How do you determine whether a dataset is normally distributed?

During my final year in college, I worked on a project analyzing survey data for a research paper. We collected responses from students regarding their study habits and grades. To check if our data was normally distributed, I first created a histogram and a Q-Q plot. The histogram showed a bell-shaped curve, while the Q-Q plot aligned closely with the diagonal line, indicating normality. This visual inspection was complemented by conducting a Shapiro-Wilk test, which resulted in a p-value greater than 0.05, further supporting that our data was normally distributed. This experience taught me the importance of using multiple methods to assess data distribution and reinforced my skills in statistical analysis.

While volunteering for a community health initiative, I helped analyze data on participants' health metrics before and after a fitness program. We needed to determine if the changes in health indicators, like blood pressure readings, were normally distributed to apply proper statistical tests. I created a box plot and used the Kolmogorov-Smirnov test. The box plot revealed no significant outliers, and the Kolmogorov-Smirnov test also suggested that the data followed a normal distribution. This hands-on experience taught me how to practically apply statistical tests and communicate these findings effectively to our team.

In my first job as a data analyst, I frequently worked with customer satisfaction survey data. One of my tasks was to determine whether the response scores were normally distributed before performing regression analysis. I utilized histograms and normality tests like the Anderson-Darling test. I found that while the data showed some skewness, it was close to normal when transformed. This experience not only improved my statistical skills but also taught me how to handle real-world data challenges and make necessary adjustments to my analysis approach.