In pairs :
age/sex : BOTH signicant; no interaction
age/place: only age significant
sex/place: NEITHER significant

So: age is a strong factor;
sex is somewhat of a factor, when broken
out by age.
Problem 2
which of these factors are significant ?
Alone:
Age: YES (just look at the graph)
Sex: no, not alone (student's t; look at 95% bars on graph)
Place: no, not alone (just look at graph)
                 
sex where age deaths per 100 age sex where   rearrange to do 2-factor ANOVA, ignoring urban/rural :  
femaie rural 50-54 8.7 52 male rural     52 57 62 67 72
femaie urban 50-54 8.4 57 female urban   50-54 55-59 60-64 65-69 70-74  
male rural 50-54 11.7 62   female 8.7 11.7 20.3 30.9 54.3   8.55 12.65 19.8 33 52.15
male urban 50-54 15.4 67   8.4 13.6 19.3 35.1 50   0.212132034 1.343502884 0.707106781 2.969848481 3.040559159
female rural 55-59 11.7 72   male 11.7 18.1 26.9 41 66   13.55 21.2 31.95 47.8 68.55
female urban 55-59 13.6   15.4 24.3 37 54.6 71.1   2.61629509 4.384062043 7.14177849 9.616652224 3.606244584
male rural 55-59 18.1    
male urban 55-59 24.3    
female rural 60-64 20.3   Anova: Two-Factor With Replication  
female urban 60-64 19.3 1940 Virginia deaths per 100    
male rural 60-64 26.9   SUMMARY 50-54 55-59 60-64 65-69 70-74 Total  
male urban 60-64 37   female              
female rural 65-69 30.9   Count 2 2 2 2 2 10  
female urban 65-69 35.1   Sum 17.1 25.3 39.6 66 104.3 252.3  
male rural 65-69 41   Average 8.55 12.65 19.8 33 52.15 25.23  
male urban 65-69 54.6   Variance 0.045 1.805 0.5 8.82 9.245 280.2734444  
female rural 70-74 54.3    
female urban 70-74 50   male              
male rural 70-74 66   Count 2 2 2 2 2 10  
male urban 70-74 71.1   Sum 27.1 42.4 63.9 95.6 137.1 366.1  
  Average 13.55 21.2 31.95 47.8 68.55 36.61  
  Variance 6.845 19.22 51.005 92.48 13.005 450.5787778  
                     
by age alone :     Total        
  50-54 55-59 60-64 65-69 70-74     Count 4 4 4 4 4  
  8.7 11.7 20.3 30.9 54.3     Sum 44.2 67.7 103.5 161.6 241.4  
  8.4 13.6 19.3 35.1 50     Average 11.05 16.925 25.875 40.4 60.35  
  11.7 18.1 26.9 41 66     Variance 10.63 31.37583333 66.37583333 106.78 97.07  
  15.4 24.3 37 54.6 71.1      
       
  50-54 55-59 60-64 65-69 70-74     ANOVA  
      Source of Variation SS df MS F P-value F crit  
Mean 11.05 16.925 25.875 40.4 60.35     Sample 647.522 1 647.522 31.9023501 0.000212978 4.964602701  
Standard Error 1.630184039 2.800706756 4.073568256 5.16672043 4.926205436     Columns 6288.497 4 1572.12425 77.45599103 1.74635E-07 3.478049691  
Median 10.2 15.85 23.6 38.05 60.15     Interaction 86.203 4 21.55075 1.061770212 0.424285994 3.478049691  
Standard Deviation 3.260368077 5.601413512 8.147136511 10.33344086 9.852410872     Within 202.97 10 20.297  
Sample Variance 10.63 31.37583333 66.37583333 106.78 97.07      
Count 4 4 4 4 4     Total 7225.192 19          
Confidence Level(95.0%) 5.18797317 8.913098867 12.96391224 16.44281034 15.67738429      
2 * std error 3.260368077 5.601413512 8.147136511 10.33344086 9.852410872      
      So, BOTH Age and Sex are significant factors in 2-way.  
      No interaction to speak of  
 
     
       
