Box plots, also known as box-and-whisker plots, are a powerful visual tool for representing data distributions. They display five key summary statistics: the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value. The box itself encompasses the interquartile range (IQR),...
Comparing the Data
In this case, we are presented with box plots for Charlie and David's movie-watching habits over a year. The box plot for Charlie shows a wider box and longer whiskers compared to David's box plot. This suggests that Charlie's data has a larger spread and greater variability.
Analyzing the Variation
To determine who had less variation in the number of movies watched, we need to focus on the interquartile range (IQR). The IQR represents the spread of the middle 50% of the data. A smaller IQR indicates less variation.
Based on the box plots, David's box plot has a smaller IQR compared to Charlie's. This indicates that David's movie-watching habits were more consistent and had less variation throughout the year. Charlie's data, on the other hand, shows a wider spread of movie-watching numbers, implying greater variability in his movie consumption habits.
Interpreting the Results
The box plots provide a clear visual comparison of Charlie and David's movie-watching data. The smaller IQR in David's box plot indicates that his movie-watching habits were more consistent and less variable compared to Charlie's. This suggests that David might have a more predictable movie-watching routine or preferences, while Charlie's habits might be more influenced by factors leading to more fluctuation in the number of movies watched.
Further Insights
While the box plots provide valuable information about the variation in movie-watching habits, additional analysis could be conducted to gain further insights. For example, we could examine the specific months where Charlie watched significantly more or fewer movies compared to David. This could help us understand the underlying reasons for the variability in Charlie's data.
Conclusion
By comparing the box plots, we can confidently conclude that David had less variation in the number of movies watched compared to Charlie. This is evident from the smaller IQR in David's box plot, indicating more consistency in his movie-watching habits.