Answer :
To find the sample standard deviation of the given scores, you can follow these steps:
Find the Mean
First, add up all the scores and divide by the number of scores.
[tex]\text{Mean} = \frac{172 + 168 + 188 + 190 + 172 + 182 + 174}{6} = \frac{1046}{6} \approx 174.33[/tex]
Calculate Each Score's Deviation from the Mean
Subtract the mean from each score and square the result:
- [tex](172 - 174.33)^2 = 5.43[/tex]
- [tex](168 - 174.33)^2 = 40.13[/tex]
- [tex](188 - 174.33)^2 = 187.43[/tex]
- [tex](190 - 174.33)^2 = 246.43[/tex]
- [tex](172 - 174.33)^2 = 5.43[/tex]
- [tex](182 - 174.33)^2 = 58.13[/tex]
- [tex](174 - 174.33)^2 = 0.11[/tex]
Find the Average of These Squared Deviations
Sum all the squared deviations:
[tex]5.43 + 40.13 + 187.43 + 246.43 + 5.43 + 58.13 + 0.11 = 541.09[/tex]
Divide by the number of scores minus 1 (since this is a sample standard deviation, not a population standard deviation):
[tex]\text{Variance} = \frac{541.09}{5} = 108.22[/tex]
Take the Square Root of the Variance
This gives you the sample standard deviation:
[tex]\text{Standard Deviation} = \sqrt{108.22} \approx 8.64[/tex]
Therefore, the sample standard deviation is closest to 8.64. The correct choice from the provided options is 8.64.
