Exercise 8 - Data Central Tendency

Suppose that the data for analysis includes the attribute age. The age values for the data tuples are (in increasing order) 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70.

(a) What is the mean of the data?

(b) What is the median?

(d) What is the midrange of the data?

(e) Can you find (roughly) the first quartile (Q1) and the third quartile (Q3) of the data?

(f) Give the five-number summary of the data.

Solution:

a) Total No of age values given = 27

Mean of the data = 809/27 = 29.96

The mean age value is 29.96

b) Median, center of the data is 14th value.

The median age value is 25

c) mode, the value that occurs most frequently in the set.

The data set is multimodal. The mode are 25 and 35.

d) Midrange, average of the smallest and largest value in the data set.

smallest value = 13

largest value = 70

midrange = 83/2 = 41.5

The midrange age value is 41.5

e) First quartile (Q1) & Third quartile (Q3)

Median (Q2) = 25

First Quartile (Q1) = 20

Third Quartile (Q3) = 35

The first quartile (Q1) age value is 20 and third quartile (Q3) age value is 35

f) Five number summary

Minimum, Q1, Median, Q3, Maximum.

The five number summary of age value is 13, 20, 25, 35, 70

Exercise 2 - Amdahl's Law

A programmer has parallelized 99% of a program, but there is no value in increasing the problem size, i.e., the program will always be run with the same problem size regardless of the number of processors or cores used. What is the expected speedup on 20 processors? Solution As per Amdahl's law, the speedup, N - No of processors = 20 f - % of parallel operation = 99% = 1 / (1 - 0.99) + (0.99 / 20) = 1 / 0.01 + (0.99 / 20) = 16.807 The expected speedup on 20 processors is 16.807

Exercise 1 - Amdahl's Law

A programmer is given the job to write a program on a computer with processor having speedup factor 3.8 on 4 processors. He makes it 95% parallel and goes home dreaming of a big pay raise. Using Amdahl’s law, and assuming the problem size is the same as the serial version, and ignoring communication costs, what is the speedup factor that the programmer will get? Solution Speedup formula as per Amdahl's Law, N - no of processor = 4 f - % of parallel operation = 95% Speedup = 1 / (1 - 0.95) + (0.95/4) = 1 / 0.5 + (0.95/4) Speedup = 3.478 The programmer gets 3.478 as t he speedup factor.

Minor, Cofactor, Determinant, Adjoint & Inverse of a Matrix

Consider a matrix Minor of a Matrix I n the above matrix A, the minor of first element a 11 shall be Cofactor The Cofactor C ij of an element a ij shall be When the sum of row number and column number is even, then Cofactor shall be positive, and for odd, Cofactor shall be negative. The determinant of an n x n matrix can be defined as the sum of multiplication of the first row element and their respective cofactors. Example, For a 2 x 2 matrix Cofactor C 11 = m 11 = | a 22 | = a 22 = 2 Determinant The determinant of A is |A| = (3 x 2) - (1 x 1) = 5 Adjoint or Adjucate The Adjoint matrix of A , adjA is the transpose of its cofactor matrix. Inverse Matrix A matrix should be square matrix to have an inverse matrix and also its determinant should not be zero. The multiplication of matrix and its inverse shall be Identity matrix. The square matrix has no inverse is called Singular. Inv A = adjA / |A| [ adjoint A / determ...

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