In: Math
0-499 | 22 |
500-999 | 201 |
1000-1499 | 1,645 |
1500-1999 | 9,365 |
2000-2499 | 92,191 |
2500-2999 | 569,319 |
3000-3499 | 1,387,335 |
3500-3999 | 988,011 |
4000-4499 | 255,700 |
4500-4999 | 36,766 |
5000-5499 | 3,994 |
0-499 | 22 |
500-999 | 201 |
1000-1499 | 1,645 |
1500-1999 | 9,365 |
2000-2499 | 92,191 |
2500-2999 | 569,319 |
3000-3499 | 1,387,335 |
3500-3999 | 988,011 |
4000-4499 | 255,700 |
4500-4999 | 36,766 |
5000-5499 | 3,994 |
D) Use the normal model to determine the proportion of babies in each class
How do I manually determine the normal mode? Please provide step by step manually (excel is what I am using, however I need to show steps.
Thank you.
Class limit | Frequency (f) | Mid value (x) | xf | x^2f |
0-499 | 22 | 249.5 | 5489 | 1369505.5 |
500-999 | 201 | 749.5 | 150649.5 | 112911800.3 |
1000-1499 | 1,645 | 1249.5 | 2055427.5 | 2568256661 |
1500-1999 | 9,365 | 1749.5 | 16384067.5 | 28663926091 |
2000-2499 | 92,191 | 2249.5 | 207383654.5 | 4.6651E+11 |
2500-2999 | 569,319 | 2749.5 | 1565342591 | 4.30391E+12 |
3000-3499 | 1,387,335 | 3249.5 | 4508145083 | 1.46492E+13 |
3500-3999 | 988,011 | 3749.5 | 3704547245 | 1.38902E+13 |
4000-4499 | 255,700 | 4249.5 | 1086597150 | 4.61749E+12 |
4500-4999 | 36,766 | 4749.5 | 174620117 | 8.29358E+11 |
5000-5499 | 3,994 | 5249.5 | 20966503 | 1.10064E+11 |
Sum= | 3344549 | 11286197976 | 3.88981E+13 | |
Average= | 3374.505195 | 11630297.32 | ||
Mean (M)= | 3374.5052 | |||
Standard deviation (S)= | 492.9625 |
Class limit | Frequency (f) | x* | z=(x*-M)/S | T | Proportion |
0 | -6.8454 | 0 | 0 | ||
0-499 | 22 | 499.5 | -5.8321 | 0 | 0 |
500-999 | 201 | 999.5 | -4.8178 | 0 | 0 |
1000-1499 | 1,645 | 1499.5 | -3.8035 | 0.0001 | 0.0001 |
1500-1999 | 9,365 | 1999.5 | -2.7893 | 0.0026 | 0.0025 |
2000-2499 | 92,191 | 2499.5 | -1.775 | 0.0379 | 0.0353 |
2500-2999 | 569,319 | 2999.5 | -0.7607 | 0.2234 | 0.1855 |
3000-3499 | 1,387,335 | 3499.5 | 0.2536 | 0.6001 | 0.3767 |
3500-3999 | 988,011 | 3999.5 | 1.2678 | 0.8976 | 0.2975 |
4000-4499 | 255,700 | 4499.5 | 2.2821 | 0.9888 | 0.0912 |
4500-4999 | 36,766 | 4999.5 | 3.2964 | 0.9995 | 0.0107 |
5000-5499 | 3,994 | 5499.5 | 4.3107 | 1 | 0.0005 |
Mean (M)= | 3374.5052 | ||||
Standard deviation (S)= | 492.9625 |
Since for normal distribution mean=mode, hence mode=3374.5052.