Question

Using the program "R", how do you find Q1, Q3, and IQR when given only mean and standard deviation of a normally distributed data set?

Example:

Find Q1, Q3, and IQR of this normally distributed data set: (mean=80,sd=6). Use "R" to calculate your answers.

Thank you so much!

Answer 1

Solution:-

Mean = 80, S.D = 6

a) Q₁ = 75.956

p-value for the first quartile = 0.25

z-score for the p-value = -0.674

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

x = 75.956

b) Q3 = 84.044

p-value for the third quartile = 0.75

z-score for the p-value = 0.674

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

x = 84.044

c) IQR = 8.088

IQR = Q3 - Q1

IQR = 84.044 - 75.956

IQR = 8.088