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These 4 box and whisker plots demonstrate the number of people who chose each food out of the four options. I created this to visualize and compare the spread of my data for each food item. I notice that the range for the penne alla vodka and caesar salad is lower than the range for the chocolate ice cream and chicken noodle soup. The wide range is created because of the very hot and very cold temperature. When it was cold weather, the chocolate ice cream was chosen much less creating low frequency values and when it was hot it was chosen much more creating this large range. I also notice that the maximum value for the chicken noodle soup and chocolate ice cream is higher than the caesar salad and penne alla vodka. This tells me that people are more likely to choose the hottest food item (chicken noodle soup) or the coldest food item (chocolate ice cream). The mid range foods were chosen less because it is less clear under which circumstances those foods would be eaten in. It is much more clear to eat an extremely cold food on a very hot day and vice versa that having mid range temperature foods. I wonder if the same results would occur if the respondents were actually experiencing the particular weather scenarios at that moment?

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This first graphic is a scatter plot. Scatter plots are a graph illustrating the connection between two variables in order to examine a connection or pattern. The layout of the resulting dots shows any correlation present when the two variables are plotted along two axes. A line of best fit is also included in a scatter plot, as seen in the first image. This line aids in determining whether the two variables have a positive, negative, or no association. The line of best fit travels in a straight line along the graph, passing through the mean of the data on the x and y-axes. The r- value, which is generated by Pearson's Product Moment Correlation Coefficient, shows how far all of these data points are from this line of best fit. The strength and direction of the association between two variables are determined by the r value. The r-value is a number between -1 and 1 that indicates a linear association. A greater correlation is a positive, strong, and linear relationship with an r-value close to 1.

The data produced a R value of 0.028. This indicates that there is a weak, positive, linear link between a celebrity's Instagram followers and their brand's annual revenue. The scatter plot above illustrates that an increase in followers leads to a slight rise in brand income. Due to the very low r-value and slope of the line of best fit, this is not a compelling claim. There is minimal evidence of a link between influencers with less than 50 million followers and their brand's annual revenue, as the dots are dispersed and do not follow any pattern or trend. This is clear in the second image of the graph's zoomed-in region. This scatter plot also displays some data outliers. These are data points that do not follow the trend in any way. One exception is Jessica Simpson's brand, Jessica Simpson Shoes, which has a revenue of over $1 billion but a following of roughly 7 million. This point is far off from the line of best fit and goes against the general trend of the data in the chart. This is an extreme example that shows virtually little link between a large following and a large profit. This outlier also has a significant impact on the R-value to decrease the correlation coefficient.

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IA  Mind Map

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In this visual representation of my data, I decided to accurately draw the graph that I created on Desmos (using functions that matched the perspectives and general shape of the subject in the painting) on graph paper. The simple shapes and lines that the functions had created gave me excellent guidelines for the sketching of the actual portrait, showing that mathematics and functions are prevalent in accurate proportions of famous artworks. This allowed me to apply the mathematical concepts and the functions in order to complete what my goal was for this exploration: to use functions to create accurate measurements of famous paintings and to be able to recreate them with the correct proportions and perspective. In this particular graph, I drew the exact functions on the graph paper. Then (on the image on the bottom right) I filled in some of the features that matched up with the lines that I created. Afterwards, I was able to find the approximate place for the details, such as the eyes and the mouth. The coordinates of the graph allowed me to plot places for every important feature of the original painting.

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This box plot is a way to measure the mean, median, minimum, maximum, Q1, and Q3 of both the data sets that I found. The blue color or group one represents the song of the year awards and the orange box or group 2 represents the album of the year awards. In this box and whisker plot the 16 is shown as a dot outside of the plot and is shown as an outlier. Additionally the 12 is not shown in the box and is also shown as an outlier. The 12 is the number of “Album of the Year” awards for the genre Rock. This shows that Rock has been awarded the most grammys for that section. This graph helps to reference that there is a larger range in the album of the year awards and different means between the two of them. Because my data from each award does not all encompass the same genres, this was the best way to compare the two together and to recognize their differences without seeing the awards per specific genres..

