# applications of discrete mathematics and statistics in IT

**Question description**

Individual project

1. Here are the salaries of 24 IT professionals in 2009 in Chicago:

$109,000 $ 65,000 $65,000 $ 59,000 $ 180,000 $ 101,325 $ 130,000

$95,000 $ 81,500 $69,000 $71,500 $ 74,880 $64,000 $72,000

$ 71,000 $ 82,300 $49,000 $51,200 $ 39,000 $48,500 $64,330

$ 41,100 $52,330 $82,000

a. Make a frequency distribution using five classes with the upper class limit of the first class as the

lower class limit of the second.

b. Make a histogram from your frequency distribution.

2. Find the prices of 10 different printers for your PC. Compute the mean, median and mode of

these prices.

3. In the following table you can see the Memory Usage at a given moment of a PC computer.

a. Find the measures of tendency and the measures of dispersion of the memory usage in Kb.

b. Once you complete the computation of the measures, complete a scatter plot of those values.

c. Identify the values that are responsible for the variance of the dataset, give a possible solution on

how the computer user could decrease his Memory usage variance.

4. There is a mathematical theory called queuing theory that studies ways in which computer jobs

are fed in CPUs and researches on how these can be reduced to a minimum. Show how can a

computer estimate the average number of jobs waiting at a queue?

Suppose that in a 5 sec interval jobs arrive as indicated in the following table ( Arrival time is

assumed to be at the beginning of each second) In the first second jobs A and B arrive. During

the second second B moves to the head of the line ( A job is completed as it took 1 sec to be

served), and C and D jobs arrive and so on.

Find:

a. The mean number of jobs in line

b. The mode of the number of jobs in line

Time in seconds Jobs

1 A,B

2 C,D

3

4 E,F

5

5. Many times, we are required to use statistical measures to try and construct a problem.

We run a program for a 10 different inputs. The times are measures in 1-second intervals and none of

them took 0 secs.

a. Suppose the standard deviation of a set of times we run the program is 0. What does this tell

you about the running times?

b. Suppose that the mean of the times is 1000.9 sec while the median is 1 sec. Explain what do you

know about the program running times for all 10 different inputs?

c. Assume now that the mean of the times is 1000.9 sec while the median is 1 sec and the

variance is 9998000. Explain what do you know about the program running times for all 10

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