In this exercise Romberg rules are derived. Assume that I(n) is an integration rule that uses n subintervals and h is the corresponding width of each subinterval. (a) It is known that the error term for the composite Simpson’s rule involves even powers of h. In particular, b a f(x)dx = IS(n) + αh4 + βh6 + γh8 + · · · . Show that the integration rule IR = 1 15 [16IS(2n) − IS(n)] has an error that is O(h6).

Name and describe the three most important measures of central tendency. choose the correct answer below. a. the mean, sample size, and mode are the most important measures of central tendency. the mean of a data set is the sum of the observations divided by the middle value in its ordered list. the sample size of a data set is the number of observations. the mode of a data set is its highest value in its ordered list. b. the sample size, median, and mode are the most important measures of central tendency. the sample size of a data set is the difference between the highest value and lowest value in its ordered list. the median of a data set is its most frequently occurring value. the mode of a data set is sum of the observations divided by the number of observations. c. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is the product of the observations divided by the number of observations. the median of a data set is the lowest value in its ordered list. the mode of a data set is its least frequently occurring value. d. the mean, median, and mode are the most important measures of central tendency. the mean of a data set is its arithmetic average. the median of a data set is the middle value in its ordered list. the mode of a data set is its most frequently occurring value.