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.

BITS Work Integrated Learning Program - M.Tech Data Science & Engineering

BITS Pilani offers work integrated learning program (WILP) on M.Tech Data Science and Engineering which is UGC approved. The course is a four semester programme designed to help work professionals to build their skills required for data science engineering which enable them to become a Data Scientist. It is a 100% online course and lectures would be delivered by BITS Pilani faculty on weekends. Those who are working in software industry as Software Engineer, Programmer, Data Analyst, Business Analyst can apply for the course. Minimum eligibility criteria to apply for the course. Those who are employed holding B.E/B.Tech/MCA/M.Sc or Equivalent with 60% marks and minimum one year relevant work experience. The candidates should have basic programming and engineering mathematics knowledge. The following subjects shall be covered in the course. Semester Subjects Data Mining Mathematical Fundamentals for Data Science Data Structure and Algorithms Design Co...

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