Before you do anything on the computer, you might want to play around
with the following data using pencil-and-paper..
0.16667 1.2215048
0.50000 1.3383699
0.83333 1.2208207
A set of data using 10 points
0.05000 0.9334473
0.15000 0.9773084
0.25000 1.0386392
0.35000 1.0875554
0.45000 1.1338109
0.55000 1.0848502
0.65000 1.0880070
0.75000 1.0290750
0.85000 0.9758076
0.95000 0.8854021
Using more care to eliminate spurious effects in measurements,
a set of data using 10 points
0.05000 0.9327684
0.15000 0.9931981
0.25000 1.0480166
0.35000 1.0858642
0.45000 1.1118785
0.55000 1.1009358
0.65000 1.0780987
0.75000 1.0424809
0.85000 0.9760648
0.95000 0.9037920
A set of data using 100 points
0.00500 0.7366168
0.01500 0.7415003
0.02500 0.7486793
0.03500 0.7562595
0.04500 0.7647081
0.05500 0.7671404
0.06500 0.7760291
0.07500 0.7798072
0.08500 0.7872230
0.09500 0.7913599
0.10500 0.7970524
0.11500 0.8043831
0.12500 0.8095252
0.13500 0.8155816
0.14500 0.8241555
0.15500 0.8273033
0.16500 0.8337304
0.17500 0.8382944
0.18500 0.8439385
0.19500 0.8489224
0.20500 0.8539289
0.21500 0.8552378
0.22500 0.8621378
0.23500 0.8724813
0.24500 0.8694023
0.25500 0.8763731
0.26500 0.8783623
0.27500 0.8815999
0.28500 0.8863101
0.29500 0.8907350
0.30500 0.8948442
0.31500 0.8977596
0.32500 0.9008088
0.33500 0.9027556
0.34500 0.9059207
0.35500 0.9076208
0.36500 0.9090755
0.37500 0.9111592
0.38500 0.9124662
0.39500 0.9175145
0.40500 0.9172040
0.41500 0.9190151
0.42500 0.9229940
0.43500 0.9199576
0.44500 0.9214416
0.45500 0.9260488
0.46500 0.9256467
0.47500 0.9245314
0.48500 0.9267373
0.49500 0.9343004
0.50500 0.9277926
0.51500 0.9229699
0.52500 0.9240677
0.53500 0.9257271
0.54500 0.9224498
0.55500 0.9232996
0.56500 0.9195110
0.57500 0.9228422
0.58500 0.9182524
0.59500 0.9153757
0.60500 0.9155391
0.61500 0.9159853
0.62500 0.9121829
0.63500 0.9076597
0.64500 0.9074920
0.65500 0.9033163
0.66500 0.9017854
0.67500 0.8975787
0.68500 0.8957095
0.69500 0.8921275
0.70500 0.8910795
0.71500 0.8853137
0.72500 0.8812839
0.73500 0.8775683
0.74500 0.8718944
0.75500 0.8758585
0.76500 0.8659040
0.77500 0.8623742
0.78500 0.8548412
0.79500 0.8516927
0.80500 0.8487598
0.81500 0.8411954
0.82500 0.8366417
0.83500 0.8309149
0.84500 0.8259759
0.85500 0.8206187
0.86500 0.8180325
0.87500 0.8081753
0.88500 0.8055414
0.89500 0.7984746
0.90500 0.7939645
0.91500 0.7882571
0.92500 0.7832073
0.93500 0.7735261
0.94500 0.7703143
0.95500 0.7646448
0.96500 0.7573175
0.97500 0.7491299
0.98500 0.7438274
0.99500 0.7379287
Using more care to eliminate spurious effects in measurements,
a set of data using 100 points
0.00500 0.7365489
0.01500 0.7430893
0.02500 0.7496170
0.03500 0.7560904
0.04500 0.7625148
0.05500 0.7687489
0.06500 0.7750383
0.07500 0.7811478
0.08500 0.7872487
0.09500 0.7931989
0.10500 0.7990913
0.11500 0.8049240
0.12500 0.8106168
0.13500 0.8162282
0.14500 0.8217867
0.15500 0.8271299
0.16500 0.8324287
0.17500 0.8375768
0.18500 0.8426297
0.19500 0.8475494
0.20500 0.8523465
0.21500 0.8569434
0.22500 0.8615230
0.23500 0.8733895
0.24500 0.8701525
0.25500 0.8743290
0.26500 0.8782655
0.27500 0.8820842
0.28500 0.8857871
0.29500 0.8893365
0.30500 0.8927298
0.31500 0.8959471
0.32500 0.8990129
0.33500 0.9019006
0.34500 0.9046546
0.35500 0.9072196
0.36500 0.9096183
0.37500 0.9118666
0.38500 0.9139351
0.39500 0.9159126
0.40500 0.9176161
0.41500 0.9191940
0.42500 0.9206462
0.43500 0.9217881
0.44500 0.9228498
0.45500 0.9238025
0.46500 0.9244831
0.47500 0.9249771
0.48500 0.9253649
0.49500 0.9330368
0.50500 0.9255542
0.51500 0.9252824
0.52500 0.9249560
0.53500 0.9244681
0.54500 0.9237092
0.55500 0.9228608
0.56500 0.9217484
0.57500 0.9206077
0.58500 0.9191387
0.59500 0.9175349
0.60500 0.9158239
0.61500 0.9139518
0.62500 0.9118290
0.63500 0.9095274
0.64500 0.9071501
0.65500 0.9045313
0.66500 0.9018058
0.67500 0.8988687
0.68500 0.8958224
0.69500 0.8925878
0.70500 0.8892518
0.71500 0.8856717
0.72500 0.8819787
0.73500 0.8781467
0.74500 0.8741329
0.75500 0.8775217
0.76500 0.8657945
0.77500 0.8614111
0.78500 0.8568156
0.79500 0.8521787
0.80500 0.8474201
0.81500 0.8424459
0.82500 0.8374120
0.83500 0.8322380
0.84500 0.8269664
0.85500 0.8215765
0.86500 0.8161353
0.87500 0.8104457
0.88500 0.8048009
0.89500 0.7989715
0.90500 0.7931008
0.91500 0.7871175
0.92500 0.7810622
0.93500 0.7748331
0.94500 0.7686558
0.95500 0.7623556
0.96500 0.7559523
0.97500 0.7494657
0.98500 0.7429744
0.99500 0.7364128