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 interquartile range as a measure
of consistency. Rick’s and Mike’s “quite large”
ranges suggest some inconsistency, especially when compared with
Sarah’s smaller interquartile range. The interquartile 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 boxandwhiskers
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.
