Math Statistics

Sosorin Ivan 11-208

Laboratory works on the subject of mathematical statistics for the 2nd year of ITIS

First Laboratory Work

Using libraries:

1. pandas
2. numpy
3. matplotlib
4. scipy

The first step was to calculate the following quantities:

1. Mean
2. Mode
3. Median
4. Biased and unbiased variance
5. Standard deviation
6. Quartiles
7. Asymmetry coefficient
8. Interquartile latitude

Then it was necessary to construct a frequency histogram

Probability histogram

Distribution function

Distribution polygon

Box Plot

Second Laboratory Work

Using libraries:

1. pandas
2. numpy
3. scipy

Task 1

Answer:

Task 2

Answer: 0.08

Third Laboratory Work

Using libraries:

1. pandas
2. numpy
3. matplotlib

Task

Result

Calculates

  Samples:
  X sample:
   [120.7 120.9 126.1 121.3 118.3 121.4 117.4 120.6 118.6 112.5 121.4 111.5
   117.  117.6 113.5 120.2 113.3 119.5 119.5 119.4 114.1 117.7 118.6 117.2
   125.6 123.  116.  120.2 122.7 114.  119.2 113.8 115.4 117.9 124.3 113.7
   118.6 109.4 110.9 117.9 115.1 121.7 120.7 117.5 116.6 125.  116.4 114.
   118.6 122.8 115.9 118.5 125.1 119.3 120.3 115.9 116.1 116.6 117.8 118.3
   128.6 117.3 111.  122.2 105.1 121.4 113.9 115.8 117.4 117.9 114.3 114.3
   115.  119.2 122.5 123.2 113.4 119.8 126.2 118.4 116.2 119.9 119.  111.4
   112.  114.8 116.4 117.5 120.8 121.6 122.3 116.9 118.4 117.8 119.4]
  
  Y sample:
   [83.1 87.5 82.8 86.  82.2 84.5 83.1 84.6 81.8 83.2 89.7 81.1 86.1 83.7
   83.7 87.2 79.  85.7 86.9 84.6 82.7 80.5 86.2 86.  84.8 84.7 81.5 78.8
   84.7 79.3 78.4 81.7 84.  82.  89.5 81.8 84.  79.8 76.9 82.8 80.1 86.
   81.8 82.5 82.4 81.9 83.4 82.7 84.3 83.7 81.2 86.5 85.4 84.7 85.5 81.8
   80.8 81.1 83.9 86.9 90.8 83.7 80.7 86.2 77.6 83.5 84.1 83.1 80.  82.3
   82.  81.5 83.3 85.2 83.2 87.7 82.7 85.9 88.1 81.8 84.6 84.1 82.7 78.9
   81.  83.9 81.9 87.1 86.5 85.9 86.8 84.3 81.8 84.3 83.1]
  
  Means:
  X mean: 118.046
  Y mean: 83.511
  
  Mean Standard Deviation:
  X standard deviation: 3.972
  Y standard deviation: 2.637
  
  Correlation coefficient: 0.643
  
  Regression coefficient: 0.968
  
  Predictions:
  X Prediction: 115.616
  Y Prediction: 81

Plot