Question

In: Statistics and Probability

Collect the Data: Use a random number generator to generate 50 values between 0 and 1...

Collect the Data: Use a random number generator to generate 50 values between 0 and 1 (inclusive).

Theoretical Distribution In words, X = The theoretical distribution of X is X ~ U(0, 1). In theory, based upon the distribution X ~ U(0, 1), find μ = __________ σ = __________ 1st quartile = __________ 3rd quartile = __________ median = __________

Construct a box plot of the data. Be sure to use a ruler to scale accurately and draw straight edges. Do you notice any potential outliers? If so, which values are they? Either way, numerically justify your answer.

Expert Solution

Random sample:

Random
0.014239
0.020079
0.037545
0.038565
0.045121
0.053843
0.065442
0.068249
0.130947
0.132351
0.136406
0.139052
0.142635
0.187176
0.20224
0.215205
0.254323
0.260139
0.309604
0.313556
0.33068
0.347827
0.36856
0.398539
0.403268
0.412967
0.42334
0.49209
0.533364
0.563387
0.580189
0.617334
0.633268
0.634619
0.657665
0.721846
0.732949
0.777444
0.780106
0.789628
0.793662
0.7973
0.808289
0.812683
0.856005
0.899802
0.913899
0.914326
0.944836
0.957423

Mean:

Standard deviation:

n=50

1st Quartile: (n+1)/4th observation= 51/4=12.75th observation= 12th +0.75(13th-12th)

1st Quartile: 0.136406+0.75*0.002687=0.141739

Median: (n+1)/2 =51/2= 25.5th observation= (26th+25th)/2= (0.403268+0.398539)/2=0.408118

3rd Quartile: 3*(n+1)/4= 3*12.75=38.25th observation= 38th+0.25(39th-38th)= 0.778811

Inter Quartile range(IQR)= Q3-Q1= 0.778811-0.141739= 0.636371

Minimum outlier range: Q1-1.5*IQR= 0.141739-1.5*0.636371= -0.81282

Maximum Outlier range: Q3+1.5*IQR= 0.778811+1.5*0.636371=1.590927

No outliers in the data set.

orchestra answered 2 years ago

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