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1. Rectangle has integer sides and area=96
(a) How many possible perimeters?
(b) Greatest perim? Least? L=? W=?
Answers
(a) 6
(b) Greatest perim:194; Least:40
Solution: 96 has 6 pairs of factors ---
1,96:2,48;3,32;4,24;6,16;8,12
Each pair has a different sum so there are 6 possible perimeters.
The greatest and least possible occur in the extreme cases, i.e., when the factors are farthest and closest apart. This is generally true.
Note: If integer condition is removed there would be no greatest perimeter and the least would be 16√6, a square!
2. Data:4,6;mean:5
(a) Avg diff from mean= ((4-5)+(6-5))/2=?
(b) v=((4-5)^2+(6-5)^2)/2=?
(c) √v=?
(d)Repeat for 3,7
Obs,Conj?
Common name for √v?
Answers
(a) 0
Note: This is always true -- the avg difference or deviation from the mean is zero! This is why we square the differences to measure deviation!
(b) v=1
Note: The avg of the squared "deviations" from the mean is called the variance.
(c) √v=1
Note: The square root of the variance is called the standard deviation!
(d) For 3,7 ---
Mean is still 5
v=(4+4)/2=4
√v=2, the stand dev.
√v gives a measure of how dispersed the data is from the mean...
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