Name Date Types of Graphs and Creating Graphs Notes Graphs are helpful visual representations of data. Different graphs display data in different ways. Some graphs show individual data, but many do not. Look for which graphs show the following characteristics: Shape of the data, frequency, relative frequency, spread of the data, dispersion, outliers, location of center Vocabulary: Frequency is a raw count of data Relative frequency is the percentage calculation of the data Dispersion is the spread of data Shapes of numeric distributions Skewed Distribution Symmetric Distribution
Line Plots (also seen as dot plots) A line plot is a graph that shows frequency of data along a number line. It is a good way to organize data and works best with moderately sized sets of data ( 25 numbers). To make a line plot out from data first determine a scale that includes all of the data in appropriate intervals. Then plot each number using X or other marks to show the frequency. Bar Graph For displaying non-numeric data Bars have to have equal width and spacing and not touch each other The frequency axis (usually vertical axis) must start at 0 The height of each bar is proportional to the number/percentage in that category Label frequency axis
Histogram A bar graph with numeric data Has categories (classes) of data, with ranges of numeric data Each class must be same width Shows shape, center, and spread of distribution, and outliers Pie Chart Categories as divisions of the whole; percent of a population
Stem-and-Leaf Plot A stemplot shows shape, center, and spread of distribution, and outliers Good for moderate data, not large sets, sparse sets, or those with a large range To create a stemplot: Find the max and min of the data Decide what the stem will be and list in a column to the left - in this case, the stems will be from 6 to 14 Draw a vertical line to the right of the stems Go through each data point and add the leafs to the proper stem If necessary, re-write the leaves in order Add a title and key to your stem-and-leaf plot
Box-and-Whisker Plots Box-and-Whisker Plots explain data by showing the spread of data in a sample. The plot is divided into four parts, each representing 25% of the data; the two whiskers on either end, and a box split by a median line.
To make a Box-and-Whisker Plot: Gather the data Organize the data from least to greatest Find the median of the data (median = second quartile) Find the first and third quartiles First quartile = median of lower half Third quartile = median of upper half Draw a number line Must contain all your points with a little extra at each end Must be numbered at even intervals Make a vertical line mark, above the number line, at each of the first, second, and third quartiles Make a box connecting the first and third quartiles, going through the second quartile Mark your upper and lower extremes with small dots Lower extreme = maximum value of data Upper extreme = minimum value of data Connect the extremes to the box with a horizontal line These are the whiskers Look at a box and whiskers plot to visualize the distribution of numbers in any data set. You can easily see, for example, whether the numbers in the data set bunch more in the upper quartile by looking at the size of the upper box, as well as the size of the upper whisker. The interquartile range (Q3-Q1), represents 50% of the data.
Overview: With numeric data, the goal of descriptive stats is to show shape, center, spread, and outliers. Key ideas: When you have a mass of data and need frequencies, don t pass through the data repeatedly, counting a different category each time. Instead, use the tally system. Relative frequency for any class or category is the number of data points in that class, divided by total sample size. For non-numeric data, make a bar graph or pie chart. Place categories in any order that seems reasonable to you. Side-by-side bar graphs and stacked bar graphs can be useful for comparing populations. Numeric data: Group continuous data in classes, tally them, and make a grouped histogram. Bars must touch, and you label them under the edges, not the middles. Do the same with discrete data that have a lot of different values. Present discrete data without too many different values in one bar for each different value. Label them under their middles. It s a matter of taste whether the bars touch (ungrouped histogram) or not (bar graph). For bar graphs and histograms, show scale on the frequency or relative-frequency axis, and show scale or category name on the data axis. Usually, each axis has a title, with a separate chart title at the top. But you can omit an axis title when it would be redundant information. In every bar graph or histogram, the frequency or relative-frequency axis must start at 0 and have consistent scale for its whole length. Be on the lookout for violations of this rule and other signs of bad graphs. Know the most common shapes of numeric distributions: uniform, bell curve, skewed left, and skewed right. The stemplot (stem-and-leaf diagram) is also an option for discrete data with moderate range and about 100 data points.