# Average of samples in a period of time

I take samples in an experiment which results low (around 0) and high (around 60) values.

In many of the tests, there are more high values at the end of the experiment than at the beginning. The time is represented with the X-values and the results are the Y-values.

The representation of the data result of the experiment is this:

ListPlot[{{0, -4.21971153288256}, {7.4 E -
4, -5.547776864829935}, {0.00123, -3.4323178972792725}, {0.00172, \
-4.496868044007073}, {0.00221, -1.6117852496623695}, {0.0027,
1.4179245817948227}, {0.00319,
63.537178667761786}, {0.00577, -3.5388612280298215}, {0.00626, \
-1.665249451788144}, {0.00675, -1.6952289288409315}, {0.00724, \
-2.675472286195846}, {0.00773, -4.530677162984227}, {0.00822, \
-3.461552206122473}, {0.008709999999999999,
0.9077104331703661}, {0.0092,
3.8855310128389275}, {0.00969, -2.513017831199726}, \
{0.010180000000000002, -6.405870742274377}, {0.010920000000000001, \
-3.6859249267819045}, {0.011410000000000002, -4.362029411866255}, \
{0.0119, -4.087845193144335}, {0.012390000000000002, \
-3.79676529883767}, {0.012880000000000003, -3.8851010703041227}, \
{0.013370000000000002, -0.31591684215142474}, {0.01386,
2.536450518838171}, {0.014350000000000002,
61.155453006747294}, {0.01693, -1.8452799908165896}, {0.01742,
0.2757925893295795}, {0.017910000000000002, -3.6410675584152714}, \
{0.0184, -5.418806227335706}, {0.01889, -0.47401640219528995}, \
{0.01938, -3.4821227540076034}, {0.019870000000000002, \
-5.030883412345734}, {0.020360000000000003, -0.13580421839758983}, \
{0.021100000000000004, -0.9736517644084542}, {0.02159,
1.0248365337186287}, {0.022080000000000002,
61.06186611180681}, {0.02466,
0.5966206022297942}, {0.025150000000000002, -1.1586992233832238}, \
{0.025640000000000003, -0.11590679920295459}, {0.026130000000000004, \
-1.4624270932452308}, {0.026620000000000005, -0.027484357767721575}, \
{0.027110000000000002, -3.281603912578161}, {0.027600000000000003, \
-5.4537316546216905}, {0.028090000000000004, -3.744556367431102}, \
{0.02858, -0.10642459611351987}, {0.029070000000000002,
1.3679477390129926}, {0.029560000000000003, -4.591255994099504}, \
{0.030050000000000004, -5.808281233986997}, {0.030540000000000005, \
-4.441742703967536}, {0.03128,
0.5966292116177748}, {0.03177000000000001, -2.8397374093834586}, \
{0.032260000000000004, -0.3871810600914405}, {0.03275,
2.420507137722945}, {0.033240000000000006,
4.699295717704492}, {0.03373, -0.8919318934537901}, \
{0.03422000000000001,
3.179261539326594}, {0.034710000000000005, -3.8863653071209994}, \
{0.0352, -3.6696969877774}, {0.035690000000000006, \
-2.4533789254816236}, {0.036180000000000004,
7.662680312588462}, {0.03667000000000001, -5.872232424058729}, \
{0.037160000000000006, -1.570987237075876}, {0.03765, \
-1.6550396789953403}, {0.03814000000000001, -4.129091616501936}, \
{0.038630000000000005, -6.238996706848717}, {0.03937,
0.03966378704733839}, {0.03986000000000001, -1.8538116273813297}, \
{0.040350000000000004, 0.6080860584561669}, {0.04084,
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{0.04182, -1.9830186293047953}, {0.04231000000000001, \
-1.5318236941349137}, {0.042800000000000005, -2.6234910736167634}, \
{0.04329, -7.295222988258394}, {0.043780000000000006, \
-3.0793664446132625}, {0.044270000000000004,
59.83484154704144}, {0.04685,
6.538856191138435}, {0.04734000000000001, -1.0161682188325618}, \
{0.047830000000000004, -4.891921973076381}, {0.04832,
0.8793246427893167}, {0.048810000000000006,
0.9823026096456664}, {0.049550000000000004, -3.2990785287863025}, \
{0.05004000000000001, -4.156589596817527}, {0.050530000000000005, \
-1.0285704882246742}, {0.05102000000000001,
1.9998773838445514}, {0.05151000000000001,
6.141538213163376}, {0.052000000000000005, -4.755445297110029}, \
{0.05249000000000001, -3.6518015797433394}, {0.052980000000000006, \
-3.7936376611341354}, {0.053470000000000004, -4.2204552511269755}, \
