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