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Averaging

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41947] Averaging
  • From: "C B" <bhatya21 at hotmail.com>
  • Date: Wed, 11 Jun 2003 03:49:40 -0400 (EDT)
  • Organization: Purdue University
  • Sender: owner-wri-mathgroup at wolfram.com

Hello,

Three repetitions of an experiment were carried out. The data is copy pated
below. I hope the main contributors on this email list are able to import
this data into a spread sheet program and have a look at it. If you are not
let me know and I should be able to send that data to you in some other
format of your preference.

In the data,

X coordinate is 'Time' expressed in minutes.
Y coordinate is 'Gas concentration' expressed in PPM.

If you look and plot the data for all the repetitions, you will see that all
the plots are not exactly the same. The difference is mainly due to the
inherrent errors and variance factors in any experiment.

What I am looking for is a mathematical tool or a treatment or some way of
coming up with one data set representing the average effect of all the three
repetions.

Repetition 1

{0,287.9},
{1,288.5},
{2,288.4},
{3,289.4},
{4,290.1},
{5,290.1},
{6,291.1},
{7,292.8},
{8,293.8},
{9,294.6},
{10,295.9},
{11,296.4},
{12,296.6},
{13,297.7},
{14,298.5},
{15,298.9},
{16,300.1},
{17,300.3},
{18,301.2},
{19,300.4},
{20,299.7},
{21,299.7},
{22,301.2},
{23,300.9},
{24,300.4},
{25,299.6},
{26,299.4},
{27,300.2},
{28,300.6},
{29,301.4},
{30,301.7},
{31,302.4},
{32,303.1},
{33,303.6},
{34,303.5},
{35,304.3},
{36,305.6},
{37,306.1},
{38,305.9},
{39,305.1},
{40,305.8},
{41,306.5},
{42,307},
{43,306.6},
{44,306.7},
{45,306.8},
{46,307.5},
{47,307.3},
{48,308.4},
{49,307.6},
{50,306.7},
{51,306.8},
{52,306.2},
{53,306.4},
{54,307.8},
{55,307.6},
{56,306.4},
{57,307.6},
{58,307},
{59,306.9},
{60,306.6},
{61,307.3},
{62,308.5},
{63,308.3},
{64,308.4},
{65,310.1},
{66,311.6},
{67,311.5},
{68,312.1},
{69,312},
{70,313.1},
{71,313.6},
{72,314.8},
{73,314.8},
{74,314.8},
{75,316},
{76,315.7},
{77,316.7},
{78,315.6},
{79,317.9},
{80,318.4},
{81,320},
{82,321},
{83,321.1},
{84,319.1},
{85,320.7},
{86,320.5},
{87,319.4},
{88,319.2},
{89,318.7},
{90,319.8},
{91,319.8},
{92,319.2},
{93,319.7},
{94,320.7},
{95,319.3},
{96,316.8},
{97,316.6},
{98,315.8},
{99,316.2},
{100,318},
{101,319},
{102,321.6},
{103,321.6},
{104,323},
{105,324.2},
{106,325.3},
{107,326.1},
{108,325.9},
{109,327.1},
{110,327.1},
{111,327.1},
{112,326.7},
{113,326.6},
{114,328.2},
{115,326},
{116,328},
{117,328.5},
{118,329.7},
{119,330.8},
{120,330.5},
{121,331.1},
{122,331.2},
{123,331},
{124,332.1},
{125,332.6},
{126,334.6},
{127,336},
{128,336.1},
{129,335.8},
{130,335.5},
{131,334.6},
{132,334.3},
{133,334},
{134,335.9},
{135,335.9},
{136,335.4},
{137,336.3},
{138,336.5},
{139,336.6},
{140,335.5},
{141,335.7},
{142,335.3},
{143,333.6},
{144,334.9},
{145,334.6},
{146,336.8},
{147,336.1},
{148,335.1},
{149,335.4},
{150,336},
{151,334.5},
{152,332.6},
{153,332.6},
{154,334.3},
{155,333.3},
{156,332.1},
{157,333.5},
{158,335},
{159,337.3},
{160,339.6},
{161,340.3},
{162,341.1},
{163,341.3},
{164,341.4},
{165,340.9},
{166,339.7},
{167,340.4},
{168,339.1},
{169,337.9},
{170,338.5},
{171,338.5},
{172,339.8},
{173,339.4},
{174,340.2},
{175,339.6},
{176,340.2},
{177,339.8},
{178,337.6},
{179,337.4},
