Question

what will be probable value of mean deviation when q3 call to 40 q1 equal to 15​

Answer 1

"For this question, you would have to make an assumption about the distribution. With no information about the distribution, I will make an assumption of the normal distribution, because certain distributions can be approximated by the normal distribution. However, you would need to verify your distribution is bell shaped to use this assumption.

With that assumption, the mean will be the average of the first and third quartiles, so we have a mean of 27.5 Now we just have to find the standard deviation. I can use the first quartile to find that.

P(X≤15)=0.25P(X≤15)=0.25

P(X−μσ≤15−27.5σ)=0.25P(X−μσ≤15−27.5σ)=0.25

P(Z≤−12.5σ)=0.25P(Z≤−12.5σ)=0.25

We can use the inverse normal CDF function to determine what z-score is actually associated with that probability.

P(Z≤−0.67449)≈0.25P(Z≤−0.67449)≈0.25

Comparing that to the previous expression, the only thing that is different is the expression for the z-score, so we can equate those since everything else is equal.

−12.5σ≈−0.67449−12.5σ≈−0.67449

σ≈18.5325σ≈18.5325

Now by mean deviation I assume you mean mean absolute deviation. I will derive a generic formula so it can be re-used. Deviations don’t depend on the mean, so I will use a mean of 0.

∫∞−∞|x|⋅12πσ2−−−−√e−x22σ2"