totalRandomList[long_, range_]:= 
Total[RandomInteger[range,{long}]]

totalRandomList[100,{0,50}]

Table[totalRandomList[100,{0,50}],{6}]

rawdata = Table[totalRandomList[100,{0,50}],{10000}];

hp= Histogram[rawdata,{5}]

randomList = RandomInteger[{1,7},{16}]

Tally[randomList]

Sort[Tally[randomList]]

histDataRaw = Sort[Tally[rawdata]];

histDataRaw//Short

Fitting this data:The following will be a numerical mistake (bad strategy)

model = a Exp[-b (x-c)^2]

histDataRaw[[1;;10]]

theParams =FindFit[histDataRaw,model,{a,b,c},x]

Plot[model/.theParams,{x,1959,3050},PlotStyle-> {Thick,Red}]

Fitting this data: Rescaling to get a reasonable fit...

histDataRaw//Short

theSums = Table[First[histDataRaw[[i]]],{i,1,Length[histDataRaw]}];
Short[theSums]

rangeX = Max[theSums] - Min[theSums]

meanX =Mean[theSums]//N

height = Max[
Table[Last[histDataRaw[[i]]],{i,1,Length[histDataRaw]}]
]

histDataScaled = Table[
{(First[histDataRaw[[i]]] - meanX)/rangeX,
Last[histDataRaw[[i]]]/height},
{i,Length[histDataRaw]}
];

histDataScaled//Dimensions

lp =ListPlot[histDataScaled]

model = a Exp[-b (x-c)^2]

anotherModel = a + b (c -x)^2

theParams =FindFit[histDataScaled,model,{a,b,c},x]

modelFit = model/.theParams

anotherParams =FindFit[histDataScaled,anotherModel,{a,b,c},x]

anotherModelFit = anotherModel/.anotherParams

Plot[{modelFit,anotherModelFit},{x,-.6,.6}]

theScaledModel = model/.theParams

theUnscaledModel = Simplify[height theScaledModel/.{x-> (realX - meanX)/rangeX}]

Show[hp,Plot[theUnscaledModel,{realX,Min[theSums],Max[theSums]},PlotStyle->{ Thickness[0.05],Red}]]

Plot[model/.theParams,{x,1959,3050},PlotStyle-> {Thick,Red}]

someData = Table[{x + RandomReal[{-.1,.1}], (1 +RandomReal[{-.15,.1}]) Sin[ 2 Pi x + RandomReal[{-.05,.05}]]},{x,0,1,.01}];

lp = ListPlot[someData]

aModel = a + b x + c x^2 + d  x^3 + e x^4

theFit1 = FindFit[someData,aModel,{a,b,c,d,e},x]

m1 = Plot[aModel/.theFit1,{x,0,1}]

Show[lp,m1]

aModel2 = a Sin[ b x + c]

theFit2 = FindFit[someData,aModel2,{a,b,c},x]

m2 = Plot[aModel2/.theFit2,{x,0,1},PlotStyle-> Red]

Dynamic[Show[lp,m1,m2]]