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I chose to make a line graph of each of my variables I was investigating, to get a good overall visual understanding of my data. I organized my data by ascending heat index, that way it would, in theory, show the relationship of the other three variables as heat index increases. I included trendlines in the graph to make this relationship more obvious. A trendline shows the general direction of a specific data set; as the graph shows, as the heat index increases, the goals scored and fouls committed remain overall neutral, and the percentage of shots on target slightly decreases. This shows that there is little to no correlation between heat index and goals scored or fouls committed, and perhaps a weak negative correlation between heat index and percentage of shots on goal.

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This scatterplot, produced in Google Sheets, helps visualize the data I have collected in a more accurate way. This plot shows the concentration of data, more specifically how a majority of the grades fall between the 90-100 range for students at this public high school, with the exception of the outlier that shows a 29.5 average. The trendline shows the correlation between our two variables, grade and hours spent reading in a day, and the R-value, or the correlation coefficient, is 0.1328, and the determination coefficient, R2 (which shows the proportion of dependent variables that are predictable from the independent) is 0.018. This data shows that there is a positive linear correlation between GPA and Hours spent reading, however it shows a weak correlation, since the R-value is greater than 0, yet less than 0.5. This data tells me that even if students spent very little time reading, they still maintain high grades.

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For my third graph, I decided to create a scatter plot because it would most appropriately show the correlation between total points and salaries. I see that the points are widely dispersed: some fall on the line of best fit, while others do not and some are clustered at the bottom of the line. This wide dispersion in the data points does not reflect my hypothesis, instead it informs me that there is a moderate, strong correlation between NHL player’s total points and salaries. The displayed correlation is understandable because there is a wide variety of points and salaries player’s receive during the regular season. Therefore, the data is going to be dispersed and inconsistent. The positive relationship also makes sense because the more total points player’s receive, the more their salary will be. I think that there are numerous factors that contributed to this outcome. Firstly, my data includes a variety of different players, including rookie players and more experienced players. Secondly, the position determines your estimated amount of points, for instance, like I mentioned before, defenseman typically do not receive as many total points because they are responsible for defending the goal, not scoring goals.

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The scatterplot shown above demonstrates all of my raw data of 2018 placed into a visual representation that can help identify the type of correlation that the two variables have. Regarding the asterisk, that is representative of the y value  on each data point representing the number of people who died from firearms in one state from every thousand people. In the data, There is heavy clumping of data along a low x value and middle to high y value which means that there are the most deaths occurring in a state when there is less funding from gun rights groups. That being said, many of the states that had no funding have the lowest death rates of all of the data. There is a specific positive strong correlation between $100,000 and $200,000 on the x axis and 7 to 21 deaths on the x axis. This strong, positive correlation can only be seen in this part of the graph so it is not representative of all of the data. Therefore, this data is not representative of my initial hypothesis. There is a very clear outlier in the data along the right side of the scatter plot however there are other possible outliers that I will calculate for.

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This bar graph assists in visualizing the drastic differences between the ratings of music enjoyers and music haters. Bar graphs are highly significant in visualizing data due to their ability to represent categorical data in a clear and concise manner. The fundamental structure of a bar graph, with its distinct bars that vary in height, makes it an effective tool for comparing and contrasting different categories or groups. By assigning each category to a separate bar, we can easily discern patterns, trends, and relative magnitudes within the data. Furthermore, bar graphs also allow for easy data interpretation and comprehension. The simplicity of the bar graph's visual representation makes it accessible to a wide range of audiences, including those without a deep understanding of statistical concepts. The clear distinction between the bars and the labeling of the axes make it straightforward to grasp the main takeaways from the data presented. This makes bar graphs an effective tool for presentations, reports, and conveying information in a visually appealing manner.

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This is a bar graph created from statistics of over 1 million players in North America, it has a live update feed. This screenshot was taken 11 minutes after the last update. Each act (ie Act 3 in this screenshot) last for about 2 months. Currently, the average of most players in this act has ended up within the median of the ranks(silver-gold). The graph is skewed right due to the number of players falling into the lower half of the ranks. This graph may not make much sense alone, but with the other presentations of data, there is a clear correlation between rank and skill to some extent. This graph consists of all live data, meaning that there is room for analysis error.

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This table presents the rate of deaths and cases of COVID-19 for different populations. It is split using elements of the five-number summary, including quartiles and the median. Each x-axis value besides the median represents a specific range of incomes. For example, Q1 includes all incomes from the minimum point, $10,966, to the maximum for that ¼ of data, $57,554. These values are all important to include as they provide a snapshot of the whole situation. By grouping the entire set of incomes into four quarters, generalizations per group of earners can be made.

