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Sagot :
Solution
- The formula for finding the variance of the sample dataset is given below:
[tex]\begin{gathered} \sum ^n_{i=1}\frac{(x_i-\bar{x})^2}{n-1} \\ \\ \text{where,} \\ \bar{x}=\text{The mean of the sample} \\ x_i=\text{ The individual data points in the dataset} \\ n=\text{The number of data points in the sample} \end{gathered}[/tex]- The data points have been given to be 12, 14, 19, 11, 8, 21, and 13.
- The formula for finding the Mean is
[tex]\begin{gathered} \sum ^n_{i=1}\frac{x_i}{n} \\ \text{where,} \\ x_i=\text{The individual data point} \\ n=\text{The number of data points in the sample} \end{gathered}[/tex]- Thus, we can simply apply the formula given above to solve the question. We shall follow these steps to solve this question:
1. Find the Mean.
2. Calculate the Variance
1. Find the Mean
[tex]\begin{gathered} \bar{x}=\frac{12+14+19+11+8+21+13}{7} \\ \\ \bar{x}=14 \end{gathered}[/tex]2. Calculate the Variance:
[tex]\begin{gathered} s^2=\sum ^n_{i=1}\frac{(x_i-\bar{x})^2}{n-1} \\ \\ =\frac{(12-14)^2+(14-14)^2+(19-14)^2+(11-14)^2+(8-14)^2+(21-14)^2+(13-14)^2}{7-1} \\ \\ =\frac{(-2)^2+0^2+5^2+(-3)^2+(-6)^2+7^2+(-1)^2}{6} \\ \\ =\frac{4+0+25+9+36+49+1}{6}=\frac{124}{6} \\ \\ s^2=20\frac{4}{6}=20.666\ldots\approx20.7\text{ (To the nearest tenth)} \end{gathered}[/tex]Final Answer
The value of the variance is
[tex]s^2=20.7[/tex]
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