Skewness

	A	B	C	D	E	F	I	J	K
1	Exact age	Male	Female	Total	Difference	Fraction	Fraction * Age	Fraction * (Age-Mean)^2	Fraction * (Age - Mean / StDev)^3
2	Exact age	Number of lives b	Number of lives b	data from https://www.ssa.gov/oact/STATS/table4c6.html
3	0	100,000	100,000	200,000	1,153	0.58%	0	35.04572076	-0.5958091205
4	1	99,370	99,477	198,847	77	0.000385	0.000385	2.280783523	-0.03827807104
5	2	99,327	99,443	198,770	50	0.00025	0.0005	1.442794132	-0.02389961226
6	3	99,298	99,422	198,720	38	0.00019	0.00057	1.067845601	-0.0174558179
7	4	99,276	99,406	198,682	30	0.00015	0.0006	0.8206955231	-0.01323676247
8	5	99,260	99,392	198,652	28	0.00014	0.0007	0.7454113754	-0.01185998978
9	6	99,245	99,379	198,624	24	0.00012	0.00072	0.6215316537	-0.009753456756
10	7	99,232	99,368	198,600	23	0.000115	0.000805	0.5791968017	-0.008962818891
11	8	99,219	99,358	198,577	21	0.000105	0.00084	0.5140335278	-0.007842360985
12	9	99,208	99,348	198,556	20	0.0001	0.0009	0.4756620887	-0.0071532288
13	10	99,197	99,339	198,536	18	0.00009	0.0009	0.4157715931	-0.006161908912
14	11	99,188	99,330	198,518	21	0.000105	0.001155	0.470898524	-0.006876234084
15	12	99,177	99,320	198,497	26	0.00013	0.00156	0.5657354726	-0.008137720103
16	13	99,162	99,309	198,471	37	0.000185	0.002405	0.7808618394	-0.01106190039
17	14	99,139	99,295	198,434	51	0.000255	0.00357	1.043444263	-0.01455419207
18	15	99,105	99,278	198,383	67	0.000335	0.005025	1.328275592	-0.01823745332
19	16	99,059	99,257	198,316	83	0.000415	0.00664	1.593627078	-0.0215332861
20	17	99,001	99,232	198,233	101	0.000505	0.008585	1.877150007	-0.0249549721
21	18	98,929	99,203	198,132	117	0.000585	0.01053	2.103772441	-0.02750898193
22	19	98,845	99,170	198,015	137	0.000685	0.013015	2.381920146	-0.03062667283
23	20	98,746	99,132	197,878	155	0.000775	0.0155	2.604247355	-0.03291749701
24	21	98,633	99,090	197,723	173	0.000865	0.018165	2.80725599	-0.03487139173
25	22	98,506	99,044	197,550	190	0.00095	0.0209	2.975823821	-0.03631644506
26	23	98,367	98,993	197,360	202	0.00101	0.02323	3.051724704	-0.03657730061
27	24	98,220	98,938	197,158	211	0.001055	0.02532	3.072764607	-0.03615946669
28	25	98,067	98,880	196,947	217	0.001085	0.027125	3.044115676	-0.03515856708
29	26	97,910	98,820	196,730	228	0.00114	0.02964	3.078798054	-0.03488780835
30	27	97,746	98,756	196,502	234	0.00117	0.03159	3.039383327	-0.03377844033
31	28	97,579	98,689	196,268	245	0.001225	0.0343	3.058613084	-0.03332522399
32	29	97,406	98,617	196,023	254	0.00127	0.03683	3.045320919	-0.03251636925
33	30	97,229	98,540	195,769	263	0.001315	0.03945	3.025754467	-0.0316476857
34	31	97,048	98,458	195,506	274	0.00137	0.04247	3.022243903	-0.0309519696
35	32	96,862	98,370	195,232	282	0.00141	0.04512	2.979444108	-0.0298639752
36	33	96,672	98,278	194,950	291	0.001455	0.048015	2.942220113	-0.02884931806
37	34	96,478	98,181	194,659	302	0.00151	0.05134	2.91914391	-0.02798653251
38	35	96,278	98,079	194,357	312	0.00156	0.0546	2.880183333	-0.02698498672
39	36	96,072	97,973	194,045	324	0.00162	0.05832	2.853362453	-0.02611152365
40	37	95,860	97,861	193,721	337	0.001685	0.062345	2.828101182	-0.02526368925
41	38	95,641	97,743	193,384	348	0.00174	0.06612	2.779583545	-0.02422419101
42	39	95,417	97,619	193,036	360	0.0018	0.0702	2.733345517	-0.02322522106
43	40	95,188	97,488	192,676	377	0.001885	0.0754	2.717394827	-0.02249716262
44	41	94,951	97,348	192,299	393	0.001965	0.080565	2.685471666	-0.02164730783
45	42	94,706	97,200	191,906	414	0.00207	0.08694	2.677991556	-0.02100307778
46	43	94,450	97,042	191,492	442	0.00221	0.09503	2.702342048	-0.0206048117
47	44	94,178	96,872	191,050	470	0.00235	0.1034	2.711530315	-0.02008362362
48	45	93,890	96,690	190,580	505	0.002525	0.113625	2.744438073	-0.01972894084
49	46	93,581	96,494	190,075	543	0.002715	0.12489	2.774647593	-0.01934109858
50	47	93,250	96,282	189,532	587	0.002935	0.137945	2.814762229	-0.01900696731
