Statistics I, VL02

construction stem-and-leaf plot

1. Sort the data in ascending order and draw a vertical line

2. Group the data into classes of equal size, number of classes = 10*log(n)

3. To the left of the line, write down the first digit(s); these form the stem.

4. To the right of the line, write down the next rounded digit of each observation; these form the leaves.

construction histogram

1. Group the data into classes [c0, c1), [c1, c2), ... with class width d1 = c1 - c0, ...

2. Compute the relative frequencies of the classes f1, f2, ...

3. Draw rectangles with widths d1, d2, ... and heights f1/d1, f2/d2, ...

histogram: unimodal distribution

one peak

histogram: bimodal distribution

two peaks

histogram: multimodal distribution

more than one peak

histogram: symmetric distribution

left half is a mirror image of the right half

histogram: right-skewed distribution

long tail to the right

histogram: left-skewed distribution

long tail to the left

empirical cumulative distribution function (ecdf)

- gives the fraction of observation less than or equal to a particular value x

- N(x) = ∑ n(ai), F(x) = N(x)/n

The mode xmod ....

gives the value of X that occurs most often

median

- "middle value" of the data

- appropriate for ordinal scales, most common measure of location for ordinal variables

- resistant to outliers, frequently used for metric variables

arithmetic mean

average