{180,337.4},
{181,337.8},
{182,338},
{183,338.1},
{184,338.6},
{185,338.5},
{186,339.4},
{187,339.2},
{188,339.4},
{189,340.3},
{190,340.5},
{191,339.3},
{192,340.3},
{193,341.3},
{194,342},
{195,341.7},
{196,343.1},
{197,344.1},
{198,343.6},
{199,343.6},
{200,345},
{201,345.1},
{202,344.8},
{203,343.6},
{204,341.8},
{205,341.5},
{206,342.2},
{207,341.8},
{208,342.6},
{209,342.2},
{210,342.9},
{211,343.8},
{212,343.4},
{213,345.7},
{214,345.3},
{215,346.7},
{216,345.1},
{217,345.2},
{218,344.5},
{219,345.1},
{220,344.6},
{221,343.3},
{222,342.8},
{223,342},
{224,340.6},
{225,342.8},
{226,344.2},
{227,345.1},
{228,344.8},
{229,343.3},
{230,343.4},
{231,344.3},
{232,346.8},
{233,349.5},
{234,348.8},
{235,349.2},
{236,349},
{237,347.9},
{238,346.4},
{239,346.3},
{240,348.2},
{241,347.6},
{242,347.8},
{243,348.4},
{244,347.6},
{245,348},
{246,347.1},
{247,346.2},
{248,346.2},
{249,346.2},
{250,344.7},
{251,344.1},
{252,344.2},
{253,345.2},
{254,345.8},
{255,345.2},
{256,346.1},
{257,345.7},
{258,347.3},
{259,346.8},
{260,348.1},
{261,349},
{262,349.5},
{263,350.5},
{264,348.2},
{265,349.1},
{266,347.7},
{267,344.2},
{268,344.4},
{269,346.2},
{270,347.1},
{271,347.2},
{272,343},
{273,340.4},
{274,341.3},
{275,341},
{276,341.2},
{277,342.1},
{278,341.6},
{279,341.2},
{280,341.3},
{281,342},
{282,342.7},
{283,342.8},
{284,343.3},
{285,343.6},
{286,344.3},
{287,344},
{288,343.1},
{289,341.6},
{290,339.8},
{291,338.6},
{292,338.8},
{293,338.1},
{294,339.1},
{295,339.8},
{296,340},
{297,341.2},
{298,341.8},
{299,342.8},
{300,342},
{301,341.4},
{302,340.8},
{303,340.6},
{304,340.8},
{305,340.5},
{306,340.1},
{308,339},
{308,339.3},
{308,340.8},
{309,339.1},
{309,339.9},
{309,340.3},
{309,341.2},
{310,341.6},
{310,343.3},
{310,343.9},
{310,345.3},
{311,345.9},
{311,347.1},
{311,349.6},
{311,351.2},
{312,356.6},
{312,362.5},
{312,368.6},
{312,372.5},
{313,375.6},
{313,381.8},
{313,387.8},
{313,390.9},
{314,389.8},
{314,397},
{314,403.3},
{314,410.6},
{315,415},
{315,416.1},
{315,414.2},
{315,411.9},
{316,408.5},
{316,408.2},
{316,406.4},
{316,400.4},
{317,392.8},
{317,394.2},
{317,390.6},
{317,387.1},
{318,384.1},
{318,387.7},
{318,383},
{318,378.9},
{319,374.2},
{319,376.1},
{319,371.6},
{319,366.1},
{320,362.9},
{320,361.9},
{320,358.3},
{320,353.6},
{321,353},
{321,353.8},
{321,350},
{321,348.9},
{322,348.1},
{322,347.9},
{322,346.3},
{322,346},
{323,345.5},
{323,344.3},
{323,343.2},
{323,342.1},
{324,342.8},
{324,341.2},
{324,339},
{324,341.2},
{325,340.2},
{325,339.6},
{325,338.4},
{325,339.8},
{326,338.1},
{326,338.7},
{326,338},
{326,339.9},
{327,337.6},
{327,336.9},
{327,335.4},
{327,336.5},
{328,335.8},
{328,334.9},
{328,332.5},
{328,334},
{329,332.7},
{329,331.4},
{329,331},
{329,331.8},
{330,330.1},
{330,327.3},
{330,327.5},
{330,327.4},
{331,325.5},
{331,324.2},
{331,324},
{331,324.5},
{332,323},
{332,321.5},
{332,321.6},
{332,322.8},
{333,321.3},
{333,320.2},
{333,319.9},
{333,320.9},
{334,319.6},
{334,318.1},
{334,319.1},
{334,318.5},
{335,318.1},
{335,317.7},
{335,318.3},
{335,317.8},
{336,317.1},
{336,317.5},
{336,316.3},
{336,315.8},
{337,315.2},
{337,315.5},
{337,315.5},
{337,314.6},
{338,314},
{338,315.1},
{338,314.4},
{338,313.6},
{339,312.9},
{339,314},
{339,313.8},
{339,312.9},
{340,313.3},
{340,314.4},
{340,312.8},
{340,312.4},
{341,314.7},
{341,315.5},
{341,315}


