Business Math And Statistical Measures Unit 3

CLEANED MM255 Business Math And Statistical Measuresunit 3 Instructor Graded

CLEANED: MM255 Business Math And Statistical Measuresunit 3 Instructor Graded

Using data from your previous assignment, compute the mean, median, and standard deviation. Create a histogram or bar graph of the data. Additionally, find an online circle graph or bar graph, post it, and analyze its message and effectiveness.

Paper For Above instruction

Introduction

In the realm of business mathematics and statistics, interpreting data accurately is essential for decision-making, forecasting, and understanding trends. This paper explores the fundamental statistical measures—mean, median, and standard deviation—applied to a set of gas price data over a specific period. Additionally, the visual representation of data through histograms and the analysis of external graphical data—such as circle or bar graphs—are examined to understand their communicative effectiveness and relevance in conveying information.

Analysis of Gas Price Data

To exemplify the process, consider a data set representing the average monthly gas prices over a year. The data might look like: 1.10, 1.13, 1.15, 1.25, 1.40, 1.35, 1.35, 1.39, 1.27, 1.25, 1.23, and 1.11. Calculating the mean involves summing these values and dividing by the total number of observations. Using the calculation: (1.10 + 1.13 + 1.15 + 1.25 + 1.40 + 1.35 + 1.35 + 1.39 + 1.27 + 1.25 + 1.23 + 1.11) / 12, the mean is approximately 1.2483, which rounds to $1.25.

The median is determined by ordering data and selecting the middle value or the average of the two middle values when the set has an even number of observations. Sorted data: 1.10, 1.11, 1.13, 1.15, 1.23, 1.25, 1.25, 1.27, 1.35, 1.35, 1.39, 1.40. The middle positions are between the two 1.25s, leading to a median of 1.25.

Standard deviation measures the dispersion of data points from the mean. Using Microsoft Excel, the function =STDEV(range) where range is the set of data, calculates the standard deviation as approximately $0.108. This indicates the degree of variation in gas prices over the year, with a low standard deviation signifying relatively stable prices.

Visualization of data via histogram involves plotting the frequency of gas prices within specified intervals. A well-constructed histogram provides insights into the distribution, highlighting whether the data clusters around certain values. For example, most gas prices might cluster between $1.20 and $1.40, showing typical fluctuations. The creation of such a graph can be done using spreadsheet software, and it visually complements the numerical measures discussed.

Analyzing External Graphs

Beyond the dataset, interpreting external circle or bar graphs enables understanding how data representations communicate messages. For instance, a circle graph on a news website may break down national energy consumption by sectors such as transportation, industry, residential, and commercial. The purpose is to visually depict the relative proportion of each sector’s energy use, aiding viewers in grasping the dominant energy consumers easily.

The effectiveness of such graphs depends on clarity, accuracy, and relevance. A well-designed circle graph with appropriate proportions clearly shows the distribution, allowing quick comprehension. Conversely, poorly labeled or cluttered graphs can mislead or confuse viewers, emphasizing the importance of thoughtful design and accurate data depiction.

Conclusion

Understanding and correctly applying statistical measures enhances data analysis and interpretation in business contexts. The mean, median, and standard deviation provide foundational insights into data characteristics, while visual tools like histograms and external graphs extend these insights by offering intuitive representations. Critically analyzing these visualizations ensures that data storytelling remains truthful and impactful, facilitating better decision-making and communication in business environments.

References

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