Question

Find the sample standard deviation of the data {76, 46, 16, 86} of four numbers. Answer:

(A) 31.6228
(B) 27.3861
(C) 56
(D) 61

Answer 1

The sample standard deviation of the data set {76, 46, 16, 86} is found to be approximately 31.6228, which corresponds to option (A). The standard deviation is calculated using the sample mean and the squared differences between each data point and the mean, followed by taking the square root.

Step-by-step explanation:

To find the sample standard deviation of the data set {76, 46, 16, 86}, it is important to first calculate the sample mean, then sum the squared differences between each data point and the mean, and finally, divide by the number of samples minus one before taking the square root.

1. Calculate the sample mean (average): (76 + 46 + 16 + 86) / 4 = 224 / 4 = 56.
2. Find the squared differences from the mean:
3. Sum the squared differences: 400 + 100 + 1600 + 900 = 3000.
4. Divide by the number of data points minus one (degrees of freedom): 3000 / (4 - 1) = 3000 / 3 = 1000.
5. Take the square root to find the sample standard deviation: √1000 ≈ 31.6228.

Therefore, the correct answer is (A) 31.6228.