Question

a series of measurements gave values of 11, 11, 11, 11, 12, 13, 13, 14, for which the arithmetic mean is 12. the population standard deviation is most nearly:

Answer 1

The population standard deviation for the given data set is calculated by finding the average of the squared differences from the mean, dividing by the number of measurements, and taking the square root. This results in a population standard deviation of approximately 1.118.

Step-by-step explanation:

To calculate the population standard deviation, we first need to find the variance. The variance is the average of the squared differences from the mean. Given the data set (11, 11, 11, 11, 12, 13, 13, 14) and the arithmetic mean (12), we perform the following steps:

• Subtract the mean from each measurement and square the result.
• Sum all the squared results.
• Since we are dealing with a population, divide by the number of measurements (N).
• Take the square root of the result to obtain the standard deviation.

Here's the calculation:

1. (11-12)^2 + (11-12)^2 + (11-12)^2 + (11-12)^2 + (12-12)^2 + (13-12)^2 + (13-12)^2 + (14-12)^2
2. 1 + 1 + 1 + 1 + 0 + 1 + 1 + 4 = 10
3. Divide by N, which is 8: 10/8 = 1.25
4. Square root of 1.25 is approximately 1.118.

The population standard deviation is most nearly 1.118.