Calculating the Standard Deviation:

To calculate the standard deviation of a series of measurements, we need to follow a few steps. Let's break down the process:

Step 1: Calculate the mean
Step 2: Calculate the deviation from the mean for each measurement
Step 3: Square each deviation
Step 4: Calculate the sum of squared deviations
Step 5: Divide the sum of squared deviations by the total number of measurements
Step 6: Take the square root of the result from step 5

Step 1: Calculate the mean:
To calculate the mean, we need to find the average of the measurements. We can do this by multiplying each measurement by its corresponding frequency, summing up the results, and dividing by the total frequency.

Mean = (0*1 + 10*3 + 20*4 + 30*2) / (1 + 3 + 4 + 2) = 140 / 10 = 14

Step 2: Calculate the deviation from the mean for each measurement:
To calculate the deviation from the mean for each measurement, we subtract the mean from each measurement.

Deviation from mean = Measurement - Mean

For the given series, the deviations from the mean are:
-10, -4, 6, 16, -4, 6, 16, -4, 6, -4

Step 3: Square each deviation:
To square each deviation, we multiply each deviation by itself.

Squared deviations = (-10)^2, (-4)^2, 6^2, 16^2, (-4)^2, 6^2, 16^2, (-4)^2, 6^2, (-4)^2

Squared deviations = 100, 16, 36, 256, 16, 36, 256, 16, 36, 16

Step 4: Calculate the sum of squared deviations:
To calculate the sum of squared deviations, we add up all the squared deviations.

Sum of squared deviations = 100 + 16 + 36 + 256 + 16 + 36 + 256 + 16 + 36 + 16 = 872

Step 5: Divide the sum of squared deviations by the total number of measurements:
To calculate the variance, we divide the sum of squared deviations by the total number of measurements.

Variance = Sum of squared deviations / Total number of measurements

Variance = 872 / 10 = 87.2

Step 6: Take the square root of the result from step 5:
The standard deviation is the square root of the variance.

Standard deviation = √(Variance) = √(87.2) ≈ 9.347

Conclusion:
The standard deviation of the given series of measurements is approximately 9.347.