added more formulae

src/statsy/Methods.py

@@ -51,3 +51,102 @@ def geometric_mean(data:list)->Number:
     Returns the geometric mean of a list of data.
     """
     return (product_notation(None,None,None,[data]) ** (1/len(data)))
+
+def trimmed_mean(trim:Number,data:list)->Number:
+    """
+    #Returns the trimmed mean of some data.
+    """
+    partial_trim = (trim/100)/2
+    # Find how many elements to remove from each side of the
+    number_to_slice_off = round((len(data) * partial_trim))
+    trimmed_data = data[int(number_to_slice_off):len(data)-number_to_slice_off]
+    return arithmetic_mean(trimmed_data)
+
+def vrange(data:list)->Number:
+    """
+    #Returns the range variability of a set of data.
+    """
+    return abs(data[0] - data[int(len(data)-1)])
+
+def interquartile_range(data:list)->Number:
+    """
+    #Also known as the H-spread. \n
+    #Returns the interquartile range of a set of data.
+    """
+    total_length = len(data)
+    if total_length & 1:
+        # If the data is of odd length
+        # Remove the median value and pass the data to the rest of the function.
+        temporary_IQR_function_data = data[:]
+        del temporary_IQR_function_data[int((total_length+1)/2)-1]
+    total_length = total_length - 1
+    return abs( median(temporary_IQR_function_data[:int(total_length//2)]) - median(temporary_IQR_function_data[int(total_length//2):]))
+
+def variance(data:list,type:str,rooted:Optional[bool]=None)->Number:
+    """
+    type = 'sample' returns the variance of a sample \n
+    type = 'population' returns the variance of a population \n
+    Returns the variance of a normally distributed set of data points. \n
+    """  
+    n = len(data)
+    if type == 'sample':
+        n = len(data) - 1
+    m = arithmetic_mean(data)
+    varian = (((  summation(None,None,lambda x: ((x - m)**2) ,[data]) / n ))) 
+    if rooted is True:
+        varian = root(2,varian)
+    return varian
+
+def standard_deviation(data:list,type:str):
+    """
+    type = 'sample' returns the variance of a sample \n
+    type = 'population' returns the variance of a population \n
+    Returns the standard deviation of a normally distributed set of data points. \n
+    """
+    return variance(data,type,True)
+
+def skewness(data:list,type:str)->Number:
+    """
+    type = 'sample' or 'population" \n
+    Return the skew of a set of data. \n
+    """
+    mew = arithmetic_mean(data)
+    n = len(data)
+    sd = standard_deviation(data,'sample')
+    fron =(n / ((n-1) * (n-2))) 
+    if type == "population":
+        sd = standard_deviation(data,'population')
+        fron = (1/n)
+    skew = fron  *   summation(None,None,lambda x: (((x - mew)/ sd) ** 3) ,[data])
+    return skew
+
+def kurtosis(data:list,type:str)->Number:
+    """
+    type = 'sample' or 'population" \n
+    Return the kurtosis of a set of data. \n
+    """
+    mew = arithmetic_mean(data)
+    n = len(data)
+    sd = standard_deviation(data,'sample')
+    fron =  (  (n * (n + 1)) / ((n-1) * (n-2) * (n-3))) 
+    end = 3     *   (  ((n-1)**2) / ((n-2)*(n-3))   )
+    sm = summation(None,None,lambda x: (((x - mew)/ sd) ** 4) ,[data])
+    if type == "population":
+        sd = standard_deviation(data,'population')
+        fron = (1/n)
+        end = 3
+        sm = summation(None,None,lambda x: (((x - mew)/ sd) ** 4) ,[data])
+    kurt = (fron * sm) - end
+    return kurt
+
+def Pearson_correlation_coefficient_r(data:List[list])->Number:
+    """
+    Returns Pearson's correlation coefficient of r.
+    """
+    n = len(data[0])
+    t1 = summation(None,None,lambda x, y: x*y,data)
+    t2 = ( summation(None,None,None,[data[0]]) * summation(None,None,None,[data[1]]) ) / n
+    b1 =  root(2,(summation(None,None,lambda x: x**2,[data[0]]) - ((summation(None,None,None,[data[0]])**2) / n)))
+    b2 = root(2,(summation(None,None,lambda x: x**2,[data[1]]) - ((summation(None,None,None,[data[1]])**2) / n)))
+    r = (t1-t2) / (b1 * b2)
+    return r