{0.05396000000000001,
63.317514464417606}, {0.05654000000000001, -4.714742876843832}, \
{0.057030000000000004, -3.4011875899239126}, {0.05752, \
-0.5297986299029621}, {0.058010000000000006, -2.6674520469230885}, \
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-0.9103148632266931}, {0.059730000000000005,
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{0.06280000000000001, -5.640244219257109}, {0.06329000000000001, \
-3.561409088311751}, {0.06378, -3.5937769278744174}, \
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-1.1380401198765036}, {0.06525, -3.567677741899776}, {0.06574,
0.12456037151551413}, {0.06623000000000001,
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5.404673181598632}, {0.06770000000000001, -3.5488341172929427}, \
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5.945381402411989}, {0.08058, -0.3671924080561901}, {0.08107, \
-1.2146270633062655}, {0.08156000000000001, -3.708277123278105}, \
{0.08205, -3.2353965737704087}, {0.08254,
3.2957369427837433}, {0.08303, -0.8732019841116816}, \
{0.08352000000000001, -0.7088332683792447}, {0.08401, \
-0.9487855476641487}, {0.0845,
4.666130419808111}, {0.08499000000000001,
3.1608211419163172}, {0.08548, -4.499008743698379}, {0.08597, \
-5.425349652244677}, {0.08646000000000001,
1.4492040905186676}, {0.08695, -5.057059729676152}, {0.08744, \
-1.636430402630993}, {0.08818000000000001, -4.720319125514575}, \
{0.08867, -4.480771834364813}, {0.08916, -4.69501100892359}, \
{0.08965000000000001,
1.9145666225125415}, {0.09014, -1.3413600013707798}, {0.09063, \
-1.0042300669262703}, {0.09112,
0.9886450785462777}, {0.09161, -2.6710890588190708}, {0.0921,
5.200284479650623}, {0.09259,
0.471745856931586}, {0.09308000000000001, -4.212203622694207}, \
{0.09357,
61.909572717919225}, {0.09615, -0.15510230567909228}, {0.09664, \
-1.0742044780981441}, {0.09713000000000001,
2.251057920696828}, {0.09762000000000001, -3.8196363697830265}, \
{0.09836000000000002,
0.5781795392564374}, {0.09885000000000001, -2.4791912913254555}, \
{0.09934000000000001, -0.9329501231260944}, {0.09983000000000002,
62.757620064009025}, {0.10241000000000001, -2.086841534268973}, \
{0.10290000000000002,
0.32386797396159794}, {0.10339000000000001, -6.144824079666088}, \
{0.10388000000000001, -0.970306650769236}, {0.10437000000000002, \
-3.0441518200267965}, {0.10486000000000001, -0.43688156894038316}, \
{0.10535000000000001, -2.139879817478951}, {0.10584000000000002,
2.835593365748931}, {0.10633000000000001, -4.821864803393876}, \
{0.10682000000000001, -5.111340612830362}, {0.10731000000000002,
3.234637140268244}, {0.1078, 65.23654598676733}, {0.11063,
0.9723524694035725}, {0.11112000000000001, -0.41456985344960473}, \
{0.11182, -1.2524187426183842}, {0.11231000000000001, \
-3.615693788101946}, {0.11280000000000001, -2.2910168875027703}, \
{0.11329, -1.7120782720001024}, {0.11378, -6.732397192657032}, \
{0.11427000000000001, -1.5255912398450102}, {0.11476, \
-2.4082727219050506}, {0.11525, -5.3146585790809455}, \
{0.11574000000000001, -3.558336116730672}, {0.11623, \
-0.43624221839098976}, {0.11672, 61.17667172967215}, {0.1193,
1.8556091846277867}, {0.11979000000000001,
56.95923599863045}, {0.12262, -5.0346368247731785}, \
{0.12311000000000001,
4.383874968695375}, {0.1236, -4.543520275166683}, {0.12409,
5.850605425625172}, {0.12458000000000001, -3.72539806176515}, \
{0.12507000000000001,
0.14389411650045228}, {0.12556, -3.2273460606496123}, {0.12605, \
-0.4660332448456194}, {0.12654, -0.6109894982146997}, {0.12703, \
-1.7066688216106038}, {0.12752, -1.2169784443183298}, {0.12801, \
-5.554596531539681}, {0.1285, 66.96386420766324}, {0.13108,
2.5861515277879654}, {0.13157000000000002, -0.3147027616729641}, \
{0.13206,
1.2496957524602823}, {0.1328, -2.816035481397038}, \
{0.13329000000000002, -2.8362501038222456}, {0.13378, \
-6.6627108124709}, {0.13427, -4.511389401655678}, \
{0.13476000000000002, -3.626925184870605}, {0.13525,
