Chapter 1 of statistics

Which of the following is NOT a value in the​ 5-number summary?

Mean

Which is relatively​ better: a score of 58 on a psychology test or a score of 49 on an economics​ test? Scores on the psychology test have a mean of 8585 and a standard deviation of 10. Scores on the economics test have a mean of 58 and a standard deviation of 3.

The psychology test score is relatively better because its z score is greater than the z score for the economics test score.

If your score on your next statistics test is converted to a z​ score, which of these z scores would you​ prefer: −​2.00, −​1.00, ​0, 1.00,​ 2.00? Why?

The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores.

In modified​ boxplots, a data value is​ a(n) _______ if it is above Q+​(1.5)(IQR) or below Q−​(1.5)(IQR). 3 1

outlier

Whenever a data value is less than the​ mean, _______.

the corresponding z-score is negative.

A data value is considered​ _______ if its​ z-score is less than −2 or greater than 2.

unusual

When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the​ mean, we call the new value a​ _______.

z-score.

With a height of 70 ​in, Roger was the shortest president of a particular club in the past century. The club presidents of the past century have a mean height of 75.1 in and a standard deviation of 2.4 in. a. What is the positive difference between Roger​'s height and the​ mean? b. How many standard deviations is that​ [the difference found in part​ (a)]? c. Convert Roger​'s height to a z score. d. If we consider​ "usual" heights to be those that convert to z scores between −2 and​ 2, is Roger​'s height usual or​ unusual?

To find the positive difference between Roger​'s height and the​ mean, subtract the mean from Roger​'s height and find the absolute value of the difference. 70 cm - 75.1 cm =5.1 in b. To determine how many standard deviations the difference​ is, compare the​ difference, 5.1, to the standard​ deviation, 2.4 5.1 Over 2.4 ≈2.13 standard deviations c. A z score is the number of standard deviations that a given value x is above or below the mean. It is found using the following expressions. Sample Population z= x- x overbar Over s or z=x- μ over σ The club is a population.​ Therefore, to convert Roger​'s height to a z​ score 70-75.1 divide 2.4 = -2.13

Below are 36 sorted ages of an acting award winner. Find Upper P using the method presented in the textbook. 30 18,18,19,21,22,25,26,26,29,31,32,34,37,41,42,42,43,45,47,49,51,5,51,52,55,58,58,59,62,63,64,65,67,74,74,76

next compute L=(k Over 100)times n where n is the total number of values in the data set and k is the percentile being used. n=36 k= 30 30/100*36 10.8 L=11 p 30=32

Below are 36 sorted ages of an acting award winner. Find the percentile corresponding to age 59 using the method presented in the textbook. 16,17,17,21,22,27,30,33,37,37,40,42,43,48,54,56,57,59,59,60,60,62,62,64,65,65,68,70,70,72,72,73,74,77,78,80

percentile of value = number of values less than x Over total number of values times 100 For this problem x=59. How many values are less than 59​? 17 What is the total number of​ values? 36 59=17/36 x100