在Python中计算均值和方差

Question

当您输入一组数字时，我有这段代码来计算平均值和方差，但我的方差偏离了应有的值。我的方差公式是否以某种方式关闭，或者我的代码中可能存在一些错误？我的输出：Input a positive number: 1mean is  1.0 variance is  0Input a positive number: 2mean is  1.5 variance is  0.125Input a positive number: 3mean is  2.0 variance is  0.3958333333333333正确输出：Input a positive number: 1mean is  1.0 variance is  0Input a positive number: 2mean is  1.5 variance is  0.5Input a positive number: 3mean is  2.0 variance is  1mean = 0variance = 0x = 0n = 0while x >= 0:    x = float(input('Input a positive number: '))  # user input for code    n += 1    if x < 0:        break    if n == 1:  # Added this if statement to avoid dividing by 0        mean = x        print('mean is ', mean, 'variance is ', variance)    else:        mean = mean + ((x-mean)/n)  # formula for calculating mean        variance = (((n-2)/(n-1)) * variance) + (((mean-x)**2)/n)  # formula for calculating variance        print('mean is ', mean, 'variance is ', variance)

Answer 1

你的方差公式是错误的。你可以在这里找到公式以便更好地理解，我这里就不解释了。

mean = 0

variance = 0

x = 0

n = 0

while x >= 0:

    x = float(input('Input a positive number: '))  # user input for code

    n += 1

    if x < 0:

        break

    if n == 1:  # Added this if statement to avoid dividing by 0

        mean = x

        print('mean is ', mean, 'variance is ', variance)

    else:

        mean = mean + ((x-mean)/n)  # formula for calculating mean

        

        variance = (((n-2)/(n-1)) * variance) + (((x-mean)*(x-pre_mean))/(n-1))  # formula for calculating variance

        print('mean is ', mean, 'variance is ', variance)

    pre_mean = mean

输出：

Input a positive number: 1

mean is  1.0 variance is  0

Input a positive number: 2

mean is  1.5 variance is  0.5

Input a positive number: 3

mean is  2.0 variance is  1.0

Input a positive number: 4

mean is  2.5 variance is  1.6666666666666665

你给出了一个错误的测试用例，

Input a positive number: 3

mean is  2.0 variance is  0.1

在这里，方差将1 not 0.1。您可以使用在线计算器轻松检查样本方差。

Answer 2

您可以使用列表来存储所有输入。

x = 0

data = [] 

while x >= 0:

    x = float(input('Input a positive number: '))  # user input for code

    if x < 0:

         break

    data.append(x)        

    N = len(data)

    mean = sum(data) / N

    var = 0

    if N > 1:

        a = [x - mean for x in data]

        a = [x**2 for x in a]

        var = sum( a) / (N-1)

    

    print( "mean is ", mean, " variance is ", var)