Answer :
To find the variance of the given data set, follow these steps:
1. Identify the Data Points and the Mean:
- Data points: 198, 190, 245, 211, 193, 193
- Given mean ([tex]\(\bar{x}\)[/tex]): 205
2. Calculate the Squared Differences from the Mean:
- Find the difference between each data point and the mean, and then square the result.
- 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 another 193: [tex]\((193 - 205)^2 = 144\)[/tex]
- The squared differences are: 49, 225, 1600, 36, 144, and 144
3. Calculate the Variance:
- Add all the squared differences together:
[tex]\[
49 + 225 + 1600 + 36 + 144 + 144 = 2198
\][/tex]
- Divide the sum by the number of data points (6 in this case) to find the variance:
[tex]\[
\text{Variance} = \frac{2198}{6} \approx 366.33
\][/tex]
Therefore, the variance of the data set is approximately [tex]\( 366.33 \)[/tex].
1. Identify the Data Points and the Mean:
- Data points: 198, 190, 245, 211, 193, 193
- Given mean ([tex]\(\bar{x}\)[/tex]): 205
2. Calculate the Squared Differences from the Mean:
- Find the difference between each data point and the mean, and then square the result.
- 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 another 193: [tex]\((193 - 205)^2 = 144\)[/tex]
- The squared differences are: 49, 225, 1600, 36, 144, and 144
3. Calculate the Variance:
- Add all the squared differences together:
[tex]\[
49 + 225 + 1600 + 36 + 144 + 144 = 2198
\][/tex]
- Divide the sum by the number of data points (6 in this case) to find the variance:
[tex]\[
\text{Variance} = \frac{2198}{6} \approx 366.33
\][/tex]
Therefore, the variance of the data set is approximately [tex]\( 366.33 \)[/tex].
