Quantitative Methods - Quiz 2: Measures of Dispersion and Distributions

Distribution

how the data is spread-out over all possibilities

Symmetry

when a distribution mirrors its left and right half

Skewness

How data is more heavily concentrated to one side, and not symmetrical

Variation

How widely the data of a data set are spread out around the center

Symmetry & the Mean/Median

In a perfectly symmetrical distribution, the mean and median are the same

Left Skewed

distribution is pulled and ‘chopped off’ on the left

Left skewness means the mean < median < mode

Right Skewed

distribution is pulled and ‘chopped off’ to the right

Right skewness means the mean > median > mode

Uniform Distribution

Has no mode because all data values have the same frequency

Single peaked or Unimodal

Shows a distribution with a single peak

Bimodal, Trimodal, etc

Shows a distribution with 2 peaks (top) and three peaks (bottom)

Standard deviation

number that measures how far away data values are from their mean

It provides:

•Numerical measure of the overall amount of variation in a dataset

•Use to determine whether data value is close to or far from mean

• The sdev will always be positive or zero

• The closer it is to 0, the more concentrated it is to the mean (closer to 0 = less variation)

Interpreting sdev.

• Positive deviation – data value is greater than the mean

• Negative deviation – data value is less than the mean

• The sdev measures the spread in the same units as the data

Describing Distributions

Concept	Importance
Symmetry	Shows whether data are balanced; Mean ≈ Median
Variation	Shows how spread out the data are
Skewness	Shows whether data are pulled toward high or low values
Describing Distributions	Focus on shape, centre, spread, and outliers
Standard Deviation (SD)	Measures typical distance from the mean
Grouped-Frequency SD	Estimates spread using class midpoints