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Problem of the Week
Problem B and Solution
Buckets of Golf Balls

Problem

Golfers will practice their golf game at a driving range. At a driving range, they hit practice balls by the bucket.

Annie works at a local driving range. Over a period of two weeks, she records the number of buckets of balls that she hands out each day. The table below displays her data.

Day Week 1 Week 2
Monday \(11\) \(14\)
Tuesday \(25\) \(32\)
Wednesday \(27\) \(34\)
Thursday \(34\) \(37\)
Friday \(44\) \(50\)
Saturday \(57\) \(70\)
Sunday \(52\) \(63\)

  1. A stacked bar graph is given for Week \(1\), showing the percentage of each day’s buckets relative to the total (\(250\) buckets) for that week. For example, on Monday Annie gives out \(11\) buckets, which is \(\frac{11}{250} = 4.4\%\) of the total; on Tuesday she gives out \(25\) buckets, which is \(\frac{25}{250}=10.0\%\) of the total.

    The vertical axis of the graph ranges from 0 to 100 by 10s. The horizontal axis has Week 1 and Week 2. Above Week 1 there are seven rectangular blocks, one for each day of the week, stacked one on top of the other with Monday at the bottom. The top of the Monday block is at a height of around 5. The tops of the Tuesday through Sunday blocks lie at approximate heights as follows: Tuesday at 15, Wednesday at 25, Thursday at 39, Friday at 56, Saturday at 79, and Sunday at 100.

    Verify that the remaining blocks of the graph accurately portray the given data for Week \(1\) by calculating the remaining daily percentages.

  2. Calculate the daily percentages for Week \(2\), and create a similar stacked bar graph for Week \(2\). Round percentages to one decimal place.

  3. By examining the bar graphs, what conclusions could you draw about the number of buckets given out each day?

Solution

  1. The remaining days’ percentages are:
    Wednesday: \(\frac{27}{250} = 10.8\%\)
    Thursday: \(\frac{34}{250}\ = 13.6\%\)
    Friday: \(\frac{44}{250} =17.6\%\)
    Saturday: \(\frac{57}{250} = 22.8\%\)
    Sunday: \(\frac{52}{250} = 20.8\%\)

    Note: We can find each percentage by rewriting the fraction as an equivalent fraction with a denominator of \(100\). We will look at the data for Wednesday and show two ways to do this.

    1. We will get the denominator to be \(1000\) by multiplying numerator and denominator by \(4\). Then, we divide each by \(10\) to get a fraction with a denominator of \(100\). \[\frac{27}{250} = \frac{108}{1000} = \frac{10.8}{100} = 10.8\%\]

    2. Since \(250 \div 100 = 2.5\), we can divide both numerator and denominator by \(2.5\) to get \(\frac{10.8}{100} = 10.8\%\).

    The heights of the remaining blocks of the graph do portray the given data for Week \(1\).

  2. During Week \(2\), Annie handed out a total of \(300\) buckets. The daily percentages and completed bar graph are below.

    Monday: \(\frac{14}{300}\approx 4.7\%\)
    Tuesday: \(\frac{32}{300}\approx 10.7\%\)
    Wednesday: \(\frac{34}{300}\approx 11.3\%\)
    Thursday: \(\frac{37}{300}\approx 12.3\%\)
    Friday: \(\frac{50}{300}\approx 16.7\%\)
    Saturday: \(\frac{70}{300}\approx 23.3\%\)
    Sunday: \(\frac{63}{300}=21.0\%\)

    Above Week 2 there are seven rectangular blocks, one for each day of the week, stacked one on top of the other with Monday at the bottom. The top of the Monday block is at a height of around 5. The tops of the Tuesday through Sunday blocks lie at approximate heights as follows: Tuesday at 15, Wednesday at 27, Thursday at 39, Friday at 56, Saturday at 79, and Sunday at 100.

  3. The tallest rectangular boxes are for Saturday and Sunday. Therefore, we can say that the most buckets are given out on either Saturday or Sunday. The data in the table shows that it is in fact on Saturday when the most buckets are given out.

    The shortest rectangular box is for Monday. Therefore, we can say that the fewest number of buckets are given out on Monday. This is verified by the table.