Solucionario Probabilidad Anderson

Chapter 3
Descriptive Statistics: Numerical Methods




Learning Objectives


1. Understand the purpose of measures of location.


2. Be able to compute the mean, median, mode, quartiles, and various percentiles.


3. Understand the purpose of measures of variability.


4. Be able to compute the range, interquartile range, variance, standard deviation,and coefficient of variation.


5. Understand skewness as a measure of the shape of a data distribution. Learn how to recognize when a data distribution is negatively skewed, roughly symmetric, and positively skewed.


6. Understand how z scores are computed and how they are used as a measure of relative location of a data value.


7. Know how Chebyshev’s theorem and theempirical rule can be used to determine the percentage of the data within a specified number of standard deviations from the mean.


8. Learn how to construct a 5-number summary and a box plot.


9. Be able to compute and interpret covariance and correlation as measures of association between two variables.


10. Be able to compute a weighted mean.Solutions:


1. [pic]


10, 12, 16, 17, 20


Median = 16 (middle value)


2. [pic]


10, 12, 16, 17, 20, 21


Median =[pic]


3. 15, 20, 25, 25, 27, 28, 30, 34


[pic] 2nd position = 20


[pic] [pic]


[pic] 6th position = 28


[pic] [pic]4. [pic]


Median = 57 6th item


Mode = 53 It appears 3 times


5. a. [pic]


b. There are an even number of items. Thus, the median is the average of the 15th and 16th items after the data have been placed in rank order.


Median =[pic] = 40.5


c. Mode = 42.0 This value appears 3 times

d. First Quartile [pic]
Rounding up,we see that Q1 is at the 8th position.


Q1 = 38.2


e. Third Quartile [pic]


Rounding up, we see that Q3 is at the 23rd position.


Q3 = 42.1


6. a. [pic]


Median is average of 10th and 11th values after arranging in ascending order.


[pic]


Data are multimodal


b. [pic]


[pic]


Data arebimodal: 19.95 (3 brokers), 29.95 (3 brokers)


c. Comparing the measures of central location, we conclude that it costs more to trade 100 shares in a broker assisted trade than 500 shares online.


d. From the data we have here it is more related to whether the trade is broker-assisted or online. The amount of the online transaction is 5 times as great but the cost of thetransaction is less.


However, if the comparison was restricted to broker-assisted or online trades, we would probably find that larger transactions cost more.


7. a. [pic]


b. Yes, the mean here is 46 minutes. The newspaper reported an average of 45 minutes.


c. [pic]


d. Q1 = 7 (value of 8th item in ranked order)


Q3 = 70.4 (valueof 23rd item in ranked list)






e. Find position [pic] 40th percentile is average of values in 12th and 13th positions.


[pic]


8. a. [pic]= 695


[pic]


The modal age is 29; it appears 3 times.


b. Median is average of 10th and 11th items.


[pic]


Data suggest at - home workers are slightly younger.


c.For Q1,


[pic]


Since i is integer,


[pic]


For Q3,


[pic]


Since i is integer,


[pic]


d. [pic]


Since i is not an integer, we round up to the 7th position.


32nd percentile = 27






9. a. [pic] Median (Position 13) = 8296


b. Median would be better because of large data...