Syntax error Find combined mean and variance of two series in Python

Find combined mean and variance of two series in Python

Suppose we have two different series A1 and A2 of size b and a respectively. We have to find the mean and variance of combined series.

So, if the input is like A1 = [24, 46, 35, 79, 13, 77, 35] and A2 = [66, 68, 35, 24, 46], then the output will be Mean = [44.1429, 47.8], sd = [548.694, 294.56], combined mean = 45.6667, d1_square = 2.322, d2_square = 4.5511, combined_var = 446.056

To solve this, we will follow these steps −

  • Define a function mean() . This will take arr

    • return average of arr elements

  • Define a function sd() . This will take arr, n

  • sum := 0;

  • for i in range 0 to n, do

    • sum := sum +((arr[i] - mean(arr)) * (arr[i] - mean(arr)))

  • sdd := sum / n

  • return sdd

  • From the main method, do the following −

  • n := size of A1, m := size of A2

  • mean1 := mean(A1), mean2 := mean(A2)

  • display mean1 and mean2

  • sd1 := sd(A1, n), sd2 := sd(A2, m)

  • display sd1 and sd2

  • combinedMean :=(n * mean1 + m * mean2) /(n + m)

  • display combinedMean

  • d1_square :=(mean1 - combinedMean) *(mean1 - combinedMean)

  • d2_square :=(mean2 - combinedMean) *(mean2 - combinedMean)

  • display d1_square, d2_square

  • comb_var :=(n *(sd1 + d1_square) + m *(sd2 + d2_square)) /(n + m)

  • display comb_var

Example

Let us see the following implementation to get better understanding −

 Live Demo

def mean(arr):
return sum(arr)/len(arr)
def sd(arr, n):
   sum = 0;
   for i in range(n):
      sum = sum + ((arr[i] - mean(arr)) * (arr[i] - mean(arr)))
   sdd = sum / n
   return sdd
def combinedVariance(A1, A2):
   n = len(A1)
   m = len(A2)
   mean1 = mean(A1)
   mean2 = mean(A2)
   print("mean_1: ", round(mean1, 2), " mean_2: ", round(mean2, 2))
   sd1 = sd(A1, n)
   sd2 = sd(A2, m)
   print("sd_1: ", round(sd1, 2)," sd_2: ", round(sd2, 2))
   combinedMean = (n * mean1 + m * mean2) / (n + m)
   print("Combined Mean: ", round(combinedMean, 2))
   d1_square = ((mean1 - combinedMean) * (mean1 - combinedMean))
   d2_square = ((mean2 - combinedMean) * (mean2 - combinedMean))
   print("d1_square: ", round(d1_square, 2), " d2_square: ", round(d2_square, 2))
   comb_var = (n * (sd1 + d1_square) + m * (sd2 + d2_square)) / (n + m)
   print("Combined Variance: ", round(comb_var, 2))
A1 = [24, 46, 35, 79, 13, 77, 35 ]
A2 = [66, 68, 35, 24, 46 ]
n = len(A1)
m = len(A2)
combinedVariance(A1, A2)

Input

[24, 46, 35, 79, 13, 77, 35 ],[66, 68, 35, 24, 46 ]

Output

mean_1: 44.14 mean_2: 47.8
sd_1: 548.69 sd_2: 294.56
Combined Mean: 45.67
d1_square: 2.32 d2_square: 4.55
Combined Variance: 446.06
Updated on: 2020-08-25T09:01:19+05:30

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