What are the abbreviations for standard deviation?
Population standard deviation symbolized as ?; sample standard deviation symbolized as s.
How should you think of the standard deviation?
The average dispersion of scores around a mean, as opposed to just the distance between the 2 most extreme scores. This gives us a better glimpse of what is going on within a distribution as opposed to just the range. The standard deviation is sensitive t
What is another way to think of standard deviation?
As a distance measure in the normal distribution.
Does sigma alone = sigma with lower case x?
Yes, it's assume that it means the standard deviation of individual scores.
What does the height of the curve represent?
The frequency or number of people or items corresponding to values or scores along the x-axis.
What is a normal curve or normal distribution?
It is a theoretical distribution with data that are symmetrically distributed around the mean.
What are some of the properties of the normal curve?
Symmetrical - Unimodal -
The mode, median, and mean are the same.
Bell-shaped.
The mean can be any positive or negative number
The SD can be any positive value.
The total area under the curve equals 1 or 100%.
Asymptotic
Are all distribution curves normal?
No, non-normal distributions do exist (e.g. J-shaped, + or - skewed, rectangular).
Can variables that are normally distributed in one context may not be normally distributed in another, such as a special group.
Yes, think of IQ in general population v. a MENSA group.
What does asymptotic mean?
Although the theoretical curve descends down, the tails never touch the x axis.
What is considered normal in the normal distribution?
All data within 2 SD of the mean, or 95%.
The standard normal curve is based on what?
The z distribution.
Why is the SD sensitive to each score?
The standard deviation is sensitive to every single score because it is based on the mean.
Is the value of the SD affected by the value of each score in a distribution?
Yes, because we are using deviation scores from every single value in the distribution so it is sensitive to every score in the distribution.
Can the standard deviation ever be negative?
No, since we square all deviation scores, we lose the negative.
What scales of measurement is it used for?
Interval and ratio, but not nominal and ordinal.
Calculate, in a normal distribution, with the mean of 100, and an individual score of 130, and the standard deviation of 15, what proportion or percentage would fall below that score?
Take the mean, add 2 SD (2 x 15) to arrive at a score of 130, and that would put 95% of the people would fall below it.
What are the SD's for 1, 2, and 3, SD in a normal curve?
68% for 1, 95% for 2, and 97.5 for 3. Or from mean going out, 34% for 1, 13.5% more to get to 2, and 2% to get to 3, and .5% to get to 4.