A large city has close to 100,000 children in the 8th grade. The mean
IQ of this population of the 8th graders is known to be 100. In a
genuinely random way you are to select 50 of these children for a
study of educational achievements. The first child tested has an IQ of
150. What do you now expect the mean IQ to be for the whole
fifty-child sample? In other words, do you expect the mean IQ of the
sample to be about 100? Or do you expect it to be slightly greater
than 100?

I basically agree with corwin02's comment based on logic and math. 
Let us assume that there are exactly 100,000 children in this city. 
The population of 99,999 children -- excluding the first child with
the 150 IQ -- still has a mean IQ of approximately 100.  (The child
would need a super-human IQ to skew the mean so much that the
remaining 99,999 children would have a much lower mean IQ than the
original mean.)   The mean IQ for the remaining 99,999 children is
actually 99.9994999949999 ... , according to the following
calcluation.  (You'll need a calculator, at least for the last step in
the calculation.)

100,000 children

times

100 IQ (mean for 100,000 children)

equals

100,000,000 IQ (total for 100,000 children)

minus 150 IQ (for one child)

equals

99,999,850 IQ (total for 99,999 children)

divided by 99,999 children

equals

99.9994999949999 ... IQ (mean for 99,999 children)

Selecting 49 children at random, you'd expect on average to get a
total IQ of 4899.9754997549975 ... (99.9994999949999 ... per child for
the 49 children).

Adding 150 IQ to that total, the total IQ for the 50 children is
5049.9754997549975 ... .

Divided by 150, the mean IQ would be 100.99950999509995 ... .  Rounded
up, it would be 101.

- justaskscott

You cannot extrapolate from a sample of 1.

Extrapolation from a sample of 1 is quite inacurate , but based on the
the figures given the mean IQ would be 101 until proven wrong by the
next sample drawn ((49*100)+150)/50