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Work Sample & Commentary: Who Is the Best?

The task
The focus of the task deals with the game of golf and therefore uses terminology that is golf related. It is not necessary to be familiar with the game of golf to solve this problem.

Students were presented with a scenario in which they had to determine which of three golfers is the “best” chipper (the term chipping refers to hitting the golf ball). Each golfer chipped ten balls. The measured distances of the balls from the cup are given. The data for this problem were devised so that the average distance from the cup is the same for all three golfers. Thus, students had to use other appropriate statistical measures to analyze the situation. “Getting close and being consistent” are the criteria on which the students were to judge the golfers.

Circumstances of performance
This sample of student work was produced under the following conditions:
alone - in a group
- in class as homework
with teacher feedback with peer feedback
timed opportunity for revision

Any time a task related to sports is used, teacher input may be necessary to clarify some terms and ensure equitable access to the task for all students.

This work sample illustrates a standard-setting
performance for the following parts of the standards:
a Statistics and Probability Concepts: The student…organizes data, and displays data with …graphs that are appropriate….
b Statistics and Probability Concepts: The student analyzes appropriately central tendencies of data by considering mean and median.
c Statistics and Probability Concepts: The student analyzes appropriately central tendencies of data by considering mean and median.
d Statistics and Probability Concepts: The student makes conclusions…based on data analysis.

What the work shows
a Statistics and Probability Concepts: The student…organizes data, and displays data with …graphs that are appropriate….
The student rewrote Sarah’s data in numerical order to illustrate median, quartiles, and extreme values of the range. It would have been good to see the same for Rick’s and Mike’s data.


b Statistics and Probability Concepts: The student analyzes data with respect to characteristics of frequency and distribution, including mode and range.

c Statistics and Probability Concepts: The student analyzes appropriately central tendencies of data by considering mean and median.

The student made meaningful comparisons of the data, keeping in mind the coach’s criteria for good chipping.

The student was thinking mathematically of the coach’s consistency criterion. He used the size of the inter-quartile range as a measure of consistency. Rick’s and Mike’s “quite large” ranges suggest some inconsistency, especially when compared with Sarah’s smaller inter-quartile range. The inter-quartile range of the middle half of the data combines notions of distribution with those of central tendency.

Rick’s farthest shot is recognized as an outlier. Indeed, his two chips that landed 312 and 320 inches away are both outliers. However, the student did not show them as such on the box-and-whiskers plot. He could have done so by plotting two isolated points at those two values instead of showing the range extending to 320 inches.

The realization that “the total yardage…was the same” suggests an understanding of average as more than a computational procedure. The total yardages are the same, just like the averages, because the golfers made the same number of chips.

d Statistics and Probability Concepts: The student makes conclusions…based on data analysis.

The student justifiably declared Sarah the winner, particularly on grounds of consistency. A strong case could have been made for Rick, though. The median value of his chips is 30 inches less than that for Sarah. Furthermore, comparing their attempts in order from closest to farthest, each of Rick’s best seven chips is closer than Sarah’s corresponding chip. Their eighth best chips are equidistant, 152 inches away from the cup. Only Sarah’s worst two chips are better than Rick’s worst two.