Discuss the below:
Q1 All measures of variation are nonnegative in value for all sets of data.
a. What does it mean for a value to be "nonnegative"?
b. Describe the conditions necessary for a measure of variation to have the value zero.
c. Describe the conditions necessary for a measure of variation to have a positive value.
Q2 Consider the sample 2, 4, 7, 8, 9, Find the following:
a. range
b. variation s'2, using formula (2.6)
c. standard deviation, s
Q3 Consider the sample 6, 8, 7, 5, 3, 7, Find the following:
a. range
b. variance s'2, using formula (2.6)
c. standard deviation, s
Q4 Given the sample 7, 6, 10, 7, 5, 9, 3, 7, 5, 13, Find the following:
a. variance s'2, using formula (2.6)
b. variance s'2, using formula (2.10
c. standard deviation, s
Q5 Fifteen randomly selected college students were asked to state the number of hours they slept last night. The resulting data are 5, 6, 6, 8, 7, 7, 9, 5, 4, 8, 11, 6, 7, 8, 7, Find the following:
a. variance s'2, using formula (2.6)
b. variance s'2, using formula (2.10
c. standard deviation, s
Q6 The article "More hours in class logged by college profs" in The Blade (January 23, 2000) reported on a study done at the four-year colleges in Ohio about the total hours spent by college professors in instructing and advising students. The times reported for the 13 schools were: 28.4, 44.4, 36.4, 33.5, 34.9, 30.5, 32.7, 24.6, 26.9, 34.7, 33.4, 29.3, 33.3
a. find the range
b. find the variation
c. find the standard deviation
Q7 Adding (or subtracting) the same number from each value in a set of data does not affect the measures of variability for that set of data.
a. Find the variance of this set of annual heating-degree day data: 6017, 6173, 6275, 6350, 6001, 6300.
b. Find the variance of this set of data (obtained by subtracting 6000 from each value in part a): 17, 173, 275, 350, 1, 300.
Q8 Recruits for a police academy were required to undergo a test that measures their exercise capacity. The exercise capacity (in minutes) were obtained for each of 20 recruits: 25, 27, 30, 33, 30, 32, 30, 34, 30, 27, 26, 25, 29, 31, 31, 32, 34, 32, 33, 30
a. draw a dotplot of the data
b. find the mean
c. find the range
d. find the variation