Introduction to Statistics (Quiz 1)
1. (10%) Classify the measurement scales of the following variables.
(1a) brand. (1b) grade point average. (1c) education. (1d) weight. (1e) temperature.
2. (25%) Distinguish between each of the following paired terms.
(2a) retrospective study versus prospective study. (2b) confounding variable versus interacting variable. (2c) categorical variable versus discrete variable. (2d) statistic versus parameter. (2e) case-control study versus matched-paired design.
3. (4%) (3%) (3%) Try to mark the relative positions of mean, median, and mode of bellshaped, right skewed, and left skewed distributions, respectively.
4. (2%)(5%)(3%) Consider the data of fourteen ninth-year students in Sydney using conventional instructional material. The number of seconds, required to arrive at a solution, are
recorded for the students. Each student was allotted at most 5 minutes to answer a question.
Is the measure of average appropriate for the considered data? Explain your answer. What
is the median time for these students to arrive at a solution?
Data: 130, 139, 146, 150, 161, 177, 228, 242, 265, 300+, 300+, 300+, 300+, 300+. (Note:
t+ represents the required time more than t seconds.)
5. (10%) Draw a box-plot via using the five-number summary: minimum=63, maximum=72,
the first quartile=68, median=70, the third quartile=71.
7. (5%) (5%) (5%) Compute the mean, variance, and coefficient of variation of the grouped
data with f1 , f2 , · · · , fg being the frequencies of the g classes [a0 , a1 ), [a1 , a2 ), · · · , [ag−1 , ag ].
7. Consider a sample of n paired quantitative variables {(X1 , Y1 ), · · · , (Xn , Yn )}.
(7a) (6%) Compute the sample correlation coefficient rXY of X and Y variables.
(7b) (6%) Explain the meanings of rXY = 1, rXY = −1, and rXY = 0, respectively.
(7c) (8%) Consider the re-scaled data {(U1 , V1 ), · · · , (Un , Vn )} with Ui = −aXi + b and
Vi = cYi + d, where a and c are positive constants and b and d are any constants. Show that
the correlation coefficient rU V = −rXY .
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