer

Is mean greater or smaller than 117?

howard-wolowitz · Answer

you said mean is Mean>100

solomonzelman · Answer

The smallest value is 117, so how can the mean be smaller than 100?

howard-wolowitz · Answer

i didnt say it was

solomonzelman · Answer

well, regardless of who "they" is, let's ignore them.

howard-wolowitz · Answer

well its my fault i confused myself

solomonzelman · Answer

Ok

solomonzelman · Answer

So, we know that A is true, right?
(i've shown that before)

howard-wolowitz · Answer

yes

solomonzelman · Answer

The mode is 117.      (most frequent value)
The smallest value is 117, and some values
are greater than 117. Therefore the mean is
greater than 117.

solomonzelman · Answer

So if,
mode=117
mean>117

then which statement is (also) true?