Calculating the Standard Deviation of a Continuous Uniform Distribution: Step-by-Step Guide

Standard Deviation for continuous uniform distribution formula (be able to calculate given values)

The formula for calculating the standard deviation (σ) of a continuous uniform distribution is given by the following formula:

σ = (b – a) / √12

where:
– ‘a’ represents the lower limit of the distribution,
– ‘b’ represents the upper limit of the distribution

The formula for calculating the standard deviation (σ) of a continuous uniform distribution is given by the following formula:

σ = (b – a) / √12

where:
– ‘a’ represents the lower limit of the distribution,
– ‘b’ represents the upper limit of the distribution.

To calculate the standard deviation of a continuous uniform distribution using this formula, follow these steps:

1. Determine the values of ‘a’ and ‘b’ (the lower and upper limits of the distribution).

2. Calculate the difference between the upper and lower limits: (b – a).

3. Take the square root of 12 (√12).

4. Divide the difference obtained in step 2 by the square root of 12 obtained in step 3.

5. The result will be the standard deviation (σ) of the continuous uniform distribution.

Here’s an example to illustrate the calculation:

Suppose we have a continuous uniform distribution with a lower limit ‘a’ of 3 and an upper limit ‘b’ of 8. We want to calculate the standard deviation for this distribution.

Step 1: Determine the values of ‘a’ and ‘b’:
– a = 3 (lower limit)
– b = 8 (upper limit)

Step 2: Calculate the difference between the upper and lower limits:
– (b – a) = (8 – 3) = 5

Step 3: Take the square root of 12:
– √12 ≈ 3.4641

Step 4: Divide the difference obtained in step 2 by the square root of 12 obtained in step 3:
– σ = (b – a) / √12
– σ = 5 / 3.4641
– σ ≈ 1.4434

Therefore, the standard deviation (σ) for the given continuous uniform distribution with a lower limit of 3 and an upper limit of 8 is approximately 1.4434.

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