2.159216127556145}, {0.13574, -4.906442161103476}, \
{0.13623000000000002, -1.4093778338437166}, {0.13693000000000002,
6.993092336920734}, {0.13763, -1.5778886154618528}, \
{0.13812000000000002,
1.23819882096618}, {0.13861, -1.514682217824923}, {0.1391, \
-0.7967901806058513}, {0.13959000000000002, -1.7099386071492209}, \
{0.14033, 1.1457716790117747}, {0.14082000000000003,
1.1089558958287216}, {0.14131000000000002, -2.961305372066544}, \
{0.1418, -0.1207607271099506}, {0.14229000000000003,
3.1333106855227513}, {0.14278000000000002, -3.0667164203128126}, \
{0.14327, -1.5326911682818778}, {0.14376000000000003, \
-3.2794210611544727}, {0.14425000000000002,
5.615636834978082}, {0.14474, -1.985977173408181}, \
{0.14523000000000003, 0.659182551101345}, {0.14572000000000002,
2.3733218013269157}, {0.14621,
4.937220905101663}, {0.14670000000000002, -1.4036006207013008}, \
{0.14719000000000002, -1.8663445722162262}, {0.14768000000000003, \
-2.8644013942881017}, {0.14842000000000002,
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1.2920677750309046}, {0.15149000000000004, -4.694163259931324}, \
{0.15198000000000003,
2.120783531435745}, {0.15289000000000003, -1.1146416832125787}, \
{0.15338000000000004,
3.4966117260108796}, {0.15387000000000003, -6.479949388169385}, \
{0.15436000000000002, -0.4500621047754909}, {0.15485000000000004,
1.3729918914676176}, {0.15534000000000003, -3.8031122878971537}, \
{0.15583000000000002, -2.1037484577210748}, {0.15632000000000004, \
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{0.15730000000000005,
1.3370530973945214}, {0.15804000000000004, -2.8245351199889637}, \
{0.15853000000000006, 0.724969319648965}, {0.15902000000000005,
5.46501962781618}, {0.15951000000000004,
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0.38945141638713776}, {0.16049000000000005, -3.8032473811441103}, \
{0.16098000000000004, -2.7436403452915457}, {0.16147000000000006, \
-5.308681176285451}, {0.16196000000000005, -1.34634379345795}, \
{0.16245000000000004, -1.1422954308400515}, {0.16294000000000006,
0.5717425373109221}, {0.16343000000000005,
1.8323805296657956}, {0.16392000000000004, -4.1133465215075296}, \
{0.16441000000000006,
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0.02689910953147949}, {0.16822000000000004, -5.539770256285777}, \
{0.16871000000000005, 66.35282179838168}, {0.17129000000000005,
0.5590104770675917}, {0.17178000000000004, -3.6343508760160286}, \
{0.17227000000000003, -3.2106619506381606}, {0.17276000000000005, \
-4.1068440010757605}, {0.17325000000000004,
0.91982167629984}, {0.17374000000000003,
2.0772627412276474}, {0.17423000000000005,
1.2893174295591887}, {0.17472000000000004, -3.3919481233833726}, \
{0.17521000000000003, 0.40267860280069634}, {0.17570000000000005,
0.6068777336399361}, {0.17619000000000004, -1.0630486175803031}, \
{0.17668000000000006,
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{0.17766000000000004, -0.610246424330567}, {0.17840000000000003, \
-4.741017401794978}, {0.17889000000000005,
65.03340912921783}, {0.18147000000000005,
63.694728828738576}, {0.18405000000000005, -1.3609695940485775}, \
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{0.18761000000000005, -1.3090899779656415}, {0.18810000000000004, \
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{0.19313000000000005, -2.7775022296343694}, {0.19362000000000004, \
-5.570522005212645}, {0.19411000000000006,
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{0.19534000000000007, -2.1557921982989505}, {0.19583000000000006,
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{0.19975000000000007, -3.000655190572768}, {0.20024000000000006,
65.20706566403955}, {0.20282000000000006, -0.8679057029534007}, \
{0.20331000000000005, -2.303368414848946}, {0.20380000000000006, \
-3.463373473656746}, {0.20429000000000005, -3.083332196735763}, \
{0.20524000000000006,
62.686627263368415}, {0.20782000000000006, -4.624967287211869}, \
