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Frequency Distribution
A table in which all of the scores are listed along with the frequency with which each occurs.
Class interval frequency distribution
A table in which the scores are grouped into intervals and listed along with the frequency of scores in each interal.
Qualitative Variable
A categorical variable for which each value represents a discrete category.
Bar Graph
A graphical representation of a frequency distribution in which vertical bars are centered above each category along the x-axis and are separated from each other by a space, indicating that the levels of the variable represent distinct, unrelated categories.
Quantitative Variable
A variable for which the scores represent a change in quantity.
Histogram
A graphical representation of a frequency distribution in which vertical bars centered above scores on the x-axis touch each other to indicate that the scores on the variable represent related, increasing values.
Frequency Polygon
A line graph of the frequencies of individual scores.
Descriptive Statistics
Numerical measures that describe a distribution by providing information on the central tendency of the distribution, the width of the distribution, and the shape of the distribution.
Measure of central tendency
A number that characterizes the "middleness" of an entire distribution.
Mean
A measure of central tendency: the arithmetic average of a distribution. It can be used with ratio and interval data. It cannot be used with nominal or ordinal data.

Mean for population:

μ = ΣX / N

where X is individual scores and N is the total number of scores in the distribution.

Mean for a sample:
_
X = ΣX / N
Median
A measure of central tendency; the middle score in a distribution after the scores have been arranged from highest to lowest or from lowest to highest. It can be used with ratio and interval data. It cannot be used with nominal data. It can be used with most ordinal data.
Mode
A measure of central tendency; the score in a distribution taht occurs with the greatest frequency. It is the only indicator of central tendency that can be used with nominal data.
Measure of Variation
A number that indicates the degree to which scores are either clustered or spread out in a distribution.
range
A measure of variation; the difference between the lowest and the highest scores in a distribution.
Standard Deviation
A measure of variation; the average difference between the scores in the distribution and the mean or the central point of the distribution, or more precisely, the square root of the average squared deviation from the mean.

Standard Deviation for a population:

σ =√[ ∑(x - μ)² ÷ N ]

Standard Deviation for Sample:
_
S =√[ ∑(x - X)² ÷ N ]

If using sample data to estimate population:

s =√[ ∑(x - X)² ÷ (N-1) ]

Dividing by N-1 helps make up for the chance of having a sample with little variability. This is called the unbiased estimator.

The standard deviation is a measure of how spread out your data are. Computation of the standard deviation is a bit tedious. The steps are:
  1. Compute the mean for the data set.
  2. Compute the deviation by subtracting the mean from each value.
  3. Square each individual deviation.
  4. Add up the squared deviations.
  5. Divide by one less than the sample size.
  6. Take the square root.

unbiased estimator
If using sample data to estimate population:

s =√[ ∑(x - X)² ÷ (N-1) ]

Dividing by N-1 helps make up for the chance of having a sample with little variability. This is called the unbiased estimator.
Average Deviation
An alternative measure of variation, that, like the standard deviation, indicates the average difference between the scores in a distribution and the mean of the distribution.

AD = ∑|x - μ| ÷ N
Variance
The Standard Deviation squared. The variance for a population is σ², for a sample is  S², and for the unbiased estimator of the population is s².
Normal Curve
A symmetrical, bell-shaped frequency polygon representing a normal distribution.
Normal Distribution
A theoretical frequency distribution that has certain special characteristics. 1) Bell-shaped and symmetrical 2) the mean, median, and mode are equal and are located at the center of the distribution 3) unimodal 4) most of the observations are clustered around the center of the distribution.
Kurtosis
How flat or peaked a normal distribution is.
mesokurtic
Normal curves that have peaks of medium height and distributions that are moderate in breadth.
leptokurtic
Normal curves that are tall and thin, with only a few scores in the middle of the distribution having a high frequency.
platykurtic
Normal curves that are short and more dispersed (broader).
positively skewed distribution
A distribution in which the peak is to the left of the the center point, and the tail extends toward the right, or in the positive direction.
negatively skewed distribution
A distribution in which the peak is to the right of the center point and the tail extends toward the left, or in the negative direction.
z-score (standard score)
A number that indicates how many standard deviation units a raw score is from the mean of a distribution. Think of z-score as a translation of raw scores into scores of the same language for comparative purposes.

When calculating an individual z-score in comparison to sample:
_
z= (X-X ) ÷ S

When calculating an individual z-score in comparison to a population:

z = (X - μ) ÷ σ
Standard Normal Distribution
A normal distribution with a mean of 0 and a standard deviation of 1.
Probability
The expected relative frequency of a particular outcome.
Percentile Rank
A score that indicates the percentage of people who scored at or below a give raw score.
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