# STA 2023 Lecture Notes - Lecture 10: Interquartile Range, Unimodality, Standard Deviation

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Distribution

The distribution of a quantitative variable slices up all the possible values of the variable into

equal width bins and gives the number of values falling into each bin

Histogram

A histogram uses adjacent bars to show the distribution of a quantitative variable. Each bar

represents the frequency of values falling in.

Gap

A region of the distribution where there are no values

Stem-and-leaf display

A Stem and leaf display shows quantitative data values in a way that sketches the distribution of

the data

Dotplot

a dot plot graphs a dot for each case against a single axis

Shape

To describe a distribution look for:

-single v. multiple modes

-symmetry v. skewness

-outliers and gaps

Center

The measures of center are mean and median

Spread

A numerical summary of how tightly the values are clustered around the center. Measures of

spread include the IQR and standard deviation.

Mode

A hump or local high point in the shape of a distribution of a variable. The apparent location of

modes can change as the scale of a histogram is changed.

Unimodal (Bimodal)

Having one mode.

Bi: two modes

Multi: many modes

Uniform

A distribution that is roughly flat is said to be uniform.

Symmetric

A distribution is symmetric if the two halves on either side of the center look approximately like

mirror images of each other.

Tails

The tails of a distribution are the parts that typically trail off on either side.

Skewed

A distribution is skewed if it's not symmetric and one tail stretches out farther than the other.

Skewed left and right.

Outliers

Outliers are extreme values that don't appear to belong with the rest of the data.

Median

The median is the middle value, with half of the data above it and half below it. If n is even, it is

the average of the two middle values. It is usually paired with IQR.

Range

The difference between the lowest and highest values in a data set.

Quartile

The lower quartile is the value with a quarter of the data below it. The upper quartile is the value

with 3/4 of the data below it.

Interquartile Range

IQR. The difference between Q1 and Q2

5-number Summary

min

Q1

median

Q3

Max

Boxplot

A box plot displays the 5-number summary as a central box.

Mean

Mean is found by summing all the data points and dividing by the count