By organizing data in this manner, it can be easily visually understood. One can see that higher deaths and cases seem to correlate with lower incomes, and vice versa. As one looks from left to right on this graph, incidence decreases. This is affirmed by the trendline, as they both are negative and linear. Further, the R2 values show how strong the model is. As it is 0.934 for cases (very strong) and 0.771 for deaths (strong), this figure shows that there is a correlation between median income and the effect of COVID-19 on a population.

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In this column chart there are 3 different colors of columns representing different groups of students. The blue represents the 9th graders, the red represents the 10th graders, and the yellow represents the 11th graders. This graph is illustrating the data from the question, How many hours of homework do you get on average a night. Based on the graph you can evidently see that in the hour per night section, there are mostly 9th and 10th graders, while there is not that many 11th graders responding saying that they get an average of an hour of work per night. Once we move to the 2 hour workload section, you can see that there are less 10th graders and about an equal amount of 9th and 11th graders. The vast difference occurs when we move to the 3 and 4 hour sections. The majority of the 11th graders resign with 3 hours of homework an average per night, and the 11th graders are the only grade that responded with 4 hours of homework per night. From going to the school I surveyed the students from, the pattern being exhibited in this graph is accurate, as I have experienced the variations of workloads throughout the years. The graph follows a trend of the higher grade you’re in, the more hours of homework you get on average a night. When we move over to 5 you notice a 9th grade outlier, where there is a response from a 9th grader. This doesn't align with the overall pattern of the data. This outlier represents a different interpretation of workload and the question asked. It shows that the question, How many hours of homework do you get on average a night, can be interpreted as how long someone is contemplating their homework on average per night, rather than actually doing it. However the outlier also represents how data, especially when surveying, is not always accurate.

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This graph represents the geographical context of income tax brackets and its relationship with happiness. Happiness can be signified by the darkest color of the circle of each recorded country. The darker green represents happiness values closest to the maximum of 7.82, whereas values closest to the minimum of 2.96 are a darker color of red. From this chart, we can see that Northern European countries generally have the highest income tax percentages, represented by the largest circles on the map. Additionally, Europe includes the darkest green circles on the graph, alongside Australia and North America

The use of a map enables me to have a broad global outlook on how my two variables relate to each other. I found this one particularly useful because it organizes the data by color, giving clear indication of the happiness value. This means that patterns and trends in the data, especially across certain regions, can be more identifiable. Additionally, I can also measure the influences of other geographical factors in the data, such as the size of a country, and its proximity to other countries.

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The two graphs above are two different ways to visualize my organized data table, Frequency Table, which looks at the classifications of states in terms of gun law strength and see how many states were in each category, in order to give me a better sense of the way my data is distributed across the United States. The first graph is a bar graph that shows the number of states in each classification, national leaders, making progress, missing key laws, weak systems, and national failures. This visualization tells the viewer that there is a significant amount of states in each category, highlighting that across the country states are all in a different place in terms of their gun law strength. It also illustrates that the least number of states are labeled national leaders, only 8 out of 50, where the most number of states are labeled national failures, 14 out of 50, almost double the leaders. This visualization is an undeniable reminder that as an overall country there is a lot of work to be done.

The second graph here is my data presented geographically, also known as geospatial data. I choose to represent my data this way because according to Everytown Research and Policy, the nonprofit source my data came from, “Even the strongest system can’t protect a state from its neighbors’ weak laws. The rankings clearly show that gun laws save lives. But no state is an island (except Hawaii), and any state may be vulnerable if its neighbors fail to protect public safety.” After reading this fact, I wanted to look at how gun law violence spreads out across the country, in order to recognize how gun control in one state may affect gun safety in another. Consequently, this diagram illustrates that the stages of the gun law process are spread out all across the country. States like Illinois, which is a national leader, are bordered by states like Missouri, which is a national failure. According to the research, while state laws may give states the power over gun control within their borders, as a country only federal law can ensure the protection of states entirely, because due to our country's geographical layout, as long as some states can choose to have weak gun violence, all other states are in danger.

