Individual Project 1: Salaries Of 24 IT Professionals

Individual Project1 Here Are The Salaries Of 24 It Professionals In

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

Make a histogram from your frequency distribution.

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

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.

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.

Many times, we are required to use statistical measures to try and construct a problem. We run a program for 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 . Explain what do you know about the program running times for all 10 different inputs.

Paper For Above instruction

Analysis of Data and Statistical Measures in IT and Business Contexts

Statistical analysis is fundamental in interpreting data, making informed decisions, and strategizing in various fields, including Information Technology (IT) and business management. The tasks outlined serve as practical applications of descriptive and inferential statistics, which enable professionals to understand data patterns, evaluate system performances, and develop effective strategies. This essay explores these statistical concepts through the analysis of salary data, printer prices, memory usage, queuing systems, and program runtimes, demonstrating their importance in real-world scenarios.

Frequency Distribution and Visualization in Salary Data

The initial task involves creating a frequency distribution from the salaries of 24 IT professionals in Chicago for the year 2009. To conduct this, salaries are first arranged in ascending order, after which five classes are defined with a particular focus on the interval specifications. For instance, considering the salaries range from $39,000 to $180,000, intervals could be established as follows: $39,000–$65,998, $66,000–$92,998, $93,000–$119,998, $120,000–$146,998, and $147,000–$180,000. By tallying the salaries falling into each class, a frequency distribution is obtained. This distribution illuminates the concentration of salaries within particular ranges, highlighting disparities in income levels among IT professionals.

Following this, a histogram can be created based on the frequency distribution. The histogram serves as a visual representation, making it easier to interpret the data by illustrating the distribution's shape, skewness, and potential outliers. Visual tools like histograms are invaluable in data analysis, providing quick insights into the data's overall pattern.

Analysis of Printer Prices: Mean, Median, and Mode

Evaluating the prices of ten different printers involves calculating measure of central tendency: the mean, median, and mode. The mean is obtained by summing the individual prices and dividing by ten, providing an average value that indicates typical pricing. The median, the middle value when the prices are ordered, offers insight into the central point of the data set, especially when the distribution is skewed. The mode identifies the most frequently occurring price, indicating a common price point among the printers. Understanding these measures helps consumers and businesses make informed purchasing decisions and recognizes market pricing trends.

Memory Usage: Measures of Tendency and Dispersion

The analysis of the memory usage at a specific moment involves calculating measures of central tendency such as the mean and median, as well as dispersion measures like the range, variance, and standard deviation. These statistics quantify the typical memory consumption and the variability across the given data set. High dispersion suggests fluctuations in memory usage, which can influence system performance and stability. Precise calculations enable system administrators to identify abnormal patterns or outliers in memory utilization, crucial for optimizing computer performance.

Creating a scatter plot of these memory values visually complements the statistical analysis, illustrating any correlations or patterns within the data. Points that are widely dispersed indicate high variability, whereas clustering suggests stability.

To reduce variance, a possible approach is to identify and manage processes or applications contributing to outliers—perhaps by closing unnecessary background applications or optimizing software performance. Such actions can stabilize memory usage, leading to more predictable and efficient system operation.

Queuing Theory and System Efficiency

Queuing theory models are instrumental in understanding and optimizing system performance, especially in computer operations involving job scheduling. Estimating the average number of jobs waiting in a queue involves analyzing the arrival and service rates within the system. If the number of jobs arriving follows a certain probability distribution, the system's utilization rate can be determined, which in turn facilitates the calculation of the expected queue length.

Applying this theory, with the provided data on job arrivals at specific seconds, involves calculating the arrival rate (average number of jobs per second) and the service rate (the system's processing capacity). Using queueing models such as M/M/1 or M/D/1, the average queue length and the probability distribution of the number of jobs can be derived. For example, if the system operates under a stable condition where the arrival rate is less than the service rate, the average number of waiting jobs is predictable and manageable.

Understanding these metrics enables system administrators to optimize scheduling policies, hardware capacity planning, and resource allocation, significantly reducing wait times and increasing throughput.

Statistical Implications of Program Runtime Data

In analyzing program runtime data for ten different inputs, statistical measures reveal important characteristics. When the standard deviation is zero, it indicates that all runtimes are identical—implying a highly consistent performance with no variation among different inputs. This suggests that the program's execution time is deterministic or that the inputs do not influence runtime significantly.

If the mean runtime is 1000.9 seconds, but the median is only 1 second, it suggests a highly skewed distribution with outliers or extreme values. Most inputs likely execute very quickly (around 1 second), but a few take significantly longer, pulling the mean upwards. This scenario is typical in systems with occasional heavy processing or bottlenecks.

The variance (or standard deviation), when large, confirms the presence of considerable variability in runtimes. It indicates that the program's performance fluctuates widely depending on input characteristics, which could pose challenges for predictability and resource planning. Understanding these statistical measures helps developers optimize algorithms, improve system stability, and anticipate performance issues under different workloads.

Conclusion

The analysis of diverse datasets—ranging from salaries to system performance metrics—underscores the importance of statistical tools in decision-making and operational efficiency. Frequency distributions and histograms facilitate understanding of data distribution, while measures like mean, median, and mode provide central tendency insights. Variability metrics such as range, variance, and standard deviation reveal the stability of processes, guiding optimization strategies. Applying queuing theory optimizes system throughput by estimating wait times and resource needs. Collectively, these analyses support evidence-based management in both IT and business spheres, fostering improved resource allocation, performance, and strategic planning.

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