-find the sample variance of the running time for the males. -Find the sample standard deviation of the running time for the males. -Find Q1 for the running times for the males -Find Q3 for the running times for the males - Find the Interquartile Range (IQR) of the running times for the males. - Provide the frequency distribution table of the running times for the males using six classes Males 23.86 24.77 25.21 28.08 24.00 25.04 25.24 33.07 24.71 25.20 26.78 Solution 26 --- mean 2.625 -- standard deviation 6.89 --- variance.

1. -How do you determine the optimum area and perimeter?
-How do you determine the optimum volume and surface area?
Solution
The determination of optimum area and perimeter, or optimum volume and surface area, will
depend on what is to be optimized and constraints on the shape of objects for which these
variables are to be minimized. For example in designing a heat exchanger we may want to
maximise the surface area for a given volume of copper used, whereas in designing a water tank
we may want to maximize the volume of tank for a given area of tank.
Then we can have different shapes and constraint. For example the tank may be rectangular,
cubical, cylindrical, spherical, or of some other shape. There may be different kind of constraint
on design for example maximum height, width, length, or diameter may be specified.
In general a circle give maximum area for a given length of perimeter. Similarly, a sphere gives
maximum volume for a given surface area.