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This graph helps visualize the data points with smaller values because when I did a chart that had all of the values the scale did not allow for a clear representation of the data. When looking at this graph it is clear that there is a very weak correlation because there are little to no values plotted on the trendline. The trendline is used to showcase the direction and common similarities between data. In this graph the data is spread out and doesn’t demonstrate a cohesive trend. This scatter plot overall helps illustrate the distribution of likes to followers. Although the dots are mostly spread out, towards the bottom there is a bigger amount bunched together and less towards the top.

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This is a Histogram to show the average stress levels and average time spent outside by each grade. This is important because it gives the reader a deeper understanding of the relationship between these variables organized in a new manner. As you see in this histogram, the grades with the highest stress levels are 8th and 11th grade. While 8th graders have an 8/10 stress level, they spend up to 6 hours outside a week and 11th graders with an 8/10 stress level spend 5 hours. We see 12th graders on this visual as well. 12th graders average to have a 5/10 stress level, and they spend 8+ hours outside. This shows that students who spend more time outside, have lower stress levels, proving my claim that spending time outdoors does lower your stress levels.

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With the data presented in these column charts, I am able to ascertain the mean wingspan of the players within each sample group. From these means, I will use speed equations, such as

S =  d/t

S being speed,

d being distance,

and t being time.

By collecting information about the average wingspan of each sample group, I can estimate at what distance the pitcher will release the ball from the plate (for example, a 6’2 pitcher releasing the ball at 56 feet from the plate).

(For context, the pitching mound is 60.5 feet away from home plate, but the stride that a pitcher takes decreases this distance).

By calculating the time it takes a 100 mph fastball to reach home plate from the largest wingspan (using s=d/t), I can implement the time of that pitch to the distances appropriate for the other 2 distances. Thus, finding the “perceived” speed of the ball when thrown closer to the plate.

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From the measures of central tendency, we can see that the mean money spent by first-place teams is $119.51, while the mean money spent by the last-place team is $57.37. This indicates that, on average, the first-place teams tend to allocate a higher budget for their season compared to the last-place team. The median values further support this observation, with the median money spent by first-place teams being $115.5, while the median money spent by the last-place team is $50.7. This suggests that the majority of first-place teams tend to spend more money compared to the majority of last-place teams. Examining the quartiles (Q1 and Q3) provides additional insights. For the first-place teams, Q1 is $49.9 and Q3 is $150.5, indicating that at least 25% of the first-place teams spend less than $49.9, and at least 25% spend more than $150.5. On the other hand, for the last-place team, Q1 is $43.54 and Q3 is $63.55, suggesting that the spending range for the last-place team is narrower compared to the first-place teams. These observations collectively suggest a positive correlation between money spent and season finish. While this data alone does not establish a definitive causal relationship, it indicates that teams that spend more money tend to have a higher likelihood of finishing in the top positions, while those with lower spending tend to be more likely to finish in lower positions. It is also important to acknowledge that other factors such as team performance, coaching, and strategic decisions can also influence the season finishes.

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What this pie graph depicts particularly was all of the NBA coaches during the 2021 NBA season, and were asked who mostly was the absolute best defender of all time in a major way. There particularly was a 4-way tie between Jordan, Kobe, Kevin Garnett, and Gary Payton, which mostly is fairly significant. This essentially was based on the sort of the best sort of defensive style and how well they essentially participated on NBA decisive analysis boards, and how they basically helped out the most on defense, or so they essentially thought. This will help my data because with NBA experts I can kind of see who the best defender kind of is and if their team particularly has kind of had any success in a pretty major way.

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These bar graphs presents average hours of sleep and average GPA for different grade levels. It provides a basic overview of the results from my data collected using the means from each grade.  The table shows that 11th grade, on average, gets significantly less sleep than 9th and 10th graders with an average of 7.1 hours of sleep per night. 9th grade gets 8 hours of sleep per night  and 10th grade gets 8.2 hours.
The graph also shows that 11th grade students have the highest average GPA at 90.6 and 10th grade students have the lowest average GPA at 86. Looking at these graphs side by side, it appears that the less sleep a student gets, the higher their GPA is, based on 11th grade having the lowest average hours of sleep and highest average GPA and 10th grade having the highest average hours of sleep and lowest GPA. This being said, this bar graph shows a broad overview of the data and I would need to use more detailed data presentations to further investigate and explore the correlation.

