Question

2. Consider the following:
We can measure program length in a variety of ways, including LOC, thousands of
LOC, the number of characters contained in the program, the number of executable
statements, and more. Suppose M is the measure of program length in LOC, while M’
captures length as number of characters. Then we can transform one to the other by
computing M’ = aM, where a is the average number of characters per line of code.
a) How the attribute of empirical relation determine the scale types of ratio and
absolute scale? Discuss your answer.
b) Identify the direct and derived measurement.

3. Suppose yesterday’s temperatures on the Celsius scale were 35°C in Tokyo and 25°C
in London, while today it is 40°C in Tokyo and 20°C in London. However, on the
Fahrenheit scale, yesterday’s temperatures were 95°F in Tokyo and 77°F London ,
today’s are 104°F in Tokyo and 68°F in London.
a) Write a meaningful statement in temperature differences.
b) The scenario above able to imply the ratio scale. Determine the mapping of
representation condition.
c) Explain the numerical relation provided in answer (b).

Answer 1

Answer 2)

a) For any measures, M and M', there is only one admissible transformation: the identity transformation. That is, there is only one way in which the measurement can be made, so M and M' must be equal. The absolute scale has the following properties:

(i) The measurement for an absolute scale is made simply by counting the number of elements in the entity set.

(ii) The attribute always takes the form "number of occurrences of x in the entity"

(iii) There is only one possible measurement mapping, namely the actual count, and there is only one way to count elements.

b)

A direct metric is a metric that does not depend upon a measure of any other attribute. In other words, a direct metric is a function whose domain is only one variable: M: F->Y. Examples of direct measures: LOC, etc.

An indirect or derived measure relies on more than one measure. In other words, a derived measure is a function whose domain is an n-tuple: M: (F, G, H)->Y. Examples of indirect measures: programmer productivity, defect density, etc.

Answer 3)

a) Temperature differences: 10⁰ C (yesterday from Tokyo and London)

20⁰ C (Today from Tokyo and London)

30⁰ C (Tomorrow from Tokyo and London)

10 * I differences.

for(I=1;I<N;I++)

{

printf("%d",10I);

}

b) Examples of interval level data include temperature and year. Examples of ratio level data include distance and area (e.g., acreage). The scales are similar in so far as units of measurement are arbitrary (Celsius versus Fahrenheit, Gregorian versus Islamic calendar, English versus metric units). The scales differ in that the zero points are arbitrary on interval scales, but not on ratio scales. For instance, zero degrees Fahrenheit and zero degrees Celsius are different temperatures, and neither indicates the absence of temperature. Zero meters and zero feet mean exactly the same thing, however. An implication of this difference is that a quantity of 20 measured at the ratio scale is twice the value of 10, a relation that does not hold true for quantities measured at the interval level (20 degrees is not twice as warm as 10 degrees).

c)

Let
⁰F be the Fahrenheit temperature,
⁰C be the Celsius temperature, and
TT be the Kelvin temperature.

tF=1.8*⁰C+32⁰F=1.8⁰C+32.

⁰C=T−273.15.⁰C=T−273.15.

Therefore, ⁰F=1.8T−459.67⁰F=1.8T−459.67.

Since we want the Fahrenheit and Kelvin values equal, that means ⁰F=T⁰F=T, so

T=1.8T−459.67T=1.8T−459.67 and

0.8T=459.670.8T=459.67.

Therefore, T=459.67/0.8=574.5875T=459.67/0.8=574.5875 and we have

574.5875 °F = 574.5875 K (which is the same temperature as 301.4375 °C).