Across 244 dining visits the average tip was 17.14% of the total bill (median 16.82%). The random forest identifies 'total_bill' as the strongest predictor of tip percentage with a %IncMSE of 38.8. 0 of 4 demographic and visit factors showed statistically significant differences in tip rate — giving operators clear levers for influencing gratuity outcomes.

The horizontal bars show each predictor's %IncMSE from the random forest — how much prediction error grows when that variable is removed. 'total_bill' ranks first with a %IncMSE of 38.8, meaning it contributes the most unique information about tip percentage. Variables with near-zero or negative %IncMSE add little beyond what the other predictors already capture.

The histogram shows the full distribution of tip percentages across all dining visits. The mean of 17.14% exceeds the median of 16.82%, indicating a roughly symmetric distribution — a small number of very generous tippers pull the average up. The highest recorded tip rate was 36%. Most visits cluster between 10% and 25%, which matches the conventional tipping norm.

Mean tip percentage varies across days: Fri shows the highest average at 19.17%. One-way ANOVA finds these day-to-day differences are not statistically significant (F=1.68, p=0.1728). Weekend diners (Saturday and Sunday) tend to be in a more relaxed mindset, which often correlates with more generous gratuities.

Grouped bars show mean tip percentage for each day-time combination, revealing whether Dinner and Lunch follow similar patterns or diverge by day. The highest-tipping combination is Fri Dinner at 19.56%. Lunch service is only available Thursday and Friday in this dataset — so day-time interaction effects are concentrated in those two days and worth monitoring separately.

The table summarizes all hypothesis tests at the alpha = 0.05 level. 0 of 4 factors show statistically significant differences in tip percentage. ANOVA was used for day-of-week (4 groups) and Welch t-tests for the three binary factors (sex, smoker status, meal time). Factors listed as 'Significant' have p-values below 0.05 and represent genuine group differences beyond random sampling variation.

Smokers tip a mean of 17.74% vs. non-smokers — a gap of approximately 0.95 percentage points. 'Yes' diners are the more generous tippers on average. The Welch t-test finds this difference is not statistically significant (p=0.2873). Even if statistically marginal, a persistent directional difference may be practically meaningful for large dining volumes.

Box plots show the tip percentage distribution for each party-size group. Solo diners average around 19.6% while large parties (4+) average around 15.5%. The 'large group' effect is well-documented in hospitality research: group dynamics, diffusion of responsibility, and automatic gratuity policies all reduce per-person tip rates. Restaurants may wish to review automatic gratuity thresholds for parties of 4 or more.

Female customers tip a higher mean percentage (17.69%) vs 16.82% — a gap of 0.87 percentage points. The Welch t-test finds this difference is not statistically significant (p=0.3323). If the gap is not statistically significant, hospitality operators should avoid assumptions about generosity by gender and focus on factors with stronger evidence.