{0.20831000000000005, 5.274947916765647}, {0.20880000000000004,
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64.39939938012007}, {0.21187000000000006,
60.81723334324778}, {0.21445000000000006,
0.2470695748591559}, {0.21494000000000005, -3.828259145044795}, \
{0.21543000000000007, -1.1575326873354164}, {0.21592000000000006, \
-2.1856885366242444}, {0.21641000000000005, -5.824811546677836}, \
{0.21690000000000006, -3.713784946295751}, {0.21739000000000006, \
-1.0134443132507533}, {0.21788000000000007, -3.328932470795433}, \
{0.21837000000000006, -5.555655081100843}, {0.21911000000000005, \
-2.811000729588306}, {0.21960000000000007, -3.5187401371600826}, \
{0.22009000000000006, -3.6075243194784674}, {0.22058000000000005, \
-1.206682658312843}, {0.22107000000000007,
6.237396874641492}, {0.22156000000000006,
2.3328445346980304}, {0.22205000000000005, -0.72014119279291}, \
{0.22254000000000007, -1.1781505499877754}, {0.22303000000000006,
0.10999586877100827}, {0.22352000000000005, -2.600625339022702}, \
{0.22401000000000007, 64.82748527195942}, {0.22659000000000007,
5.739829296307084}, {0.22708000000000006,
65.23927577550782}, {0.22966000000000006,
7.217435953720645}, {0.23015000000000008,
2.3027413430623893}, {0.23064000000000007, -0.9496760044185293}, \
{0.23138000000000006, -1.5290928193330697}, {0.23187000000000008,
0.9142508458121581}, {0.23236000000000007,
62.55263608636477}, {0.23494000000000007, -0.2345328990125753}, \
{0.23543000000000006, -3.045685561137864}, {0.23592000000000007, \
-0.18859478751536693}, {0.23662000000000008,
1.2062196178307891}, {0.23711000000000007, -1.722792458672667}, \
{0.23760000000000006, -2.140971708544918}, {0.23809000000000008,
2.71110685127647}, {0.23858000000000007,
1.3541454907601898}, {0.23907000000000006, -3.1399042239313375}, \
{0.23956000000000008, -1.9920458858212398}, {0.24005000000000007,
1.9761622850891805}, {0.24054000000000006, -0.8682658565352814}, \
{0.24128000000000005, -1.2393370398138568}, {0.24177000000000007, \
-0.9040957853799915}, {0.24226000000000006,
67.99043163036376}, {0.24484000000000006, -1.3519778743129067}, \
{0.24533000000000005, 2.388503516255738}, {0.24582000000000007,
64.41533785521901}, {0.24840000000000007,
61.18136896641892}, {0.25098000000000004,
1.0851126578687416}, {0.2514700000000001, -5.738591598286216}, \
{0.25217000000000006, -1.3609294631731488}, {0.25266000000000005, \
-0.637824287347214}, {0.25315000000000004, -2.249012915737521}, \
{0.2536400000000001, -1.830781423325676}, {0.2541300000000001, \
-3.3030589251834215}, {0.2550800000000001,
62.955529153642516}, {0.25766000000000006, -1.0210034201498235}, \
{0.25815000000000005, -1.023328359378934}, {0.2586400000000001, \
-1.8151386299655734}, {0.2591300000000001, -0.7468306210022748}, \
{0.2596200000000001, 1.629359084043922}, {0.26011000000000006,
64.29035876832984}, {0.2626900000000001,
62.79811265272916}, {0.26527000000000006, -4.6104535662448605}, \
{0.26576000000000005, -3.6863651674244013}, {0.2662500000000001, \
-2.900211407331716}, {0.2667400000000001, -3.6798114572174496}, \
{0.2672300000000001, 5.392105011018144}, {0.26772000000000007,
2.726063265876721}, {0.26821000000000006,
3.436259926413556}, {0.26870000000000005,
4.107574275552611}, {0.26944000000000007, -3.8554771033500272}, \
{0.27014000000000005, 67.26580101637062}, {0.2727200000000001,
65.4436330967934}, {0.27530000000000004,
3.680845699890802}, {0.27579000000000004,
0.44318058319759324}, {0.27628, -2.81232168434949}, \
{0.27677000000000007,
0.8421569943297059}, {0.27726000000000006, -3.944242300947105}, \
{0.27775000000000005, -3.452535674225927}, {0.27824000000000004, \
-1.5182354779764915}, {0.27873000000000003,
0.17023810189013736}, {0.27922, -2.4037738800318755}, \
{0.27971000000000007,
1.3732564443994448}, {0.28020000000000006, -3.0298648869200524}, \
{0.28069000000000005, 6.681552746727705}, {0.28143000000000007,
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PlotRange -> {{0, 0.46}, All}]


