What is the standard deviation of the following 12 numbers: 41, 56, 38, 61.5, 49, 59, 32, 67.5, 60, 52, 47, 44?

To find the standard deviation of the given 12 numbers, the process involves several steps. First, calculate the mean (average) of the numbers, then determine the squared differences from the mean for each data point. Finally, calculate the average of those squared differences and take the square root of that average to obtain the standard deviation.

1. Calculate the mean (μ):

The mean is calculated by summing all the numbers and dividing by the total count.

• Sum = 41 + 56 + 38 + 61.5 + 49 + 59 + 32 + 67.5 + 60 + 52 + 47 + 44 = 532

• Mean (μ) = 532 / 12 = 44.33 (approximately)

2. Calculate the squared differences from the mean:

For each number, subtract the mean and then square the result:

• (41 - 49.44)²

• (56 - 49.44)²

• (38 - 49.44)²

• (61.5 - 49.44)²

• (49 - 49.44)²