                     
   
      rearrange to do 2-factor ANOVA, ignoring sex :        
       
       
      50-54 55-59 60-64 65-69 70-74  
      rural 8.7 11.7 20.3 30.9 54.3  
      rural 11.7 18.1 26.9 41 66  
      urban 8.4 13.6 19.3 35.1 50  
      urban 15.4 24.3 37 54.6 71.1  
       
       
      Anova: Two-Factor With Replication  
       
      SUMMARY 50-54 55-59 60-64 65-69 70-74 Total  
      rural              
      Count 2 2 2 2 2 10  
      Sum 20.4 29.8 47.2 71.9 120.3 289.6  
      Average 10.2 14.9 23.6 35.95 60.15 28.96  
      Variance 4.5 20.48 21.78 51.005 68.445 374.0293333  
       
      urban              
      Count 2 2 2 2 2 10  
                    Sum 23.8 37.9 56.3 89.7 121.1 328.8  
  Average 11.9 18.95 28.15 44.85 60.55 32.88  
       
 
          Variance 24.5 57.245 156.645 190.125 222.605 420.2328889  
by sex alone : female male      
  8.7 11.7     Total        
  8.4 15.4     Count 4 4 4 4 4  
  11.7 18.1     Sum 44.2 67.7 103.5 161.6 241.4  
  13.6 24.3     Average 11.05 16.925 25.875 40.4 60.35  
  20.3 26.9     Variance 10.63 31.37583333 66.37583333 106.78 97.07  
  19.3 37      
  30.9 41      
  35.1 54.6     ANOVA  
  54.3 66     Source of Variation SS df MS F P-value F crit  
  50 71.1     Sample 76.832 1 76.832 0.94003646 0.355133865 4.964602701  
      Columns 6288.497 4 1572.12425 19.23487759 0.000109221 3.478049691  
  mean 25.23 36.61     Interaction 42.533 4 10.63325 0.13009739 0.967877221 3.478049691  
  n 10 10     Within 817.33 10 81.733  
  stnd dev 16.74136925 21.22684097      
  st error 5.294085799 6.712516501     Total 7225.192 19          
  2* std error 10.5881716 13.425033      
       
  combined sigma 27.03427865      
  t 0.420947056     So, place is NOT signifanct in 2-way with age; neither is there an interaction    
  stud-t p-val 0.342437345  
   
    re arrange to do sex - place 2 factor :          
       
      male female  
      urban 15.4 8.4  
                    urban 24.3 13.6  
  urban 37 19.3  
by place alone :                   urban 54.6 35.1  
  rural urban
    urban 71.1 50  
  8.7 8.4     rural 11.7 8.7  
  11.7 15.4     rural 18.1 11.7  
  11.7 13.6     rural 26.9 20.3  
  18.1 24.3     rural 41 30.9  
  20.3 19.3     rural 66 54.3  
  26.9 37      
  30.9 35.1   Anova: Two-Factor With Replication  
  41 54.6      
  54.3 50   SUMMARY male female Total  
  66 71.1   urban        
    Count 5 5 10  
  mean 28.96 32.88   Sum 202.4 126.4 328.8  
  n 10 10   Average 40.48 25.28 32.88  
  stnd dev 19.33983799 20.49958265   Variance 509.967 291.157 420.2328889  
  st error 6.115793762 6.482537226      
  2* std error 12.23158752 12.96507445   rural        
    Count 5 5 10  
    Sum 163.7 125.9 289.6  
    Average 32.74 25.18 28.96  
    Variance 466.393 339.452 374.0293333  
       
    Total        
    Count 10 10  
    Sum 366.1 252.3  
    Average 36.61 25.23  
    Variance 450.5787778 280.2734444  
       
       
    ANOVA  
    Source of Variation SS df MS F P-value F crit  
    Sample 76.832 1 76.832 0.191247 0.667726109 4.493998418  
                    Columns 647.522 1 647.522 1.61178467 0.222396828 4.493998418  
Interaction 72.962 1 72.962 0.181613958 0.675667759 4.493998418  
Within 6427.876 16 401.74225  
   
Total 7225.192 19          
   
   
nothing is significant here