High School

Dear beloved readers, welcome to our website! We hope your visit here brings you valuable insights and meaningful inspiration. Thank you for taking the time to stop by and explore the content we've prepared for you.
------------------------------------------------ Find the variance of the data set:

[tex]
\begin{array}{c}
198, 190, 245, 211, 193, 193 \\
\bar{x} = 205
\end{array}
[/tex]

Variance [tex]\left(\sigma^2\right) =[/tex] [tex]\square[/tex]

Answer :

To find the variance of the given data set, let's go through the process step-by-step:

1. Understand the data: We have the data points 198, 190, 245, 211, 193, and 193, with a given mean ([tex]\(\bar{x}\)[/tex]) of 205.

2. Calculate the deviations: For each data point, subtract the mean and square the result. This is called the squared deviation.
- For 198: [tex]\((198 - 205)^2 = 49\)[/tex]
- For 190: [tex]\((190 - 205)^2 = 225\)[/tex]
- For 245: [tex]\((245 - 205)^2 = 1600\)[/tex]
- For 211: [tex]\((211 - 205)^2 = 36\)[/tex]
- For 193: [tex]\((193 - 205)^2 = 144\)[/tex]
- For 193: [tex]\((193 - 205)^2 = 144\)[/tex]

3. Sum the squared deviations: Add all the squared deviations calculated in step 2.
- Total = [tex]\(49 + 225 + 1600 + 36 + 144 + 144 = 2198\)[/tex]

4. Calculate the average of the squared deviations: Divide the total sum of squared deviations by the number of data points. This gives us the variance.
- Variance [tex]\(\sigma^2 = \frac{2198}{6} = 366.3333\)[/tex]

Therefore, the variance of the data is approximately [tex]\(366.33\)[/tex].