Why is there 16% of the data above z = 1?
VISUAL ANSWER: If you start this video I have in a previous Course FAQ post (https://www.youtube.com/watch?v=Dh5sBdlVPaA&feature=youtu.be) at 3 minutes and 21 seconds, you will see me explain why it is 16% while drawing out the normal curve.
OTHER ANSWERS: I have the explanation also in words on the Measures of Spread Google Doc in Module 3, right below my comment about 16% of the data is above. I will expand on that in two ways below to help with this idea.
1st way:
- There is 100% for total area under the curve.
–> If 68% lies within ± 1 standard deviations, then 32% is left over. (100 – 68 = 32.)
- 32% is left over then below -1 and above 1.
–> The normal curve is symmetrical so if there is a total of 32% left over in these two tail ends of the curve, we would have 16% in each tail. (32 / 2 = 16.)
Let’s check to make sure we have a total of 100% for the curve:
- All the way at the left end to z = -1 (16%)
- 68% lies within ± 1 standard deviations // From -1 to 0 (34%) From 0 to 1 (34%)
- Above z = 1 (16%)
——————————–
Another way to think about it:
- 68 % of the data is from z = -1 to z = 1
- 34% from -1 to 0 and 34 % from 0 to 1 (since the standard normal curve is symmetrical)
We want ABOVE z = 1.
- We know that half the curve on the left will have 50% of the data and
- We know that half the curve on the right will have 50% of the data.
Looking JUST at the right side of the curve from z = 0 to the right end:
- from z = 0 to z = 1 (34%)
- from 0 to the right end aka half the curve (50%)