How do you determine if a data set is normally distributed?

During my final year in college, I worked on a research project analyzing student performance data. To determine if the test scores were normally distributed, I created a histogram and noticed a bell-shaped curve, which suggested normality. Additionally, I used a Q-Q plot, which showed that the data points closely followed the diagonal line, further supporting the idea that my data was normally distributed. This experience taught me the importance of visual tools in data analysis and how to interpret them effectively.

I volunteered for a local charity where I analyzed data from a fundraising campaign. I collected data on the amounts raised each week and plotted it to see if it followed a normal distribution. I noticed that while the data had some outliers, the bulk of the data formed a symmetric shape. I also calculated the skewness and kurtosis, finding they were close to zero, which suggested a normal distribution. This experience helped me appreciate how statistical methods can guide decision-making even in non-profit sectors.

In my first job as a data analyst, I was tasked with evaluating customer satisfaction scores. To check for normal distribution, I used both a histogram and conducted the Shapiro-Wilk test. The histogram revealed a roughly bell-shaped curve, and the test results indicated that I could not reject the null hypothesis of normality. This analysis was crucial for determining the right statistical methods for further analysis, reinforcing my understanding of how to apply theoretical knowledge in a practical context.