1.2 Displaying Quantitative Data With Graphs

HISTOGRAMS

  • preferred ways of displaying a quantitative variable when the variable takes on a large range of values, or when the data set is large (100+)

  • takes the who span of values for the variable and splits the span up into evenly spaced intervals called bins

DOTPLOTS

  • a dotplot is a simple way to display numerical data when the data set is reasonably small

STEM-AND-LEAF DISPLAYS

  • a graphical display similar to histograms, but one in which the original set of data is preserved

    • suited for smaller sets of data

  • the stem is the first part of the number and the leaf is the last part of the number

  • ex. male weights

    • [9|7, 10|2, 11|7…)

    • 9, 10, 11… | 7, 2, 7

  • the numbers to the left of the line are the stems and the right is the leafs

  • must include a legend with units

  • leafs are usually single digits (no commas)

  • best if the leaves are in numerical order

  • back-to-back stemplots are useful for comparing distributions

  • when a data set is very compact, it is often useful to repeat stems to stretch the display to investigate the shape; called a split stemplot

  • when a data is is very spread out, it is often useful to truncate the data to shrink the display

DESCRIBING A DISTRIBUTION

  • important to discuss three main features whenever describing a distribution: shape, center, and spread

    • shape: is the distribution skewed left (negatively skewed), skewed right (positively skewed), symmetric, uniform, unimodal, bimodal

    • center: the value that divides the distribution in half

    • spread: the extent of the data from smallest value to largest value

    • unusual values

    • context: the variable you are measuring

  • recommended you use “fudge words”: approximately, somewhat, fairly

  • outliers: data values that fall out of the pattern of the rest of the distribution

  • clusters: isolated groups of values

  • gaps: large spaces between values

COMPARING DISTRIBUTIONS

  • when comparing two or more distributions, be sure to use explicit comparison phrases such as “higher than”, “similar to”, “approximately the same”, “less than”, etc.

  • do not say words like, “while”

TIMEPLOTS

  • a plot that displays quantitative variables as it changes over time

  • look for an overall pattern or trend; long-term upward or downward movement over time