Final answer:
The approximate standard deviation of the set of numbers 10, 20, 12, 14, 12, 27, 88, 2, 7, and 30 is calculated to be around 24.7.
Step-by-step explanation:
To find the approximate standard deviation for the given set of numbers: 10, 20, 12, 14, 12, 27, 88, 2, 7, and 30, we'll follow these steps:
- Calculate the mean of the data set.
- Subtract the mean from each data point and square the result.
- Find the average of these squared differences.
- Take the square root of this average to get the standard deviation.
Let's calculate:
Mean (μ) = (10 + 20 + 12 + 14 + 12 + 27 + 88 + 2 + 7 + 30) / 10 = 222 / 10 = 22.2
Next, we calculate the squared differences from the mean:
(10 - 22.2)^2 = 148.84, (20 - 22.2)^2 = 4.84, (12 - 22.2)^2 = 104.04, (14 - 22.2)^2 = 67.24, (12 - 22.2)^2 = 104.04, (27 - 22.2)^2 = 23.04, (88 - 22.2)^2 = 4339.24, (2 - 22.2)^2 = 408.04, (7 - 22.2)^2 = 230.04, (30 - 22.2)^2 = 60.84.
The sum of these squared differences is 5489.20. Since we're looking for a sample standard deviation and not the population standard deviation, we divide by N-1 (which is 10 - 1 = 9):
Variance (σ^2) = 5489.20 / 9 ≈ 609.9111
Finally, take the square root to find the standard deviation:
Standard deviation (σ) = √609.9111 ≈ 24.7
Therefore, the approximate standard deviation of the data set is 24.7.