# The Interquartile Range (IQR) for a set of normally distributed data with mean µ = 80 is 12. What is the approximate value of σ ?

##### 1 Answer

Dec 28, 2014

IQR holds 50% of the data. So in your case between 74 and 86.

A difference of 6, 25% off-mean

Between

So

Since the bell curve is already reasonably steep at the 25%-off points, I would - without calculating - estimate

**Calculator:**

If you own a TI-84 or something like that, you can set up two functions:

Y1= normalcdf(74,86,80,X) -- (left, right, mean, unknown std)

Y2=0.50 -- fraction of data in this part (50%)

And then use Intersect. The X-value will be

**Tip:**

*Always* make a sketch of the curve and draw in the things that you know. This helps to visualise the problem.