How do you calculate the standard deviation for the following set of numbers: 73, 76, 79, 82, 84, 84, 97?

To calculate the standard deviation of the numbers 73, 76, 79, 82, 84, 84, and 97, follow these steps:

1. Find the mean: Add all the numbers together and divide by the total count.
   Mean = (73 + 76 + 79 + 82 + 84 + 84 + 97) / 7 = 80.71 (approximately).
2. Calculate the squared differences: Subtract the mean from each number and square the result:
   – (73 – 80.71)² = 59.71
   – (76 – 80.71)² = 22.53
   – (79 – 80.71)² = 2.92
   – (82 – 80.71)² = 1.66
   – (84 – 80.71)² = 10.92
   – (84 – 80.71)² = 10.92
   – (97 – 80.71)² = 261.42
3. Calculate the variance: Find the average of these squared differences.
   Variance = (59.71 + 22.53 + 2.92 + 1.66 + 10.92 + 10.92 + 261.42) / 7 = 50.48 (approximately).
4. Calculate the standard deviation: Take the square root of the variance.
   Standard Deviation = √50.48 = 7.1 (approximately).

Therefore, the standard deviation for the given set of numbers is approximately 7.1.