Question

Using the following set of data (the same as in the previous problem), find the sample standard deviation: 10,8,5,6,4,9 Select the correct answer below:

a-2.4
b-5.4
c-8.4
d-6.4
e-1.4

Answer 1

To find the sample standard deviation, you need to find the sample mean, calculate the differences between each data point and the mean, square each difference, find the mean of the squared differences, and take the square root of the mean. For the given set (10, 8, 5, 6, 4, 9), the sample standard deviation is approximately 2.16.

Step-by-step explanation:

To find the sample standard deviation, you can follow these steps:

1. Find the sample mean by adding up all the numbers in the set and dividing by the number of data points. For the given set (10, 8, 5, 6, 4, 9), the mean is (10+8+5+6+4+9)/6 = 42/6 = 7.
2. Find the differences between each data point and the mean. For the given set, the differences are (10-7), (8-7), (5-7), (6-7), (4-7), and (9-7), which are 3, 1, -2, -1, -3, and 2.
3. Square each difference to get the squared differences. For the given set, the squared differences are 9, 1, 4, 1, 9, and 4.
4. Find the mean of the squared differences by adding them up and dividing by the number of data points. For the given set, the mean is (9+1+4+1+9+4)/6 = 28/6 = 4.67.
5. Take the square root of the mean of the squared differences to get the sample standard deviation. For the given set, the sample standard deviation is √4.67 ≈ 2.16.