Exploratory Data Analysis 2.1-2.2

Measures of Location

• used if it is of interest to measure other parts of the distribution of data other than its center

• numerical measures that give the relative position of a data value to the entire data set

Quantiles or Fractiles

Partition of data into groups with roughly the same number

of values

MEASURES OF VARIABILITY/ DISPERSION

—indicates how observations in a data set are scattered about an average

Measures of Central Tendency

- Value at the center or at the middle of a data set

- Value where the data tend to cluster

- Also called average

MEAN

The arithmetic average obtained by adding up all the data values and dividing by the total number of observations.

MEDIAN

The value that divides the distribution into two equal parts, so that half of the cases are above it and half below it.

MODE

The value(quantitative) or category(qualitative) with the largest frequency (or percentage) in the distribution.

RANGE

–measures how far the highest value is from the lowest value

VARIANCE

the average squared difference of the observations from the mean

STANDARD DEVIATION

- the average deviation between the individual scores in the distribution and the mean for the distribution; square root of the variance

COEFFICIENT OF VARIATION

a measure that indicates the magnitude of variation relative to the magnitude of the mean

STANDARD ERROR of the MEAN

– a measure of statistical accuracy of an estimate

– indication of reliability of the mean

Chebyshev’s Theorem

enables us to make statements about the proportions of data values that must be within a specified number of standard deviations of the mean

Skewness

Measures of __________ help us to know to what degree and in which direction (positive or negative) the frequency distribution has a departure from symmetry.

Normal (Symmetric Distribution)

Symmetric meaning the left side

is just the mirror image of the

right side

Positively Skewed (Skewed to the right)

Distribution tapers more to the right than to the left

Negatively Skewed (Skewed to the left)

Distribution tapers more to the left than

to the right

Dover (1979)

________________ suggests the use of rule of thumb to determine the magnitude of asymmetry or skewness:

Stem and Leaf Plot

- A way to organize data

- It sorts data quickly

- Gives an overview of the spread of the data

- Able to tell minimum value, maximum value and range in a

glance.

Boxplot

• graph that is very useful for displaying the following features

of data:

▪ Location

▪ Spread

▪ Symmetry

▪ extremes/outliers

Histogram (etymology)

comes from the Greek histos, meaning pole or mast, and gram, which means chart or graph.

histogram

• It is a graphical display of data using bars of

different heights.

• It is used to display the distribution of data values along the

real number line

• It is created by dividing up the range of the data into a small

number of intervals or bins.

• The number of observations falling in each interval is counted.

This gives a frequency distribution.

Scatterplot

- shows the relationship between two sets of data

- The data is plotted on the graph as "Cartesian (x,y) Coordinates”