Final answer:
The sample variance of the numbers 17, 11, 5, 9, and 10 is 18.8, and the sample standard deviation is approximately 4.3 when rounded to the nearest tenth.
Step-by-step explanation:
To find the sample variance and standard deviation of the numbers 17, 11, 5, 9, and 10, you need to follow these steps:
- Calculate the mean (average) of the numbers.
- Subtract the mean from each number to find the deviations.
- Square each deviation to get the squared deviations.
- Sum all the squared deviations.
- Divide the total by the number of data points minus 1 (since it's a sample) to get the sample variance.
- Take the square root of the sample variance to find the sample standard deviation.
Let's perform the calculation:
- Mean: (17 + 11 + 5 + 9 + 10) / 5 = 52 / 5 = 10.4
- Deviations: (17-10.4), (11-10.4), (5-10.4), (9-10.4), (10-10.4)
- Squared Deviations: (6.6)^2, (0.6)^2, (-5.4)^2, (-1.4)^2, (-0.4)^2
- Sum of Squared Deviations: (43.56 + 0.36 + 29.16 + 1.96 + 0.16)
- Sample Variance: (75.2) / (5 - 1) = 18.8
- Sample Standard Deviation: sqrt(18.8) ≈ 4.34
The sample variance is 18.8 and the sample standard deviation, rounded to the nearest tenth, is 4.3.