51	48	92,893	96,052	188,945	638	0.00319	0.15312	2.864928178	-0.01872102293
52	49	92,505	95,802	188,307	696	0.00348	0.17052	2.920277104	-0.01844593958
53	50	92,082	95,529	187,611	758	0.00379	0.1895	2.964627321	-0.01807964353
54	51	91,622	95,231	186,853	824	0.00412	0.21012	2.996422635	-0.01762017852
55	52	91,122	94,907	186,029	898	0.00449	0.23348	3.027833868	-0.01714467282
56	53	90,577	94,554	185,131	974	0.00487	0.25811	3.036026216	-0.01652905801
57	54	89,986	94,171	184,157	1,057	0.005285	0.28539	3.036113521	-0.01586751149
58	55	89,345	93,755	183,100	1,145	0.005725	0.314875	3.020172039	-0.01512565139
59	56	88,651	93,304	181,955	1,236	0.00618	0.34608	2.982495485	-0.01428662888
60	57	87,903	92,816	180,719	1,329	0.006645	0.378765	2.921593378	-0.01335784725
61	58	87,098	92,292	179,390	1,420	0.0071	0.4118	2.830992993	-0.01232631681
62	59	86,236	91,734	177,970	1,511	0.007555	0.445745	2.718250375	-0.01124271649
63	60	85,316	91,143	176,459	1,611	0.008055	0.4833	2.60062415	-0.01018914923
64	61	84,333	90,515	174,848	1,716	0.00858	0.52338	2.470369451	-0.009140154287
65	62	83,286	89,846	173,132	1,821	0.009105	0.56451	2.321641406	-0.008083641495
66	63	82,177	89,134	171,311	1,923	0.009615	0.605745	2.154229283	-0.00703100735
67	64	81,013	88,375	169,388	2,025	0.010125	0.648	1.97551191	-0.006016948178
68	65	79,795	87,568	167,363	2,142	0.01071	0.69615	1.801162469	-0.005093178611
69	66	78,518	86,703	165,221	2,275	0.011375	0.75075	1.629346439	-0.004252053886
70	67	77,172	85,774	162,946	2,417	0.012085	0.809695	1.453858461	-0.003477075921
71	68	75,755	84,774	160,529	2,570	0.01285	0.8738	1.276855765	-0.002775335606
72	69	74,263	83,696	157,959	2,735	0.013675	0.943575	1.099875976	-0.002150830641
73	70	72,691	82,533	155,224	2,925	0.014625	1.02375	0.9285875736	-0.001613394873
74	71	71,027	81,272	152,299	3,138	0.01569	1.11399	0.7618537981	-0.001157578074
75	72	69,261	79,900	149,161	3,364	0.01682	1.21104	0.5991305433	-0.0007796927629
76	73	67,384	78,413	145,797	3,598	0.01799	1.31327	0.4440580976	-0.0004810590817
77	74	65,390	76,809	142,199	3,848	0.01924	1.42376	0.3029739621	-0.0002621559591
78	75	63,272	75,079	138,351	4,129	0.020645	1.548375	0.1818941645	-0.0001177267119
79	76	61,015	73,207	134,222	4,434	0.02217	1.68492	0.08588763147	-0.00003686102448
80	77	58,611	71,177	129,788	4,742	0.02371	1.82567	0.02222877531	-0.000004693121907
81	78	56,065	68,981	125,046	5,050	0.02525	1.9695	0.0000254375469	0.0000000001760501738
82	79	53,383	66,613	119,996	5,355	0.026775	2.115225	0.02850165087	0.000006412015931
83	80	50,573	64,068	114,641	5,684	0.02842	2.2736	0.1173168343	0.00005197359702
84	81	47,629	61,328	108,957	6,019	0.030095	2.437695	0.2766166103	0.0001828624429
85	82	44,553	58,385	102,938	6,326	0.03163	2.59366	0.5141433545	0.000451992317
86	83	41,361	55,251	96,612	6,592	0.03296	2.73568	0.8344947088	0.0009155795587
87	84	38,074	51,946	90,020	6,815	0.034075	2.8623	1.239712814	0.00163048952
88	85	34,718	48,487	83,205	6,997	0.034985	2.973725	1.729846179	0.002652311934
89	86	31,321	44,887	76,208	7,134	0.03567	3.06762	2.301030588	0.004029826436
90	87	27,915	41,159	69,074	7,209	0.036045	3.135915	2.940274542	0.005790467376
91	88	24,539	37,326	61,865	7,200	0.036	3.168	3.622889067	0.007924750764
92	89	21,241	33,424	54,665	7,092	0.03546	3.15594	4.315456732	0.01038066301
93	90	18,070	29,503	47,573	6,866	0.03433	3.0897	4.969705806	0.01303807357
94	91	15,080	25,627	40,707	6,519	0.032595	2.966145	5.535486535	0.01572941293
95	92	12,322	21,866	34,188	6,057	0.030285	2.78622	5.962805395	0.01824384917
96	93	9,837	18,294	28,131	5,493	0.027465	2.554245	6.205804842	0.0203405025
97	94	7,656	14,982	22,638	4,853	0.024265	2.28091	6.23650992	0.02180100864
98	95	5,798	11,987	17,785	4,153	0.020765	1.972675	6.023514677	0.02236986175
99	96	4,269	9,363	13,632	3,439	0.017195	1.65072	5.590845018	0.0219821111
100	97	3,057	7,136	10,193	2,756	0.01378	1.33666	4.991214216	0.02071280965