1. Find the sample variance and standard deviation 6, 53,11,49,35,26,28,28,31,31 s squared = (round to the nearest hundredth as needed)
To find the sample variance and standard deviation, follow these steps:
Step 1: Calculate the mean.
Add all the values together and divide the sum by the number of values to find the mean.
Mean = (6 + 53 + 11 + 49 + 35 + 26 + 28 + 28 + 31 + 31) / 10 = 31.8
Step 2: Calculate the difference between each value and the mean.
Subtract the mean from each value to get the differences.
Differences: (-25.8, 21.2, -20.8, 17.2, 3.2, -5.8, -3.8, -3.8, -0.8, -0.8)
Step 3: Square each difference.
Square each difference to eliminate negative signs.
Squared differences: (666.12, 449.44, 432.64, 295.84, 10.24, 33.64, 14.44, 14.44, 0.64, 0.64)
Step 4: Calculate the sum of squared differences.
Add up all the squared differences calculated in the previous step.
Sum of squared differences = 666.12 + 449.44 + 432.64 + 295.84 + 10.24 + 33.64 + 14.44 + 14.44 + 0.64 + 0.64 = 1918.72
Step 5: Calculate the sample variance.
Divide the sum of squared differences by n-1, where n is the number of values.
Sample variance = 1918.72 / (10-1) = 213.19 (rounded to the nearest hundredth)
Step 6: Calculate the sample standard deviation.
Take the square root of the sample variance to get the sample standard deviation.
Sample standard deviation = √213.19 ≈ 14.59 (rounded to the nearest hundredth)
Therefore, the sample variance is approximately 213.19 (rounded to the nearest hundredth), and the sample standard deviation is approximately 14.59 (rounded to the nearest hundredth).