Question

A marine biologist collects data on the length of rainbow trout on a protected western river. She finds that the length of adult trout in her study are approximately normally distributed with mean 14 inches. She also reports that the minimum length was 10 inches and the maximum was 18 inches. Based on this information what is the most likely value of the standard deviation?

Answer 1

The standard deviation of the data is 2 inches.

Explanation:

We are given the following information in the question:

Mean, μ = 14

We are given that the distribution of length of adult trout is a bell shaped distribution that is a normal distribution.

Minimum length = 10 inches

Maximum length = 18 inches

Range

= Maximum length - Minimum length = 18 - 10 = 8

Thumb Rule of Standard Deviation:

• The Range Rule of Thumb says that the range is about four times the standard deviation.
• 
  `\text{Range} = 4* \text{Standard Deviation}`
• The standard deviation tells us how data is clustered around the mean.

Thus, by thumb rule, we get,

`\text{Standard Deviation} = \displaystyle\frac{\text{Range}}{4} = (8)/(4) = 2`

Thus, the standard deviation of the data is 2 inches.