How do you determine whether a dataset is normally distributed, and what are the implications of normality for statistical analysis?

In one of my college projects, I conducted a survey on student study habits. After gathering the data, I wanted to see if the distribution of study hours per week was normal. I created a histogram and noticed it formed a bell-shaped curve, which suggested normality. To confirm, I performed a Shapiro-Wilk test, which resulted in a p-value above 0.05, indicating that the data did not significantly deviate from normality. This understanding was crucial because it allowed me to use parametric tests to analyze the relationship between study hours and academic performance, ultimately leading to more reliable conclusions in my research.

While working part-time at a retail store, I was tasked with analyzing our weekly sales data to identify trends. I first plotted a histogram of the sales figures. The distribution appeared somewhat skewed, so I also created a Q-Q plot to check for normality. The points on the plot did not align well with the diagonal line, suggesting that the data was not normally distributed. This insight was vital because it guided my decision to use a non-parametric test for my analysis. Understanding the data's distribution helped the team make more accurate promotional decisions based on customer purchasing behavior.

In my first job as a data analyst, I was responsible for analyzing customer feedback scores. To determine if the scores were normally distributed, I used both visual assessments and statistical tests. The histogram showed a slight skew to the right, and the results from the Kolmogorov-Smirnov test indicated non-normality. Recognizing this allowed me to apply transformations to the data, making it suitable for further analysis. This experience taught me the importance of checking distribution assumptions and how it directly affects the reliability of the insights derived from the data.