Answer: 2.7
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Explanation:
To find the mean, we add up the numbers and divide by the number of items in the set.
For example, the mean of {1,2,6} is 3 because (1+2+6)/3 = 9/3 = 3.
Unfortunately, we don't know how many rooms are in each terraced house. But we do know that the rooms in each terraced house adds to some variable S. Dividing it over 40 gets us the mean of 2.2 rooms per terraced house.
S/40 = 2.2
S = 40*2.2
S = 88
When considering the terraced houses only, there are 88 rooms in total.
Through similar steps, there are 50*2.9 = 145 rooms in the semi-detached houses
And there are 10*3.7 = 37 rooms in the detached houses.
Overall we have 88+145+37 = 270 rooms among the 100 houses total.
The mean number of rooms when considering all three types of houses is 270/100 = 2.7 rooms per house.
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Another approach:
2.2 is the mean number of rooms for the terraced houses
this represents 40/100 of the entire list
So we'll have (40/100)*2.2 as part of the calculation.
We'll also have (50/100)*2.9 and (10/100)*3.7
The final calculation can be done as this:
(40/100)*2.2 + (50/100)*2.9 + (10/100)*3.7 = 2.7
For more information, check out the concept of a weighted mean.