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Pi charts helps to organize data by showing the data as a percentage of a whole. My whole number of data is 92. 70.7 percent which can be seen in the darker red, about ⅔  of the whole, represents the amount of people who don't use energy supplements when working out. 29.3, about ⅓ of my whole, which is represented by the lighter red, is the amount of people who do take energy supplements to workout. Since the circle it’s self is to represent the “whole”(amount of people surveyed) the slices are to be the different categories, its easy to visulize and see my data. Theres a clear view of the whole, and what makes up the whole, and how much makes up the whole.

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This bar chart shows the frequency that each height range shows up at each year range. This is very helpful because it allows you to look for any trends of how much one class of player fits into each bracket. Looking at the graph above it is hard to point out any real correlation. One thing that stands out to me is that the player between 6’9” and 6' 11” consistently lasts longer than any other height range. Additionally, there is a slight trend with players >6’11”, we can see that there aren’t many of them but they show up slightly more under 11 years than they do over, with more investigation this could lead me to confirm my hypothesis that taller players do get hurt more. There is also a trend that the short players don’t play for super long times, this could lead me to a conclusion that to last long in the NBA there is an ‘optimal height’.

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This scatter plot graph shows the correlation between how many seasons each NBA player played (x axis) versus their annual salary (y-axis). There is a line of best fit, however the points are distributed all around, meaning that there is not one clear correlation. This means that the correlation is weak and positive. I can conclude that this is because players don't get paid annually for their experience, they get payed for their skill, and maybe their draft picking. However it is positive and there is still little correlation because players experience most of the time does impact their skill, and therefore the more you play the better you could get.

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The first thing I did when I received my information was creating a line graph of how many people wrote what sport they played. some examples of them are basketball, tennis, and soccer. I then used the totals of the each sport and used that as my Y-axis, and calculated the percentage of each sport and how they connect to the certain genre and music(that data is on another chart). I then used the title of each sport as the x-axis to show the percentage and the sport.

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These two pie charts together show the disparities in the levels of wealth and success in the United States. It shows each category as a slice in the pie chart. In percentages of the richest and most successful, Male and White are by far the largest percentages. However, this isn’t reflective of the percentages of these groups in the United States. In the United States, the percentages of the Male and Female population is just about equal, with women actually being the slightly larger category. 0.3% of the richest and most successful people are Black, while in the United States they make up 6.3% of the population. This leads me to infer that a White Male is much more likely to get on the richest list in the United States than a person of color, or a female.

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For my first data set I decided to use a bar graph to show the results of a survey that asked 100 people their stress levels before and after they exercised (1-10, 10 being very stressed). I felt that a bar graph was the best way to represent my data as it is very organized and quite easy to understand. The X axis represents the scale of stress with 10 being the greatest amount of stress and red being the least. The Y axis represents how many people responded for each stress level. Total I had 100 responses per question meaning this data table has 200 responses. The blue bar represents the stress levels before exercising and the red bar shows stress levels after exercising. Based on these results, the majority of people said that their stress levels were an 8/10 before working out, and after working out the majority of people responded with a 5 and 6 out of 10 stress level.

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Stress levels before exercising and Stress levels after exercising

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Based on the chart above, current champions were most likely to win by decision, then knockout, then submission. When it comes to finishing fights, you are far more likely to win through out-striking an opponent then you are through out-grappling your opponent. In MMA, winning a fight is the most important factor, making the fact that there have been more knockout victories than submission victories all the more important. Still, we see that fighters are more likely to win by decision by 3.3% then they are to win by knockout. Consistently, fights have been mostly draws, especially championship fights where it is more difficult to shut someone's lights off because the skill level is so high that fighters are relatively even. Still, if fights are finished through punches, kicks, knees, and elbows far more than they are by chokes, armbars, and kimoras, then it is more important to learn how to do striking then it is grappling to win a fight.

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Bar graphs are used to compare multiple different values. Bar graphs can also have different groups or categories of bars if all the data can be measured the same way but the data is distinguished in different ways.

