Final answer:
The standard deviation calculation involves finding the mean of the data set, subtracting the mean from each data point, squaring those values, averaging them, and then taking the square root of this average. Option 4 is the correct nearest answer.
Step-by-step explanation:
To calculate the standard deviation of the given data set (29, 7, 8, 30, 15), we first need to find the mean of the data. The mean (μ) is the sum of all data values divided by the number of values. Once the mean is calculated, we subtract the mean from each data value and square the result. We then find the average of these squares, which is the variance. The standard deviation is the square root of the variance.
- Find the mean of the data set: (29 + 7 + 8 + 30 + 15) / 5 = 89 / 5 = 17.8
- Subtract the mean from each data point and square the result: (29 - 17.8)², (7 - 17.8)², (8 - 17.8)², (30 - 17.8)², (15 - 17.8)²
- Calculate the sum of these squares and divide by the number of data points minus one (n - 1) for a sample standard deviation: Σ(x - μ)² / (n - 1)
- Take the square root of this result to find the standard deviation
Calculations must be done to find the final standard deviation value, rounded to the nearest tenth. The correct option will include this calculated value.