Question

For the following set of data, find the sample standard deviation,

to the nearest hundredth.
34, 47, 16, 43, 73, 17, 56


Summary:​

Answer 1

The sample standard deviation of the given data set is approximately 20.72.

Step-by-step explanation:

To find the sample standard deviation, we can use the following steps:

1. Calculate the mean of the data set by adding up all the numbers and dividing by the total number of values. In this case, (34+47+16+43+73+17+56) / 7 = 38.57.
2. Subtract the mean from each value to get the deviations from the mean: 34-38.57 = -4.57, 47-38.57 = 8.43, 16-38.57 = -22.57, 43-38.57 = 4.43, 73-38.57 = 34.43, 17-38.57 = -21.57, 56-38.57 = 17.43.
3. Square each deviation: (-4.57)^2 = 20.89, (8.43)^2 = 70.92, (-22.57)^2 = 509.94, (4.43)^2 = 19.60, (34.43)^2 = 1185.37, (-21.57)^2 = 465.28, (17.43)^2 = 303.88.
4. Add up all the squared deviations: 20.89 + 70.92 + 509.94 + 19.60 + 1185.37 + 465.28 + 303.88 = 2576.88.
5. Divide the sum of squared deviations by the sample size minus 1: 2576.88 / (7-1) = 429.48.
6. Take the square root of the result from step 5 to get the sample standard deviation: sqrt(429.48) ≈ 20.72.