For an assignment, I am required to find the value of a piece of data in the 70th percentile using mean and standard deviation.
Here is my organized data in ascending order:
0, 1, -4, 0, -3, 0, -4, -2, 0, 1, -1, 2, 0, -4, 5, -2, 0, 3, -3, 0.
The image link attached below called
'Percentiles With Normal Distribution' is the work I have done to find the value. (For some reason I can`t seem to upload the actual image here...)
Just in case you cannot access the image, I will explain what I did.
I created the normal distribution graph and shaded approximately 70% of it, leaving a little part on the right side empty.
I am finding b, where P(X > b) = p, where p = 0.7. I reversed this and it is now
P(X > b) = 1 - p (where p = 0.7).This means to find the (1-p)Th percentile for X.
Next, I found the corresponding percentile for Z by looking in the body of the Z-Score Table, and finding the probability that is closest to p = 0.7, to which I did this:
(1-0.7) = 0.3 so the closest value to this is 0.3015, which falls under row = -0.5 and column = 0.02.This means the
70th percentile for Z is equal to -0.52.
Lastly, I just changed the Z-Score value back into an x-value (original units).
x = Mean + Z(Standard Deviation).I substiuted my mean value of -0.55, Z-Score value of -0.52, and standard deviation of 2.4 and solved for x.
x = -2.
Now, if you look at the organized data set I provided above, you
d see that there are two -2s. This is confusing me because I`m not sure whether there can be two numerical values to represent the value of a certain percentile.