# THE FARMER HAS FEMALE SHEEP AND LAMBS (CAMBRIDGE PAST PAPER)

The farmer has 20 female sheep.
Each sheep has 0, 1, 2 or 3 lambs.
The table shows this information.

Mathematics Cambridge IGCSE Test (0580 m16 qp 32)
i) Calculate the mean number of lambs per sheep.

Mean number of lambs per sheep is

= ( 0x1 + 1x4 + 2x12 + 3x3 ) lambs divided by total sheep

= ( 0x1 + 1x4 + 2x12 + 3x3 ) lambs / 20 sheep

=  1.85

ii) The farmer takes 1 lamb away from each of the sheep with 3 lambs.
These lambs are given to 3 of the 4 sheep that have 1 lamb.
Complete the table after the farmer has done this.

1 lamb is taken away from each of the sheep with 3 lambs. So there is no                      sheep which has 3 sheep.

Then for every 1 lamb which is already taken, will be given to the sheep which          only has 1 lamb.

So only  one sheep which has 1 lamb.

Finally, the sheep which has 2 lambs are 18 sheeps.

(iii)  Explain why the mean number of lambs per sheep does not change.

Same total number of sheep and same total number of lambs.