4. Explain how the relationship between the mean and the median provides

information about the symmetry or skewness of the data's distribution.

5. What is the primary disadvantage of using the range rather than the

variance to compare the variability of two data sets?

6. Can standard deviation of a variable be negative?

7. A sample is drawn from the population of all adult females in Canada

and the height in centimetres is observed. One of the observations has a

sample z-score of 6. Describe in one sentence what this implies about that

particular member of the sample.

8. In archery practice, the mean distance of the points of impact from the

target centre is 5 inches. The standard deviation of these distances is 2

inches. At most, what proportion of the arrows hit within 1 inch or beyond

9 inches from the target centre? Hint: Use 1/k2

.

a) 1/4

b) 1/8

c) 1/10

d) cannot be determined from the data given.

e) none of the above

8. You know the minimum, the maximum, and the 25th, 50th, and 75th percentiles

of a distribution. Which of the following measures of central tendency or

variability can you determine?

mean, median, mode, trimean, geometric mean, range, interquartile range,

variance, standard deviation

9. For the numbers 1, 3, 4, 6, and 12:

Find the value (v) for which ?(X-v)2 is minimized.

Find the value (v) for which ?|x-v| is minimized.

10. Your younger brother comes home one day after taking a science test. He says

that some- one at school told him that "60% of the students in the class scored

above the median test grade." What is wrong with this statement? What if he had

said "60% of the students scored below the mean?

1 Let f (x, y) = 512 xy if 0