Calculating the 95th percentile: Comparing normal distribution, R Quantile, and Excel approaches

I was trying to compute the 95th percentile on the following dataset. I came across a few online references of doing it.

Approach 1: Based on sample data

The first one tells me to obtain the `TOP 95 Percent` of the dataset and then choose the `MIN` or `AVG` of the resultant set. Doing so for the following dataset gives me:

``````AVG: 29162
MIN: 0
``````

Approach 2: Assume Normal Distribution

The second one says that the 95th percentile is approximately two standard deviations above the mean (which I understand) and I performed:

``````AVG(Column) + STDEV(Column)*1.65: 67128.542697973
``````

Approach 3: R Quantile

I used `R` to obtain the 95th percentile:

``````> quantile(data\$V1, 0.95)
79515.2
``````

Approach 4: Excel’s Approach

Finally, I came across this one, that explains how Excel does it. The summary of the method is as follows:

Given a set of `N` ordered values `{v[1], v[2], ...}` and a requirement to calculate the `pth` percentile, do the following:

• Calculate `l = p(N-1) + 1`
• Split `l` into integer and decimal components i.e. `l = k + d`
• Compute the required value as `V = v[k] + d(v[k+1] - v[k])`

This method gives me `79515.2`

None of the values match though I trust R’s value is the correct one (I observed it from the ecdf plot as well). My goal is to compute the 95th percentile manually (using only `AVG` and `STDEV` functions) from a given dataset and am not really sure what is going here. Can someone please tell me where I am going wrong?

``````93150
93116
93096
93085
92923
92823
92745
92150
91785
91775
91775
91735
91727
91633
91616
91604
91587
91579
91488
91427
91398
91339
91338
91290
91268
91084
91072
90909
86164
85372
83835
83428
81372
81281
81238
81195
81131
81030
81011
80730
80721
80682
80666
80585
80565
80534
80497
80464
80374
80226
80223
80178
80178
80147
80137
80111
80048
80027
79948
79902
79818
79785
79752
79675
79651
79620
79586
79535
79491
79388
79277
79269
79254
79194
79191
79180
79170
79162
79154
79142
79129
79090
79062
79039
79011
78981
78979
78936
78923
78913
78829
78809
78742
78735
78725
78618
78606
78577
78527
78509
78491
78448
78289
78284
78277
78238
78171
78156
77998
77998
77978
77956
77925
77848
77846
77759
77729
77695
77677
77382
70473
70449
69886
69767
69704
69573
69479
69398
69328
69311
69265
69178
69162
69104
69100
69072
69062
68971
68944
68929
68924
68904
68879
68877
68799
68755
68726
68666
68623
68588
68547
68458
68457
68453
68438
68438
68429
68426
68394
68374
68363
68357
68337
68300
68256
68250
68228
68216
68180
68149
68124
68114
68060
68029
68029
68025
68004
67996
67981
67964
67938
67925
67914
67901
67853
67819
67818
67788
67770
67767
67688
67670
67669
67629
67618
67609
67602
67583
67540
67479
67475
67470
67433
67420
67387
67343
67339
67337
67315
67273
67224
67208
67160
67137
67102
67045
66449
66408
66338
66211
63784
63557
63091
63021
62895
62663
62182
62079
62044
61907
61888
61856
61847
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60773
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60194
59673
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57264
57158
57106
56288
56245
56054
56031
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55841
55533
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55316
55281
55230
55196
55111
55101
50957
50870
49580
48353
21349
21319
21288
21274
21270
21255
21232
21208
21196
21184
21164
21150
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21143
21129
21108
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20908
20882
20871
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20800
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20757
20752
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20671
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20572
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20551
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20484
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20415
20398
20368
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19500
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19353
19338
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19273
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19258
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19072
19067
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19049
19045
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19043
19043
19032
19005
18996
18968
18957
18948
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18897
18897
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18884
18878
18878
18878
18871
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18862
18862
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18851
18851
18848
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18842
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18762
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18675
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18672
18665
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18609
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18578
18578
18578
18572
18569
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18563
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18554
18551
18548
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18503
18502
18497
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18496
18495
18493
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18487
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18485
18482
18479
18473
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18470
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18459
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18408
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18398
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18378
18357
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18349
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18328
18319
18314
18313
18302
18295
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18269
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18257
18251
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18234
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18225
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18214
18214
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18213
18210
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18206
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18203
18194
18192
18191
18190
18187
18184
18179
18179
18179
18175
18171
18170
18156
18152
18151
18151
18149
18149
18148
18148
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18146
18140
18139
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18137
18136
18135
18135
18134
18133
18133
18128
18128
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18127
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18117
18110
18108
18108
18099
18097
18096
18096
18095
18087
18085
18084
18083
18067
18060
18056
18056
18054
18053
18050
18049
18048
18038
18036
18033
18033
18028
18027
18025
18023
18022
18010
18010
18010
18000
17995
17983
17980
17978
17975
17974
17974
17968
17968
17967
17965
17964
17962
17961
17956
17955
17943
17938
17935
17934
17933
17932
17930
17925
17923
17919
17912
17912
17904
17897
17896
17894
17884
17880
17874
17872
17870
17865
17857
17856
17854
17854
17845
17843
17841
17836
17834
17831
17831
17828
17822
17821
17821
17816
17804
17803
17799
17798
17794
17794
17793
17790
17787
17786
17783
17782
17781
17777
17777
17777
17772
17772
17771
17766
17766
17758
17750
17747
17743
17715
17699
17694
17683
17682
17681
17668
17668
17630
17619
17617
17610
17609
17609
17607
17607
17599
17587
17565
17551
17542
17532
17531
17514
17514
17512
17509
17503
17483
17481
17475
17465
17463
17449
17433
17404
17397
17356
17356
17214
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
``````

If you want to work out the 95th percentile yourself, order the numbers from smallest to largest and find a value such that 95% of the data is below that value. R probably uses some sort of interpolation between data points. A simple approximation might be `sort(data\$V1)[0.95*length(data\$V1)]`.