# Can I have high variance and correlation at the same time?

I am a newbie in stats who is self-studying bivariate normal. I am trying to understand how variance and correlation are interpreted graphically.

But I am puzzled by the next question: if I have two variables $$x_1$$ and $$x_2$$ each of them has high variance, can I have high correlation as well?

I cannot picture them in my head since, with high variance, I see them as 2 uniforms and can't imagine them having a high correlation.

• 1) Please include the self-study tag. 2) Think about measurements that you can understand as having high correlation. Let's say that you've made these measurements in meters. Now convert the measurements to centimeters. The numbers are much larger, meaning that the variances are much larger (exercise: how much larger?), yet the graph better still look the same. – Dave Nov 18 '19 at 1:48