askvity

How to Find the Relative Deviation?

Published in Statistics 2 mins read

The relative deviation, also known as the relative standard deviation (RSD) or coefficient of variation (CV), is found by dividing the standard deviation by the mean (average) and then multiplying by 100 to express it as a percentage.

Here's a breakdown of how to calculate it:

1. Calculate the Mean (Average):

  • Sum all the values in your dataset.

  • Divide the sum by the total number of values.

    Mean (x̄) = (Sum of all values) / (Number of values)

2. Calculate the Standard Deviation:

  • For a sample standard deviation (s):

    • Subtract the mean (x̄) from each value (xi) and square the result: (xi - x̄)2.
    • Sum all the squared differences.
    • Divide the sum by (n-1), where 'n' is the number of values in the sample. This gives you the variance (s2).
    • Take the square root of the variance to get the sample standard deviation (s).

  • For a population standard deviation (σ):

    • Subtract the mean (μ) from each value (xi) and square the result: (xi - μ)2.
    • Sum all the squared differences.
    • Divide the sum by N, where 'N' is the number of values in the population. This gives you the variance (σ2).
    • Take the square root of the variance to get the population standard deviation (σ).

3. Calculate the Relative Standard Deviation (RSD):

  • Divide the standard deviation (s or σ) by the mean (x̄ or μ).

  • Multiply the result by 100 to express it as a percentage.

    RSD = (Standard Deviation / Mean) * 100

Formula:

RSD = (s / x̄) 100 (for sample data)
or
RSD = (σ / μ) 100 (for population data)

Example:

Let's say you have the following dataset: 2, 4, 6, 8, 10

  1. Mean: (2 + 4 + 6 + 8 + 10) / 5 = 6
  2. Sample Standard Deviation (s): (Calculated using the steps above, you'll find s ≈ 3.16)
  3. Relative Standard Deviation (RSD): (3.16 / 6) * 100 ≈ 52.67%

Interpretation:

The RSD indicates the precision of your data. A lower RSD suggests higher precision (less variability relative to the average), while a higher RSD indicates lower precision (more variability relative to the average). The RSD is useful for comparing the variability of datasets with different means or different units.

Related Articles