26 SUMMARIZATION OF DATA Ch. 2 



Other similar information can be read from the above tables and 

 graphs. Moreover, it will be shown later that the r.c.f. graph can be 

 employed to determine quartile, decile, and even percentile limits if 

 the graph is drawn with sufficient care. In addition it will be shown 

 in the next section that in some situations good approximations to fi 

 and a can be computed from the frequency distribution table. In 

 brief, the frequency and r.c.f. tables and graphs serve as visual guides 

 and as sources of good approximations. If more precise information 

 is needed or desired (and it seldom is) , one can analyze the individual 

 observations. 



The graph of the r.c.f. distribution sometimes is called an ogive. 



PROBLEMS 



1. Following are some numbers of house flies counted on individual dairy 

 cows which had been sprayed with a 3 per cent solution of Thanite in 40 oil: 

 35, 37, 41, 103, 174, 7, 11, 32, 23, 7, 6, 3, 14, 23, 23, 36, 25, 27, 3, 3, 13, 14, 14, 6, 

 15, 9, 11, 21, 9, 12, 3, 15, 19, 29, 26, 1, 8, 4, 9, 7, 12, 5, 1, 3, 5, 60, 11, 6, 4, 7, 22, 

 28, 5, 3, 6, 15, 1, 2, 11, 4, 27, 1, 0, 0, 19, 6, 2, 3, 4, 13, 5, 12, 11, 14, 45, 4, 38, 5, 17, 

 27, 39, 33, 13, 9, 8, 33, 19, 6, 12, 32, 11, 35, 18, 11, 25, 23, 45, 30, 4, 4, 15, 15, 16, 



11, 16, 18, 32, 49, 129, 7, 21, 26, 76, 40, 5, 7, 5, 7, 4, 62, 91, 133, 61, 59, 20, 26, 10, 



12, 6, 7, 8, 8, 2, 24, 21, 51, 110, 11, 6, 4, 4, 5. 5, 5, 13, 3, 6, and 7. Construct 

 frequency and relative cumulative frequency distributions for these data, esti- 

 mate the median, and decide whether fi or md is the preferable average for 

 these data. Is this a skewed distribution? Use class intervals: 0-8, 9-17, etc. 



2. Graph the distributions asked for in problem 1. 



3. Compute the arithmetic mean and the median of the counts in problem 1. 

 Compare them, and draw appropriate conclusions. SX = 3031, 1,X 2 = 163,439. 



4. Estimate from the ogive {r.c.j. curve) for problem 1 what percentage of 

 the fly counts lie between 5 and 25, inclusive. Check your calculation by 

 actually counting in problem 1. Ans. Graph, 46; by count, 45. 



5. Use the following frequency distribution table of 8-week weights (in grams) 

 of male White Rock chickens raised at the Kansas State College Poultry Farm 

 and the accompanying graphs to: (a) estimate n, (b) determine what percentage 

 of the weights exceeded 800 grams, (c) determine the range covered by the 

 "middle" 50 per cent of the weights, that is, excluding the upper and lower 

 25 per cent of the weights. 



6. Construct the frequency and the relative cumulative frequency distribu- 

 tions for the following counts, which are similar to those numbers in problem 1 : 

 6, 8, 13, 36, 48, 65, 34, 24, 49, 24, 40, 18, 20, 34, 87, 28, 14, 30, 24, 53, 57, 93, 36, 

 80, 33, 48, 57, 98, 73, 135, 21, 40, 32, 58, 4, 20, 30, 33, 20, 22, 28, 11, 23, 46, 41, 

 41, 44, 23, 18, 41, 48, 81, 80, 70, 5, 2, 13, 21, 21, 171, 1, 7, 10, 5, 2, 17, 9, 35, 6, 8, 

 10, 23, 19, 3, 25, 16, 131, 19, 19, 24, 12, 10, 4, 5, 2, 14, 17, 18, 10, 8, 4, 0, 4, 12, 

 14, 111, 17, 33, 3, 2, 7, 10, 17, 4, 5, 2, 48, 4, 11, 31, 18, 32, 26, 3, 18, 19, 101, 10, 

 10, 3, 27, 14, 29, 24, 13, 26, 31, 5, 20, 16, 13, 6, 7, 32, 17, 25, 6, 8, 5, 24, 13, 8, 7, 

 2, 1, 3, 26, 38, 44, 3, 5, 6, 22, 28, 16, 22, 8, 19, 12, 3, 24, 10, 8, 33, 20, 29, 3, 15, 



