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CDA认证小程序

The daily office hours X (measured in hours) of employees in a certain department follow a normal distribution. The office hours for 6 employees on a particular day are as follows: 9, 10, 6, 7, 8.3, 7.7. Calculate the variance of this sample (rounded to 2 decimal places).
A. 1.43
B. 2.036
C. 1.69
D. 1.72
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题目解析
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To calculate the sample variance, subtract one degree of freedom. In this case, the denominator is 6-1=5.

首先,我们需要计算这6名员工的日常办公时间的样本均值(平均值)。

1. 计算样本均值:
\[
\bar{X} = \frac{9 + 10 + 6 + 7 + 8.3 + 7.7}{6} = \frac{48}{6} = 8
\]

2. 计算每个数据点与样本均值的差值的平方:
\[
(9 - 8)^2 = 1
\]
\[
(10 - 8)^2 = 4
\]
\[
(6 - 8)^2 = 4
\]
\[
(7 - 8)^2 = 1
\]
\[
(8.3 - 8)^2 = 0.09
\]
\[
(7.7 - 8)^2 = 0.09
\]

3. 求这些平方差值的总和:
\[
1 + 4 + 4 + 1 + 0.09 + 0.09 = 10.18
\]

4. 计算样本方差(注意这里使用的是样本方差公式,分母为 n-1):
\[
s^2 = \frac{\sum (X_i - \bar{X})^2}{n-1} = \frac{10.18}{6-1} = \frac{10.18}{5} = 2.036
\]

因此,样本方差为2.036,答案是B。