Question

3.1 warm-up
notice and wonder: dot plots
the dot plots represent the distribution of the amount of tips, in dollars, left at 2 different restaurants on the same night.
what do you notice? what do you wonder?
two dot plots: first with x-axis 0–11 labeled “tip amount (dollars)”, second with x-axis 7–18 labeled “tip amount (dollars)”

Explanation:

Notice:

• The two dot plots have a similar shape of distribution (unimodal, with the peak around the middle - like values). For the first plot, the tip amounts range from 1 to 10 dollars, and for the second, from 8 to 17 dollars. The second plot's values are all 7 dollars more than the corresponding positions in the first plot (e.g., the peak in the first is at 4, in the second at 11; 4 + 7 = 11).
• The number of dots (frequency) at each position seems to be the same between the two plots when we account for the 7 - dollar shift. For example, at tip amount 1 (first plot) there's 1 dot, at 8 (second plot) there's 1 dot; at 2 (first) and 9 (second) both have 2 dots, etc.

Wonder:

• Why is there a consistent 7 - dollar shift in the tip amounts between the two restaurants?
• Do these two restaurants have a relationship (like one being a branch of the other, or same menu pricing with a 7 - dollar difference in base prices) that causes the tip amounts to be shifted by 7 dollars?
• Are the customer bases similar in terms of tipping behavior, just with a 7 - dollar offset in the total bill (and thus tip) amounts?

Answer:

Notice:

• The two dot plots have a similar frequency distribution, and the second plot’s tip amounts are 7 dollars higher than the first’s (e.g., peak at 4 vs 11, 1 vs 8, etc.).
• Both are unimodal with frequencies matching when shifted by 7.

Wonder:

• Why is there a 7 - dollar shift in tip amounts?
• Do the restaurants have a pricing - related relationship causing this shift?
• Are customer tipping behaviors similar with a 7 - dollar bill offset?