Answer:
Step-by-step explanation:
We can calculate the standard deviation of a set of data using the formula:
σ = sqrt[Σ(xi - μ)² / N]
Where:
- σ is the standard deviation
- Σ is the sum of the values
- xi is each individual value
- μ is the mean (average) of the values
- N is the total number of values
First, we need to calculate the mean of the data set:
Mean = (11.36 + 11.37 + 11.49 + 11.38 + 11.39) / 5 = 11.398
Next, we can calculate the range of the data by subtracting the smallest value from the largest value:
Range = 11.49 - 11.36 = 0.13
To estimate the standard deviation using the range, we can use the following formula:
σ ≈ Range / 4
σ ≈ 0.13 / 4 = 0.0325
Alternatively, we can use the square root of the number of measurements averaged to estimate the standard deviation. Since we have 5 measurements in this data set, we can use the following formula:
σ ≈ Range / sqrt(N)
σ ≈ 0.13 / sqrt(5) = 0.058
Therefore, the estimated standard deviation of this data set is approximately 0.0325 using the range of the data and 0.058 using the square root of the number of measurements averaged.