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1. Identify the proper scale for each of the following measures: LOC McCabe s cyclomatic number Average depth of nesting Maximum depth of nesting 2. Show that the temperature scales of Celsius and Fahrenheit are an interval scale using the Celsius temperatures of 20, 30, and 40 degrees. 3. Show that McCabe s cyclomatic number satis es the representational theory of measurement. 4. Show that McCabe s cyclomatic number is an interval scale measure. 5. Calculate McCabe s cyclomatic number on the following source code. Draw a control ow graph. Label the regions with Roman numerals. read x,y,z; type = scalene ; if (x == y or x == z or y == z) type = isosceles ; if (x == y and x == z) type = equilateral ; if (x >= y+z or y >= x+z or z >= x+y) type = not a triangle ; if (x <= 0 or y <= 0 or| z <= 0) type = bad inputs ; print type;

float average(float xl, float x2, float x3, float x4) 4.47 Write and test the following average ( )

function that returns the average of up to four posi-

tive numbers:

float average(float xl, float x2=0, float x3=0, float x4=0)

1 Explain why the height example satis es the criteria for valid metrics Criteria 1: Di erent people can be di erent heights Criteria 2: Any two people that we feel are related in height, their numerical heights would agree Criteria 3: Each additional height on a person matches the increase in numerical height Criteria 4: Di erent people can be the same height 2 A study of grade school children found a high correlation between shoe size and reading ability Does this mean that shoe size is a good measure of intelligence No, shoe size correlates well with age Age correlates well with reading ability Neither would be a good measure, since neither would satisfy the representation condition 3 Explain why is money a ratio scale measure and not just an interval scale Money has a well-understood notion of zero.

PASSING BY REFERENCE 4.48 Write and test the following compu t eC i rc 1 e ( > cumference c of a circle with given radius r : void computeCircle(float&

function that returns the area a and the cir-

a, float& c, float r).

4.49 Write and test the following compu t eRec tang1 e ( > function that returns the area a and the perimeter p of a rectangle with given side width w and height h: void computeRectangle(float& a, float& p, float w, float h).

In all monetary systems, there is a zero and it is equivalent to zero in all other systems The intervals are xed Thus, if you have twice as much in US dollars as I do, it will still be twice as much if we convert both our monies into British pounds (assuming no conversion penalties and using the same exchange rate) 4 Explain why GPA is not sound by measurement theory For grade points to be averaged, then grade points must be an interval scale This implies that the di erence between values is comparable That is, the di erence between an A and a B is the same as the di erence between a D and an F Normally, this is not even considered when allocating grades 5 Why is complexity not readily measurable Complexity is not well de ned.

4.50 Write and test the following compu t eTr i angl e ( > function that returns the area a and the perimeter p of a triangle with given side lengths a, b, and c: void computeTriangle(float& a, float& p, float a, float b, float c).

4.51 Write and test the following c ompu t esphere void computeSphere(float& 4.52 Write and test the following computecyl

(> surface area s of a sphere with given radius r:

v, float& s, float r).

There are many aspects to complexity, and each person may have a slightly di erent interpretation of what is complex In fact, complexity could be considered the interaction between a person and the code 6 What is the advantage of having a partial order on the empirical relation system The empirical relation system must have an accepted relation It is often easier to nd a partial order that is well accepted, whereas nding agreement on all cases might be di cult 7 Why is the number of decisions plus 1 an important method for calculating McCabe s cyclomatic number It would be very time-consuming to have to construct the control ow graph for large programs 8.