Normal Distibution Curve and Z scores Flashcards
Standard deviation is a measure of _____
spread
Spread gives us an idea of _____
Variation e.g. are people at extremes or scoring very similarly?
In a normally distributed curve, the peak of distribution is the same value as the ______, _______ and ______.
mean, median, mode
In a normal distribution curve what do the numbers along the bottom represent?
They represent how many standard deviations away from the mean that point is (rather than measurement units.
The further away from the mean you go…..
The fewer people there are
Name the 2 properties of the normal distribution curve.
Symmetrical
Perfect (irl it’s messier!)
How many scores are between 0 and -1 SD?
34.13%
What is a z score?
A z score is how many SDs someone is away from the mean.
__ SD away from the mean is quite a common score, however __ SDs away from the mean is quite unusual.
1
2
What percent of scores lie beyond +2 SD?
2.28%
What percent of scores lie within 1.96 SD ( between -1.96 and +1.96) of the mean?
95%
On the z score table what does A stand for?
the z score
On the z score table what does B stand for?
the area between the mean and the Z score.
On the z score table what does C stand for?
the area beyond Z.
If the area between the mean and the Z score is 9.10 what does this mean?
9.10% of the scores are between the mean and the z score.
If the area beyond Z is 40.90 what does this mean?
40.90% of the scores are higher than the z score.
On the z score table why are there only positive values?
because the graph is symmetrical so it’s the same either way :)
How do you calculate a Z score?
z = (score-mean) / SD
Calculate the Z score:
Mean is 150
SD is 15
James’ Score is 128
(score - mean)/SD
128-150/ 15 = -1.47
What does a negative z score mean?
It means it is below the mean instead of above.
James’ Z score is -1.47. The area beyond Z is 07.08, what does this mean?
This means that 7.08% of people scores lower than James’ score.
James’ Z score is -1.47.
The area between mean and Z = 42.92.
What percentage of people scored above James?
42.92 + 50 = 92.92% scored above poor james :(
What can you use z scores to do which is quite useful?
You can use z scores to compare scores that cannot be directly compared i.e. if they are on different scales.
What is the magic number for z scores?
1.96!
95% of all scores within 1.96 DS of mean (between -1.96 and +1.96
A _____ expresses how far a score is from the mean, in terms of standard deviations.
Z score
What does a positive Z score mean?
It is above the mean
What does a negative Z score mean?
It is below the mean.
Using Z scores what 2 things can we do?
- we can find out what percentage of people scores above or below and individual’s score.
- we can compare scores on different measures.
