Ch. 2 



REVIEW PROBLEMS 



47 



14. Calculate the median and the lower limits of the second quartile and of 

 the 85th percentile of the data in problem 13. Ans. 98.14, 90.99, 107.32. 



15. What percentage of the bonds of problem 13 had prices below 100? 



16. Within what limits do the prices of the "middle" 60 per cent of the 

 bonds lie (that is, excluding the lower and also the upper 20 per cent of the 

 prices in the array)? Ans. 88.85 to 105.99. 



17. The figures recorded below are the batting averages of all American Asso- 

 ciation players who were at bat at least 100 times, as reported by the Kansas 

 City Star on July 29, 1951. The averages are arrayed from highest to lowest. 

 Make a frequency distribution table, and compute /x and a. 



18. Referring to problem 17, write numbers from 1 to 84, inclusive, on pieces 

 of pasteboard, mix them well, and then draw 5 at random. Consider each 

 number drawn as the rank of a person's batting average in the above list, 

 starting at the top. Do this 10 times, and record the range of batting averages 

 in each set of 5 so drawn. Compare the average range with the standard 

 deviation obtained in problem 17. If another such set of batting averages had 

 twice as large a standard deviation, what general effect do you think this would 

 have on the range? 