Repetition 2


{0,255.8},
{1,257},
{2,256.6},
{3,256.5},
{4,256.2},
{5,256.5},
{6,256.8},
{7,257.3},
{8,257.1},
{9,257.2},
{10,258.1},
{11,256.9},
{12,257.9},
{13,259},
{14,259.5},
{15,258.2},
{16,258.9},
{17,259.7},
{18,259.6},
{19,259.2},
{20,259.4},
{21,261.4},
{22,259.6},
{23,260.2},
{24,260.1},
{25,260.4},
{26,260.3},
{27,260.7},
{28,260.7},
{29,262.1},
{30,260.2},
{31,261.1},
{32,261.8},
{33,263.2},
{34,261.8},
{35,263.2},
{36,264.6},
{37,264.2},
{38,263.8},
{39,265.8},
{40,266.7},
{41,265.7},
{42,266.6},
{43,267.1},
{44,269.1},
{45,268.8},
{46,270.3},
{47,271.1},
{48,272},
{49,270.6},
{50,271.9},
{51,273.3},
{52,273.9},
{53,271.9},
{54,272.8},
{55,274.2},
{56,274.4},
{57,274},
{58,275.1},
{59,276.3},
{60,276.9},
{61,277.3},
{62,278.3},
{63,279.7},
{64,278.9},
{65,279.3},
{66,279.9},
{67,280.1},
{68,279.8},
{69,280.6},
{70,280.1},
{71,281.4},
{72,279.3},
{73,279.2},
{74,278.9},
{75,278.6},
{76,277.9},
{77,279.5},
{78,280.9},
{79,280.8},
{80,281.8},
{81,282.6},
{82,283.3},
{83,281.9},
{84,281.3},
{85,281.8},
{86,282.4},
{87,282.3},
{88,282.4},
{89,283.1},
{90,283.8},
{91,283.1},
{92,283.3},
{93,283.6},
{94,285.1},
{95,283.7},
{96,284.2},
{97,283.8},
{98,283.9},
{99,283.4},
{100,283.6},
{101,283.9},
{102,283.1},
{103,281.4},
{104,282},
{105,283.4},
{106,282.5},
{107,282.4},
{108,284.1},
{109,285},
{110,286.1},
{111,283.7},
{112,283.7},
{113,283.5},
{114,283.6},
{115,283.9},
{116,282.7},
{117,285},
{118,284.3},
{119,285.9},
{120,284.4},
{121,284},
{122,281.1},
{123,282.3},
{124,283.1},
{125,281.8},
{126,282},
{127,281.4},
{128,281.9},
{129,279.6},
{130,279.5},
{131,280.6},
{132,281.4},
{133,281},
{134,284.1},
{135,285.4},
{136,286.5},
{137,286.5},
{138,286},
{139,287.2},
{140,286.9},
{141,287.1},
{142,286.2},
{143,285.4},
{144,283.7},
{145,284.7},
{146,285.5},
{147,284.6},
{148,285.5},
{149,286.8},
{150,286.5},
{151,284.5},
{152,285.2},
{153,284.9},
{154,283.3},
{155,285},
{156,286.4},
{157,287.7},
{158,286.1},
{159,286.7},
{160,287.6},
{161,287.3},
{162,289.8},
{163,291.9},
{164,290.9},
{165,290.4},
{166,289.1},
{167,289.9},
{168,287.2},
{169,287.7},
{170,286.7},
{171,287.6},
{172,290.4},
{173,293.1},
{174,293.9},
{175,294},
{176,293.9},
{177,292.8},
{178,291.3},
{179,292.3},
{180,293.3},
{181,292},
{182,291.1},
{183,291.1},
{184,291.3},
{185,291},
{186,291.5},
{187,291.7},
{188,290.9},
{189,290.8},
{190,291},
{191,290.9},
{192,291.6},
{193,292.4},
{194,293.3},
{195,295.7},
{196,295.9},
{197,297.4},
{198,296.6},
{199,297.5},
{200,298.4},
{201,297.1},
{202,298.2},
{203,297.2},
{204,295},
{205,296.1},
{206,296.8},
{207,294.2},
{208,294.8},
{209,295.3},
{210,293.7},
{211,294.6},
{212,295.4},
{213,294},
{214,295.9},
{215,297.4},
{216,296.1},
{217,297.3},
{218,297},
{219,296},
{220,296.9},
{221,297.7},
{222,296.8},
{223,298.2},
{224,297.8},
{225,296.9},
{226,298.5},
{227,298.6},
{228,297.7},
