The standard deviation of the distribution is 8.06
Concept:
Inter Quartile Range:-
The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.
Standard deviation
A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out
Given,
The Inter Quartile Range of a normal distribution, IQR = 10.8
Standard deviation of the distribution, σ = [tex]\frac{IQR}{1.34}[/tex]
∴ σ = [tex]\frac{10.8}{1.34} = 8.06[/tex]
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