Question

Find the sample standard deviation of the following data set, using the statistical functions on your calculator. 0.78 0.56 0.42 0.45 0.46 0.47

Answer 1

Standard Deviation = 0.1488

Step-by-step explanation:

To find the sample standard deviation of a data set, you can use the statistical functions on a calculator. Here are the steps:

1. Enter the data points into a list on your calculator: 0.78, 0.56, 0.42, 0.45, 0.46, 0.47
2. Calculate the mean of the data set by using the sum function and dividing by the number of data points: mean = (0.78 + 0.56 + 0.42 + 0.45 + 0.46 + 0.47) / 6 = 0.515
3. Subtract the mean from each data point and square the result: (0.78 - 0.515)^2, (0.56 - 0.515)^2, (0.42 - 0.515)^2, (0.45 - 0.515)^2, (0.46 - 0.515)^2, (0.47 - 0.515)^2
4. Calculate the sum of the squared differences: sum = (0.78 - 0.515)^2 + (0.56 - 0.515)^2 + (0.42 - 0.515)^2 + (0.45 - 0.515)^2 + (0.46 - 0.515)^2 + (0.47 - 0.515)^2
5. Divide the sum by (n-1) to find the sample variance: variance = sum / (6-1) = 0.022133
6. Take the square root of the variance to find the sample standard deviation: standard deviation = sqrt(variance) = sqrt(0.022133) = 0.1488

Answer 2

The standard deviation of a sample is 0.1343

Step-by-step explanation:

The mean of the sample is
`\bar x = 0.5233`

The standard deviation of a sample is given by:

`S =(1)/(n-1) \sum (x_(i)-\bar x)^2 = (1)/(6-1)[(0.78 - 0.5233)^2 + (0.56 - 0.5233)^2 + (0.42 - 0.5233)^2 + (0.45 - 0.5233)^2 + (0.46 - 0.5233)^2 + (0.47 - 0.5233)^2] = (1)/(5)[0.6715] = 0.1343`