Comprehensive Statistics Assignment: Boolean Algebra and Data Analysis

This assignment delves into the application of Boolean algebra and statistical methods to analyze real-world datasets. It begins with constructing frequency distributions and histograms from salary data of IT professionals, followed by interpreting the results from a histogram representing the time taken by programmers to complete a task. The assignment then explores the calculation of central tendency measures (mean, median, mode) and quartiles for laptop prices. Furthermore, the assignment examines the analysis of memory usage data, including the calculation of mean, median, range, variance, and standard deviation, and explores the impact of data bias on variance. The assignment concludes with a discussion on the conditions under which the standard deviation becomes zero and a comparison of standard deviations for different datasets. The solution includes tables, figures, and calculations to demonstrate the statistical concepts and their application.

Running head: BOOLEAN ALGEBRA AND STATISTICS
Boolean algebra and Statistics
Name of the student:
Name of the University:
Author note:

1
BOOLEAN ALGEBRA AND STATISTICS
Table of Contents
Answer to the question 1............................................................................................................2
Part (a)....................................................................................................................................2
Part (b)....................................................................................................................................2
Answer to the question 2............................................................................................................2
Part (a)....................................................................................................................................2
Part (b)....................................................................................................................................2
Part (c)....................................................................................................................................3
Part (d)....................................................................................................................................3
Answer to the question 3............................................................................................................3
Part (a)....................................................................................................................................3
Part (b)....................................................................................................................................3
Answer to the question 4............................................................................................................4
Part (a)....................................................................................................................................4
Part (b)....................................................................................................................................4
Part (c)....................................................................................................................................4
Part (d)....................................................................................................................................4
Answer to the question 5............................................................................................................5
Part (a)....................................................................................................................................5
Part (b)....................................................................................................................................5
Bibliography...............................................................................................................................6

2
BOOLEAN ALGEBRA AND STATISTICS
Answer to the question 1
Part (a)
Table 1 Frequency Distribution
Part (b)
Figure 1 Histogram on Annual salary
Answer to the question 2
Part (a)
There are 7 classes in the histogram.
Part (b)
The class width of the histogram is 5

3
BOOLEAN ALGEBRA AND STATISTICS
Part (c)
Total number of observations = 100
The number of programmers complete the task in 30 hours = 20
Therefore the percentage of programmers complete the task in 30 hours = ( 20
100) *
100%
= 20%
Part (d)
The majority of the programmer complete the task in 25 hours. The number of
programmer is 45.
Answer to the question 3
Part (a)
The mean of the prices = $ 703.845
The median of the prices = $ 534.99
The mode of the prices = $ 399.99
Part (b)
The first quartile of the prices = $ 374.99
The third quartile of the prices = $ 962.24

4
BOOLEAN ALGEBRA AND STATISTICS
Answer to the question 4
Part (a)
Figure 2 Scatter Plot on Memory Usage
Part (b)
The mean of the memory usage = 32871.14 KB
The mode on memory usage does not exist, because there is no repetition of the data
set.
The median of the memory usage = 8268 KB
Part (c)
The range of the memory usage = 434792 KB
The variance of the memory usage = 6832652086.94 KB
The standard deviation of the memory usage = 82659.86 KB
Part (d)
The responsible values for the variance of the data set is 436344 KB.

5
BOOLEAN ALGEBRA AND STATISTICS
To reduce the variance the computer user should add bias.
Answer to the question 5
Part (a)
The standard deviation is zero, when there is no difference between the data points
and the means. In this case, all the observations are equal to the mean of the data set.
Part (b)
Yes. The set 2 has a higher standard deviation, because in the set 1, the difference
between each observations is 1 and in the set 2, the difference between each observations is 2.
In other words low variability has a low standard deviation.

6
BOOLEAN ALGEBRA AND STATISTICS
Bibliography
Amrhein, V., Trafimow, D., & Greenland, S. (2019). Inferential statistics as descriptive
statistics: There is no replication crisis if we don’t expect replication. The American
Statistician, 73(sup1), 262-270.
Bonner, M. D. (2018). Descriptive statistics. Police Abuse in Contemporary Democracies,
257.
Hinton, P. R. (2014). Statistics explained. Routledge.
Holcomb, Z. C. (2016). Fundamentals of descriptive statistics. Routledge.