[CIT] Measures of Central Tendency, Variability, T-Test and Correlation Analysis

Central Tendency

• A useful way to describe a group as a whole is to find a single number that represents what is average or typical of that data set. 

• It is called _______ because it is located toward the middle or center of a distribution where most of the data tends to be concentrated.

Mode

• The most frequently occurring or repetitive value in an array or range of data.

• It can easily be found by inspection rather than by computation.

Median

• The geographical center

• The middlemost point in a distribution.

• The measure of central tendency that cuts the distribution into two equal parts.

geographical

Median is the _________________ center in a distribution.

Mean

• The mathematical center.

• The sum of the value of each observation in a dataset divided by the number of observations. This is also known as the arithmetic average

Mean

• This measure of central tendency cannot be calculated for categorical data, as the values cannot be summed.

• As this includes every value in the distribution, it is influenced by outliers and skewed distributions.

Mean

• This measure of central tendency can be used for both continuous and discrete numeric data.

Dispersion

the state of getting dispersed or spread.

Statistical Dispersion

• The extent to which numerical data is likely to vary about an average value.

• In other words, this helps to understand the distribution of the data.

Variability

• an index of how the scores are scattered around the center of distribution. i.e. to know how homogeneous or heterogeneous the data is.

• Also known as SPREAD, WIDTH OR DISPERSION.

Range

• The difference between the highest and lowest scores in a distribution. 

Deviation

• The distance of any given raw score from its mean.  Subtract the mean from any raw score.

Mean Deviation

Measure of variability that takes into account every score in a distribution (rather than only two score values), take the absolute deviation or distance of each score from the mean of distribution, add these deviations and then divide this sum by the number of scores.

Population Variance

• typically represented by a lower-case sigma squared, can only be truly calculated if you have observations for every member of your population, which is almost never the case. It's used more often by statisticians and using it should never be your first instinct. 

Sample Variance

typically represented by s², is what you should almost always use instead.

Variance

•  (S²)

• Like the equation for the mean, it looks more complicated than it is. Because it's a squared measurement, it's rarely reported and is instead more useful for statisticians.

• Standard deviation is calculated from this, and is generally a more understandable and useful measurement.

Standard Deviation

• Represented by “S”

• A measure of variability we obtain by summing the squared deviations from the mean, dividing by N and then taking the square root.

• Like variance, this can theoretically be calculated for both a population and a sample.

two middlemost values

When a dataset has an even number of values, the median is the mean of the ________ in a data set.