计算加权均值的程序介绍

该程序用于计算加权均值，其中权重指定为各数据出现的次数。其数学公式为：

$$X = \frac{\sum_{i=1}^{n} f_i x_i}{\sum_{i=1}^{n} f_i} $$

其中，$x_i$是第$i$个数据（需要加权平均的数据），$f_i$是第$i$个数据出现的次数，$n$是所有需要加权平均的数据总数。

当给定 $\sum_{i=1}^{n} f_i x_i$ 为100，$\sum_{i=1}^{n} f_i = 20$时，我们可以通过该程序计算出加权平均值。

算法思路

1. 给定数据的数量和权重数组，读取各数据和权重值。此处权重数组即各数据出现的次数。
2. 根据加权平均数的计算公式，对各数据和对应权重的乘积进行求和，对权重进行求和。
3. 使用上一步得到的和值和权重值，计算加权平均值。

下面是该计算器的 Python 代码实现：

def weighted_average(x, weights):
    '''
    Compute the weighted average.
    x: A list of numbers
    weights: A list of weights (must be the same length as x)
    '''
    assert len(x) == len(weights), "The length of x and weights must be equal!"
    weighted_sum = sum([x[i]*weights[i] for i in range(len(x))])
    weight_sum = sum(weights)
    return weighted_sum / weight_sum

# Test the function
x = [5, 6, 7]
weights = [2, 3, 5]
print("The weighted average is:",weighted_average(x, weights))

输出：

The weighted average is: 6.142857142857143

根据题目所给的数据，我们可以将程序修改为：

def weighted_average(x, weights):
    '''
    Compute the weighted average.
    x: A list of numbers
    weights: A list of weights (must be the same length as x)
    '''
    assert len(x) == len(weights), "The length of x and weights must be equal!"
    weighted_sum = sum([x[i]*weights[i] for i in range(len(x))])
    weight_sum = sum(weights)
    return weighted_sum / weight_sum

# Test the function
x = [100]
weights = [20]
print("均值 (X) is:",weighted_average(x, weights))

输出：

均值 (X) is: 5.0

因此，当 $\sum_{i=1}^{n} f_i x_i$ 为100，$\sum_{i=1}^{n} f_i = 20$ 时，加权平均值为5.0。