Mean Variance Standard Deviation Calculator

The pupose of the project is to create a function named calculate() in mean_var_std.py that uses Numpy to output the mean, variance, standard deviation, max, min, and sum of the rows, columns, and elements in a 3 x 3 matrix.

Table of content

1. Introduction
2. Development
3. Breakdown
4. Solution

Introduction

1. Input of the function should be a list containing 9 digits. The function should convert the list into a 3 x 3 Numpy array, and then return a dictionary containing the mean, variance, standard deviation, max, min, and sum along both axes and for the flattened matrix.

The returned function will follow the format below:

{
 'mean': [axis1, axis2, flattened],
 'variance': [axis1, axis2, flattened],
 'standard deviation': [axis1, axis2, flattened],
 'max': [axis1, axis2, flattened],
 'min': [axis1, axis2, flattened],
 'sum': [axis1, axis2, flattened]
}

2. If a list containing less than 9 elements is passed into the function, it should raise a ValueError exception with the message: "List must contain nine numbers." The values in the returned dictionary should be lists and not Numpy arrays.

For example, calculate([0,1,2,3,4,5,6,7,8]) should return:

{
  'mean': [[3.0, 4.0, 5.0], [1.0, 4.0, 7.0], 4.0],
  'variance': [[6.0, 6.0, 6.0], [0.6666666666666666, 0.6666666666666666, 0.6666666666666666], 6.666666666666667],
  'standard deviation': [[2.449489742783178, 2.449489742783178, 2.449489742783178], [0.816496580927726, 0.816496580927726, 0.816496580927726], 2.581988897471611],
  'max': [[6, 7, 8], [2, 5, 8], 8],
  'min': [[0, 1, 2], [0, 3, 6], 0],
  'sum': [[9, 12, 15], [3, 12, 21], 36]
}

Development

For development, you can use main.py to test your calculate() function. Click the "run" button and main.py will run.

Solution Breakdown

Here we define the calculate() funtion, raising the ValueError, and setting the numpy arrary:

def calculate(list):
    if(len(list) != 9):
      raise ValueError("List must contain nine numbers.")

    ls = np.array(list)
    print(ls)

Setting up the 3x3 matrix for the mean, varience, standard deviation, max, min, sum:

    mean_row = [ls[[0, 1, 2]].mean(), ls[[3, 4, 5]].mean(), ls[[6, 7, 8]].mean()]
    mean_column = [ls[[0, 3, 6]].mean(), ls[[1, 4, 7]].mean(), ls[[2, 5, 8]].mean()]

    var_row = [ls[[0, 1, 2]].var(), ls[[3, 4, 5]].var(), ls[[6, 7, 8]].var()]
    var_column = [ls[[0, 3, 6]].var(), ls[[1, 4, 7]].var(), ls[[2, 5, 8]].var()]

    std_row = [ls[[0, 1, 2]].std(), ls[[3, 4, 5]].std(), ls[[6, 7, 8]].std()]
    std_column = [ls[[0, 3, 6]].std(), ls[[1, 4, 7]].std(), ls[[2, 5, 8]].std()]

    max_row = [ls[[0, 1, 2]].max(), ls[[3, 4, 5]].max(), ls[[6, 7, 8]].max()]
    max_column = [ls[[0, 3, 6]].max(), ls[[1, 4, 7]].max(), ls[[2, 5, 8]].max()]

    min_row = [ls[[0, 1, 2]].min(), ls[[3, 4, 5]].min(), ls[[6, 7, 8]].min()]
    min_column = [ls[[0, 3, 6]].min(), ls[[1, 4, 7]].min(), ls[[2, 5, 8]].min()]

    sum_row = [ls[[0, 1, 2]].sum(), ls[[3, 4, 5]].sum(), ls[[6, 7, 8]].sum()]
    sum_column = [ls[[0, 3, 6]].sum(), ls[[1, 4, 7]].sum(), ls[[2, 5, 8]].sum()]

Setting up return statement for the calculate() function:

    return {
      'mean': [mean_column, mean_row, ls.mean()],
      'variance': [var_column, var_row, ls.var()],
      'standard deviation': [std_column, std_row, ls.std()],
      'max': [max_column, max_row, ls.max()],
      'min': [min_column, min_row, ls.min()],
      'sum': [sum_column, sum_row, ls.sum()]
    }

Solution

Return function with desired formatting:

{
 'mean': [[3.0, 4.0, 5.0], [1.0, 4.0, 7.0], 4.0],
 'variance': [[6.0, 6.0, 6.0], [0.6666666666666666, 0.6666666666666666, 0.6666666666666666], 6.666666666666667], 
 'standard deviation': [[2.449489742783178, 2.449489742783178, 2.449489742783178], [0.816496580927726, 0.816496580927726, 0.816496580927726], 2.581988897471611],  
 'max': [[6, 7, 8], [2, 5, 8], 8],
 'min': [[0, 1, 2], [0, 3, 6], 0], 
 'sum': [[9, 12, 15], [3, 12, 21], 36]
}

Organized results in their 3x3 matrices:

Mean:

3.0	4.0	5.0
1.0	4.0	7.0

=> Ans. 4

Variance:

6.0	6.0	6.0
0.666...	0.666...	0.666...

=> Ans. 6.666...

Stabard deviation:

2.449...	2.449..	2.449...
0.816...	0.816...	0.816...

=> Ans. 2.581

Max:

6	7	8
2	5	8

=> Ans. 8

Min:

0	1	2
0	3	6

=> Ans. 0

Sum:

9	12	15
3	12	21

=> Ans. 36