I would like to compute the mean value of the experiment but taking into account the time.

Probably, the solution is to get the area of the plot and divide by the period of time, but I do not know if there is a simple way the solve it. I would like to compute the mean without integrating.

Regards

It's hard to see what use the mean is going to be here. It looks like you have bivariate data, so a more meaningful measure might be to take the mean of all the high values and the mean of all the low values. Nonetheless, you can easily take the mean. Let dat be your data (I have used all the values on the x-axis between 0 and 0.45605, you can change this easily). Using first order interpolation (to weight all the time values equally):

f = Interpolation[dat, InterpolationOrder -> 1];
Integrate[x f[x], {x, 0, 0.45605}] // N

2.94748

• Thanks. I should then divide this result by the period of time 0.45605, isn't it? May 6, 2019 at 18:19
• It's interesting that you get a significantly different answer if you do a zeroth order interpolation. There seem to be larger time gaps when dropping from a high value to a low one, and it effects the integral. May 6, 2019 at 20:48
• @MikeY -- Yes exactly. This is why the phrase "taking into account the time" is ambiguous. Depending on how you account for the times between the sample points, you can get different answers. May 6, 2019 at 23:02
• @MikeY Let me present the experiment shortly. I am trying to characterize with a single number the signal power received in an antenna. The signals are slotted. The slots can be of 3 types: (1) empty, (2) with interferences, and (3) successful. The successful slots can have high signal power and are larger (takes more time) than the other 2 slot types, which use to be smaller in size. In the current experiment configuration, it is more likely to have more successful events after many slots empty and with interferences. May 7, 2019 at 8:20
• @MikeY When I say the signals are slotted I meant that the time is slotted and the signals (Y-values) samples are taken during each slot. This process is random so if I repeat the experiment with the same parameters a second time the result will be slightly different but the evolution will be similar (more successful slots at the end). I would like to have a single number to get an average of n repetitions of this experiment. May 7, 2019 at 8:25

Try using MovingAverage. For your data, experiment with

len = Length@data
(* 541 *)

Manipulate[ListPlot@MovingAverage[data, r], {r, 1, len, 1}]


Here's a plot with the moving window including 48 terms.

• Thank you. The solution is nice. I was looking for a single number to represent all. I do not know if it that is possible. May 6, 2019 at 18:23
• You can run the MovingAverage all the way out to the length of your dataset and get a single point (x and y value). Not sure exactly what you are looking for. I adjusted my answer to have the manipulate go all the way to 541. May 6, 2019 at 18:44

It seems you want to use TimeSeriesAggregate, which uses a specification of the time-interval width. (Not MovingAverage as suggested in another answer.)

(* Dropping the outlier and make a time series object. *)
ts = TimeSeries[Select[data, #[[1]] < 5 &]]

(* Do moving average with disjoint time intervals of length 0.01 .*)
ts2 = TimeSeriesAggregate[ts, 0.01]

(* Plot. *)
ListPlot[ts2, PlotRange -> All, PlotTheme -> "Detailed"]