At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
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]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.
