NORMAL DISTRIBUTION Flashcards
What measure of central tendency allow you to tell whether a score is above of below the average in that distribution?
The mean.
What measure of central tendency allow you to tell you how much above or below the average is in relation to the spread of scores in the distribution?
The standard deviation.
salary example:
- suppose the standard deviation of for salary/hr. at Company XYZ is 3
- the person with a salary of 26/hr. is 2 standard deviations above the mean - thus the person salary/hr. is above average
What is the Z score?
The number of standard deviations a specific score is above or below the mean. Its a way to standardize the data, making it on the same scale (in order to be able to compare two different types of measurements fairly - for example scores from two different tests)
It is not the same as the standard deviation (which is 3 for this example: suppose the standard deviation of for salary/hr. at Company XYZ is 3
- the person with a salary of 26/hr. is 2 standard deviations above the mean (Z SCORE)
Why is the raw score and z score considered two different ways to measure the same thing?
a) raw score is simply the ordinary score
b) z score designates how many standard deviations the corresponding raw score is above or below the mean
c) raw score (inches); z score (centimeters)
What is ALWAYS the mean and standard deviation of Z scores?
The mean if always 0 (because they cancel eachother out).
The standard deviation is always 1, as ……
What is the formulas for changing a raw score to a Z score (for both the mean of sample set of scores and mean of population set of scores?
Z= ( X- X barre en haut ) / s
Z = ( X - m )/ σ
What is the formula for changing a Z score to a raw score?
X = (Z)(s) + X avec barre en haut
X = (Z)(σ) + m
What would it mean to finish 1,5 standard deviation above the mean?
That you are better than the average.
if you’re within -1 and 1, what would it mean?
that you fit in with the average scores
What is an outlier? Which data values are considered to be outliers? What are three possibilities as to where these data values come from?
1) An unusually small or unusually large value in a data set.
2) A data value with a z-score less than -3 or greater than +3 might be considered an outlier
3)
* an incorrectly recorded data value
- a data value that was incorrectly included in the
data set - a correctly recorded data value that belongs in
the data set
What does “standardized values” refer to?
To normalized raw scores
What does “statistical inference” refer to?
Statistical inference is the process of using data from a sample to make generalizations or draw conclusions about a larger population. It’s a way of making educated guesses or predictions based on observed data.
What is the normal probability distribution?
The most important distribution for describing a continuous random variable.
While normal distributions can differ in size (mean, SD), they all follow the same basic principles, just like all circles are fundamentally the same despite varying in size.
What are the 7 characteristics of the normal probability distributions?
1) The distribution is symmetric; its skewness measure is zero (remember; positively skewed, negatively skewed distribution). The tails of the normal curve extend to infinity in both directions and theoretically never touch the horizontal axis. In mathematical jargon, the curve approaches the x-axis asymptotically (EXAM! meaning tails never touch the x axis, valeurs tendent vers l’infini.
- Even if you have all the values from a population, the curve of the normal distribution would still not touch the x-axis. This is because the normal distribution is a mathematical model that assumes an infinite population with a continuous range of possible values, even beyond what is observed in reality.
2) The entire family of normal probability distributions is defined by its mean μ and its
standard deviation σ. (think about it, a raw score would mean nothing without something reference in it to)
3) The highest point on the normal curve is at the mean, which is also the median and mode.
4) The mean can be any numerical value: negative, zero, or positive.
5) The standard deviation determines the width of the curve: larger values result in wider, flatter curves (raw score values sont plus dispersées)
6) Probabilities for the normal random variable are given by areas under the curve. The total area under the curve is 1 (.5 to the left of the mean and .5 to the right).
7) The empirical rule states that in a normal distribution, virtually all observed data will fall within three standard deviations of the mean.
68.26% of values of a normal random variable
are within +/- 1 standard deviation of its mean.
95.44%
are within +/- 2 standard deviations of its mean.
99.72%
are within +/- 3 standard deviations of its mean.
(you don’t have to memorize the numbers, we will have a table. If you want a visual example go look at diapo 27)
What is a standard normal probability distribution? What letter is used to designate the standard normal random variable?
A random variable having a normal distribution with a mean of 0 and a standard deviation of 1 is said to have a STANDARD normal probability distribution.
The letter z (sur l’axis des x) is used to designate the standard normal random variable.
What does the standard normal probability table represent?
- The probability that a normal random variable is within any specific interval. To find it, we must compute the area under the normal curve across this interval
When z=0, the probability of being either over or under the mean is?
0,5 = 50%
Is the area under the normal curve exact or an approximation?
An approximation.
“The shape of the normal curve is standard”. Meaning?
There is a known percentage above or below any particular point. C’est le standard/la norme
Example:
50 % of scores are on either side of the mean.
68% of the scores fall within 1 standard deviation of the mean. (34 above, 34 under)
What are the three types of probabilities we need to compute?
1) the probability that the standard normal random variable z will be less than or equal to a given value
2) the probability that the standard normal random variable z will be greater than or equal to a given value
3) the probability that the standard normal random variable z will be between two values
