Question

What is the standard deviation of the following: 31, 49, 44, 26, 33, 31?

Answer 1

To calculate the standard deviation of the data set (31, 49, 44, 26, 33, 31), we find the mean, calculate the squared differences, compute the variance, and then take the square root of the variance to get the standard deviation, which is approximately 8.07.

Step-by-step explanation:

To calculate the standard deviation of the data set 31, 49, 44, 26, 33, 31, we would follow these steps:

1. First, calculate the mean (average) of the numbers.
2. Next, for each number, subtract the mean and square the result to find the squared differences.
3. Then, find the average of these squared differences, which is the variance.
4. Finally, take the square root of the variance, which gives us the standard deviation.

Let's go through these steps:

1. Mean: (31+49+44+26+33+31) / 6 = 214 / 6 = 35.67 (rounded to two decimal places)
2. Squared differences:
   
3. Variance: (21.89 + 177.11 + 69.57 + 93.07 + 7.11 + 21.89) / 6 = 390.64 / 6 = 65.11 (rounded to two decimal places)
4. Standard deviation: √65.11 = 8.07 (rounded to two decimal places)

The standard deviation of the given data set is approximately 8.07.