 # Descriptive Statistics

Subject Mathematics Applied Statistics

## Question

You have a need to determine the density of a material you are working with. To do this you take a sample of known mass and measure volume. In order to determine how accurate your measurements are, you take a series of 100 repeated volume measurements and 50 repeated mass measurements. The attached list contains this mass (g) and volume (mL) data.

a. Use this data to determine the standard deviation in your volume and mass measurements.
b. If the average volume of your samples is 25mL and the average mass is 35g, how accurately can you determine the density using your technique?

V                   m
24.63971686 34.42830462
24.8706771 34.39550467
25.81219568 34.46680019
24.88891016 34.43781593
25.07934324 34.48397509
25.34053305 34.62927027
24.94746126 34.71743988
24.88547136 34.47263012
25.36784427 34.49123066
25.55839377 34.54303567
25.0638813 34.53674906
25.34724273 34.50052653
24.92701612 34.43871422
24.30540304 34.42279843
25.02156249 34.52034418
25.22350363 34.64111199
25.03039633 34.54591687
24.46430111 34.39555251
24.63524116 34.63265176
25.51640545 34.54381744
25.2832483 34.38399953
25.19422097 34.48890381
24.77829349 34.56713263
24.95988227 34.57939479
25.16465397 34.48055966
24.00227808 34.37694436
24.57648599 34.5361596
24.77193369 34.59796197
24.74429169 34.48244313
24.99635188 34.52640182
25.37187808 34.55913611
24.4716144 34.53277455
25.38867201 34.62100159
24.70565224 34.41346585
24.84372696 34.43128032
24.92447757 34.53978593
24.92846297 34.28529768
24.89725058 34.33283685
25.26874955 34.64507139
25.02772859 34.48382145
25.25079695 34.35404805
25.77226765 34.41575077
25.08889144 34.42542604
24.66260092 34.42940303
24.50874523 34.41784633
24.77544728 34.53252661
24.67695764 34.45060702
24.79113316 34.46471655
25.34866028 34.55099847
24.69033534 34.63651034
24.57689614
24.85406061
24.91740697
24.94365821
25.57573363
25.26200115
25.24479576
24.83696926
25.10571049
25.10474234
25.56002442
25.48815313
25.32607152
25.31916946
25.09242264
25.23771362
24.90152038
24.74330521
25.4345111
25.12151446
24.80764067
25.33991246
24.93551037
24.49834532
24.81397709
24.88458248
25.66290483
25.28144779
24.22002576
24.60229688
24.48808058
25.17790259
25.16904974
24.79703063
25.2105481
24.86438697
24.9664503
24.79862982
24.78531979
24.54455911
25.063457
24.67721966
24.97371838
25.26803206
24.67926124
25.09754315
24.72343945
25.22430839
25.66840636
24.63175248

## Solution Preview

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Volume    Mass
Mean 24.99 34.5
Standard Deviation 0.3443 0.09067

If mean 25 35

Density = Mass/Volume = 34.5/24.99 1.3802

Percentage error = absolute(Experimental value-accepted value)/accepted value X 100%...

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