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].
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].