{229,298.9},
{230,299.7},
{231,299.3},
{232,299.8},
{233,299.6},
{234,300.4},
{235,301},
{236,299.5},
{237,300.5},
{238,300.9},
{239,299.4},
{240,300.3},
{241,301.1},
{242,299.9},
{243,301},
{244,300.8},
{245,301.1},
{246,302.8},
{247,301.9},
{248,302.8},
{249,302.9},
{250,301.1},
{251,301.9},
{252,302.2},
{253,301.8},
{254,303},
{255,302},
{256,302.5},
{257,303.1},
{258,301.8},
{259,302.3},
{260,302.4},
{261,300.8},
{262,301},
{263,300.2},
{264,300.5},
{265,301},
{266,299.3},
{267,300.2},
{268,300.5},
{269,299.2},
{270,299.4},
{271,298.2},
{272,299.1},
{273,299.9},
{274,298.8},
{275,299.4},
{276,298.6},
{277,298.4},
{278,298.9},
{279,296.6},
{280,298.2},
{281,298.6},
{282,297.1},
{283,296.8},
{284,296},
{285,296.3},
{286,296.3},
{287,295.9},
{288,296.1},
{289,295.7},
{290,295.3},
{291,295.9},
{292,294.7},
{293,294.8},
{294,295},
{295,294.3},
{296,294.7},
{297,293},
{298,294},
{299,294},
{300,293},
{301,293.9},
{302,291.7},
{303,292.9},
{304,292.5},
{306,290.2},
{306,291.9},
{306,291.6},
{307,291.5},
{307,291.7},
{307,291.1},
{307,290.5},
{308,291.3},
{308,292},
{308,292.3},
{308,293.3},
{309,292.5},
{309,293.5},
{309,294.1},
{309,297},
{310,299.4},
{310,299.9},
{310,298.9},
{310,301.5},
{311,304.9},
{311,305},
{311,305.9},
{311,307.6},
{312,307.5},
{312,307.8},
{312,307.8},
{312,306.4},
{313,307.5},
{313,307.5},
{313,307.2},
{313,306.7},
{314,306},
{314,304.6},
{314,303.4},
{314,303.8},
{315,302.5},
{315,301.5},
{315,300.5},
{315,298.8},
{316,297.4},
{316,297.3},
{316,296.9},
{316,295},
{317,293.6},
{317,292.4},
{317,291.6},
{317,290.3},
{318,289.7},
{318,288.7},
{318,288.4},
{318,286.2},
{319,286.7},
{319,285},
{319,283.2},
{319,283.7},
{320,283.8},
{320,282.3},
{320,281.9},
{320,280.3},
{321,279.1},
{321,279.1},
{321,279},
{321,278.9},
{322,277.5},
{322,277.4},
{322,276.1},
{322,275.1},
{323,275.1},
{323,275.2},
{323,274.9},
{323,274.1},
{324,273.2},
{324,272.1},
{324,272.4},
{324,272.6},
{325,271.6},
{325,271},
{325,271},
{325,270.3},
{326,269.3},
{326,269.5},
{326,270},
{326,269.3},
{327,269.4},
{327,269.1},
{327,268.3},
{327,267.4},
{328,268.9},
{328,268.4},
{328,267.5},
{328,268.2},
{329,266.8},
{329,266.7},
{329,266},
{329,267},
{330,267.1},
{330,266.5},
{330,265.8},
{330,265.7},
{331,264.7},
{331,265.7},
{331,265.8},
{331,265.1},
{332,265.6},
{332,265},
{332,264.2},
{332,264.4},
{333,264.9},
{333,264.1},
{333,264.5},
{333,263.9},
{334,263.7},
{334,262.7},
{334,263.2},
{334,263.7},
{335,264.4},
{335,263.8},
{335,263.2},
{335,262.6},
{336,261.8},
{336,263.2},
{336,262.8}


Repetition 3

{0,296.5},
{1,294.5},
{2,292.2},
{3,291.4},
{5,292.5},
{5,293.3},
{6,293.3},
{8,293.9},
{8,293.9},
{9,293},
{11,293.8},
{11,294.5},
{12,294.5},
{14,295.6},
{14,295.2},
{15,294.1},
{16,294.9},
{17,295.9},
{18,296.3},
{19,297.1},
{21,297.6},
{21,297},
{22,297.4},
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