On this bar graph, the control group, which is the group that does not have congenital heart disease, and the case group, which is the group that has congenital heart disease are measured in the same way but need to be distinguished because they are different. This graph measures the frequency of different numbers of attributes. According to the graph, the control group’s frequency of attributes decreases as the number of attributes increases. In the case group, this trend is similar but the frequency of having zero attributes in the case group is lower than the frequency of having one attribute in the case group. It can also be drawn from this graph that the case group has a higher frequency of one or more attributes while the control group has a lower frequency of having one or more attributes.

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I created Box and Whisker plots on Google Sheets to visually display the five-number summary for each value of the x-variable. The five-number summary consists of the minimum (least) value, the lower quartile (the value under which 25% of the data points are found), the median (the data point in the middle of the set), the upper quartile (the value under which 75% of data points are found), and the maximum (highest value). While the scatterplots estimated the strength of the correlation between the two variables and the bar graph seeks to find a correlation using fewer data points, the box and whisker plots assess the spread of the data, which can be measured by standard deviation. The affect of the standard deviation on my hypothesis is explored in further detail later on.

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This graph represents the distance and time of the arch of one of my basketball shots at the free throw line. It shows the trendline, a cubic function slope that the shot arch took. The equation that represents a cubic function follows the format ax³+bx²+bx+c. The R² value shows how well the trendline fits my data; the closer to one  it is, the more I can trust my function model. Here, .984 is very strong. I can also use the slope and trendline to answer my research question because it shows what the most effective slope is at increasing my shit percentage. Furthermore, I can compare each shot arch to find, overall, which is the most effective. I can also find which one is the least effective and try to avoid that when playing. For example, this is the arch of a free throw shot that I made; now I know that I should try to not have an arch bigger than about 150 inches or 12.5 feet when I play.

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This table uses a scatter plot to place each data point from the survey. The x axis represents the years after high school that both parents received combined. The Y axis represents the SAT scores students received. The y and x axes were both set up to only include ranges that scores were actually found. This means that the y axis ranges from 960 to 1600, because this is the range of the data that was actually found. The x axis represents data from two years to twenty years because this was the range found.

The scatter plot shows that despite not being extremely strong, there is a correlation between these two variables. As the years of education after high school increase, there is a general increase in the SAT score. This is clear in the line of best fit which is included in the graph. The line of best fit has an upward slope. There are clear points which deviate from this correlation. The 960 is an outlier as it has a large distance from the line of best fit. As you get further from the line of best fit there will be more outliers visible.

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This chart is really interesting because it allows students to say how their sleep affects their gpa. More than half of the students say that they cannot complete assignments because they are tired from lack of sleep. This implies that sleep deprivation is the independent variable and that gpa is dependent. However 24% of the students say that their hw causes them to sleep less because they stay up late to finish their hw. In this case, hw is the independent variable and sleep is the dependent.

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In this scattergram, the x axis is the forecasted precipitation, and the y axis is the wave size. Each data point represents one day at a different location that I recorded the precipitation and wave size data for. The line of best fit/ trendline shows the correlation between these two variables in relation to how the data is distributed. By looking at this graph, I can see that there is a weak positive correlation between the forecasted precipitation and the wave size of these 100 surf breaks. This means that as the precipitation percentage increases, there is a higher chance that the wave size will also increase. I know this data has many outliers because there are a couple of points that are very far from the rest of the data and the line of best fit. For example, at one location the waves are 10 feet at 1% precipitation  Another example of an outlier is a location where the waves are 0 feet and the precipitation is 95%. These both have a very low quantity paired with a very high one or vice versa, and most of this data has a positive correlation between both variables. This data tells me that precipitation amounts can correlate with larger waves, but definitely not exclusively and there are large/small waves for any given precipitation level.

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This graph represents the correlation between each of the distances given the distance between the cue ball and the pocket. It helps to illustrate how altering the variable of the distance between the cue ball and the pocket, alters all of the other variables. This could possibly mess up the results or make them less reliable. It prevents me from being able to measure a correlation relationship because there are too many changing variables.

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This is a line chart or a line graph which displays how data has been collected and changed over depending on a certain aspect. The blue represents the year 2000 and the red represents the year 2023, it can be seen that the population fluctuates according to the body of water in which the data is recorded. This line chart provides me with basic visual information about how the fish populations have changed over time, and where they identify to have changed the most or the least. I will make use of this line graph because it visually displays the differences that basic numerical do not prove. Additionally, the line graph truly emphasizes the influence of bodies of water over the last 23 years.