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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 coefficient of variation (or relative standard deviation) of this sample (rounded to 2 decimal places).
A. 0.21
B. 0.2
C. 0.18
D. 0.3
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题目解析
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The coefficient of variation is calculated as the standard deviation divided by the mean.

要计算样本的变异系数(或相对标准差),我们需要先计算样本的标准差和均值,然后用标准差除以均值。

1. **计算均值**:
\[
\text{均值} = \frac{9 + 10 + 6 + 7 + 8.3 + 7.7}{6} = \frac{48}{6} = 8
\]

2. **计算标准差**:
首先计算每个数据点与均值的差的平方,然后求和,再除以样本数减1,最后开平方根。

\[
\begin{align*}
(9 - 8)^2 & = 1 \\
(10 - 8)^2 & = 4 \\
(6 - 8)^2 & = 4 \\
(7 - 8)^2 & = 1 \\
(8.3 - 8)^2 & = 0.09 \\
(7.7 - 8)^2 & = 0.09 \\
\end{align*}
\]

\[
\sum (X_i - \bar{X})^2 = 1 + 4 + 4 + 1 + 0.09 + 0.09 = 10.18
\]

\[
\text{样本方差} = \frac{10.18}{6 - 1} = \frac{10.18}{5} = 2.036
\]

\[
\text{标准差} = \sqrt{2.036} \approx 1.43
\]

3. **计算变异系数**:
\[
\text{变异系数} = \frac{\text{标准差}}{\text{均值}} = \frac{1.43}{8} \approx 0.17875
\]

四舍五入到两位小数:

\[
\text{变异系数} \approx 0.18
\]

正确答案是C: 0.18。