Sec. 2.5 CALCULATION OF /* AND <r FROM TABLES 33 



is perfectly symmetrical (no skewness) the arithmetic mean and the 

 median are equal. The more skewed the distribution, the farther 

 apart the median and this mean may become. 



PROBLEMS 



1. Compute the arithmetic mean of the following numbers by Method A of 

 Table 2.52: 



A': 24, 8, 7, 14, 21, 10, 12, 14, 17, 9, 11, 5, 15, 16, 8, 2, 13, 18, 12, 3, 15, 4, 16, 19, 

 and 11. 



Use class intervals 2-5.9 . . . , etc., to 22-25.9 



2. Compute the arithmetic mean and the standard deviation for problem 1 

 exactly, and compare with the values obtained by the methods of Table 2.52. 



Ans. fi = 12.2, a = 5.5; they are 12.8 and 5.3 by table. 



3. Put the numerical measurements of problem 1, section 2.4, into a fre- 

 quency distribution table with class intervals of equal lengths, and compute 

 the standard deviation of those counts. 



4. Do as in problem 3 for the data of problem 6, section 2.4. Ans. 23.7. 



5. Calculate the mean and standard deviation for the hypothetical data in 

 the following table. Also, compare six times the standard deviation with the 

 range as nearly as it can be derived from the table. 



6. Graph the relative cumulative frequency distribution for problem 5 and 

 read from it the percentage of the measurements which exceed 23. Which ex- 

 ceed the arithmetic mean. Which lie between the mean and 23. 



Ans. 28%, 50%, 22%. 



7. What is the median for problem 5 as read from the r.c.j. curve? Which is 

 the modal class? Would you expect the mode and the median to differ by 

 as much as two units ; or less than two units? Give reasons. 



8. Graph the following actual or estimated age distributions of the United 

 States population and draw appropriate conclusions regarding apparent trends 

 during the decades covered. Consider top class as 0-4 and bottom one as 75-79. 



