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Exam statistics

If you have done the Battleship exercise, this one will follow the same structure. We will go step by step, giving solutions in case you get stucked. At the end you can look to the solution file Exam.py.

Ready? The computing starts here:

• This are the grades of some students:

  grades = [100, 100, 90, 40, 80, 100, 85, 70, 90, 65, 90, 85, 50.5]
  

  We are going to make a function to print them.
  • Define a function called print_grades() with one argument, a list called grades.
  • nside the function, iterate through grades and print each item on its own line.
  • After your function, call print_grades() with the grades list as the parameter.

Solution 1

>>> grades = [100, 100, 90, 40, 80, 100, 85, 70, 90, 65, 90, 85, 50.5]
>>>
>>> def print_grades(grades):
...     for grade in grades:
...         print grade
...
...
>>> print_grades(grades)
100
100
90
40
80
100
85
70
90
65
90
85
50.5
>>>

• The next step in the creation of our grade statistics program involves computing the mean (average) of the grades.
  • Define a function grades_sum() that does the following.
  • Takes in a list of scores, scores
  • Computes the sum of the scores
  • Returns the computed sum
  • Call the newly created grades_sum() function with the list of grades and print the result.

Solution 2

>>> grades = [100, 100, 90, 40, 80, 100, 85, 70, 90, 65, 90, 85, 50.5]
>>>
>>>
>>>
>>> def grades_sum (scores):
...     total = sum (scores)
...     return total
...
>>>
>>> print grades_sum(grades)
1045.5
>>>
>>>

Note:You can also use a for loop.

• Define a function grades_average(), below the grades_sum() function that does the following:

  • Has one argument, grades, a list
  • Calls grades_sum with grades
  • Computes the average of the grades by dividing that sum by float(len(grades)).
  • Returns the average.
  • Call the newly created grades_average() function with the list of grades and print the result.

Solution 3

>>> def grades_average(grades):
...     tot =grades_sum(grades)
...     ave=tot/float(len(grades))
...     return ave
...
>>> print grades_average(grades)
80.4230769231

• We're going to use the average for computing the variance. The variance allows us to see how widespread the grades were from the average.
  • Define a new function called grades_variance() that accepts one argument, scores, a list.
  • First, create a variable average and store the result of calling grades_average(scores).
  • Next, create another variable variance and set it to zero. We will use this as a rolling sum. for each score in scores: Compute its squared difference: (average - score) ** 2 and add that to variance.
  • Divide the total variance by the number of scores.
  • Then, return that result.
  • Finally, after your function code, print grades_variance(grades).

Solution 4

>>> def grades_variance(scores):
...     average=grades_average(scores)
...     variance=0
...     for score in scores:
...         add=(average-score)**2
...         variance += add
...     var_tot=variance/len(scores)
...     return var_tot
...
>>> print grades_variance(grades)
334.071005917

• The standard deviation is the square root of the variance. You can calculate the square root by raising the number to the one-half power.

  • Define a function grades_std_deviation(variance). return the result of variance ** 0.5
  • After the function, create a new variable called variance and store the result of calling grades_variance(grades).
  • Finally print the result of calling grades_std_deviation(variance).

Solution 5

>>> def grades_std_deviation(variance):
...     return variance**0.5
...
>>> variance=grades_variance(grades)
334.071005917
>>> print grades_std_deviation(variance)
18.2776094147