Question

marie started working as a waitress at an italian restaurant. the scatterplot below shows the relationship between the number of hours she works each day and the tips that she has earned in that time.
maries daily earnings
based on the scatterplot, approximately how much does she earn in tips in a 10 - hour shift?

Explanation:

Step1: Locate 10 on x - axis

Find the position corresponding to 10 hours on the horizontal axis (number of hours worked in a day).

Step2: Estimate y - value

Since the x - axis (number of hours) has no mark for 10, we can observe the trend. The points generally show an upward trend. If we assume the trend continues, and looking at the right - most points (around 9 hours, tips are in the 40s - 50s range). But if we consider the pattern of increase (not a strict linear, but a general upward movement), and if we extend the visual trend, we can estimate.

Another way: If we consider that the scatter - plot has a positive association. There is no exact point at \(x = 10\), but if we assume a rough linear - like trend (even though it's not a perfect line). The highest tip value is around 68 at \(x=7\). But if we consider the spread, and since the data is scattered, but if we assume that the upper - bound of the trend (if we were to draw a line of best fit approximately in the upper part of the data cloud), we can estimate.

Looking at the grid, each vertical grid line is 5 units. If we assume that the value at \(x = 10\) (even though there is no point) follows the upper - end trend of the data. The upper - end values at \(x=7\) is 68, at \(x = 8\) is 60, at \(x=9\) is 45. But this is not a good approach. A better way is to note that the data has a positive correlation. If we consider that for \(x = 5\) (tips around 47), \(x=6\) (tips around 36), \(x=7\) (tips 68), \(x = 8\) (tips 60), \(x=9\) (tips 45). If we assume that the value at \(x = 10\) is in the range of 50 (by looking at the overall spread and the fact that the data has values mostly above 40 for \(x\geq5\) and the upper - end values for higher \(x\) (even with variability)).

Answer:

\(50\) (The answer is an estimate based on the positive trend and spread of the scatter - plot data)