Statistics (Ch. 2 from Lecture)

Bar graph

represents data by using vertical or horizontal bars whose heights or lengths represent the frequencies of the data (used for qualitative data)

Distribution of graphs

Important to recognize shapes of distibution values. Be able to identify shape of distribution. Bell shaped Uniform Right skewed Left skewed J shaped Reverse J shaped Bimodal U shaped

Frequency distribution

Organization of raw data in table form, using classes and frequencies

Time series graph

Represents data that occur over specific period of time (time is x axis)

Misleading graphs

Review notes -Truncating/zooming -Missing/skewed scale -Graphical misrepresentations (with images)

Notes on frequency polygons & histograms

2 ways to represent the same data Show overall shape of the distribution of the variable

Converting graphs to relative frequency graphs

All three graphs can be converted into relative frequency graphs by converting the frequencies into proportions/percents (Y axis would change to relative) To convert frequency to proportion, divide frequency (or cumulative) for each class by the total of the frequencies Use relative frequencies on y-axis rather than the frequencies Page 58 READ

Suggestions for drawing pareto charts

Bars same width Arrange data from largest to smallest according to frequency Make units equal in size

Three types of frequency distributions

Categorical (qualitative) Grouped (quantitative) Ungrouped

Stem & leaf plot

Data plot that uses part of the data value as the stem and part as the leaf to form groups or classes

Notes on time series graphs

Do not extend ends of the time series to the x axis unless it make sense that the data would fall to zero Two data sets can be compared on each graph (compound time series) Look for patterns or trends that occur over time

Class width

Found by subtracting the lower class limit of one class from the lower class limit of the next class Width = range/# classes (always round UP to nearest whole number - exhaustive)

Frequency polygon

Graph that displays data by using lines that connect points plotted for the frequencies at the MIDPOINT OF CLASSES; frequencies represented by heights of points Class midpoint = low bound + up bound/2

Histogram

Graph that displays data using contiguous vertical bars of various heights to represent frequencies of classes Frequency on Y axis Class boundaries on X axis Remember to Title and say as much as possible on the title and axis labels

Ogive

Graph that represents the cumulative frequencies for the classes in a frequency distibution Line graph w/ cumulative values on Y axis and other variable on X

Pareto Chart

Used to represent a frequency distribution for a categorical variable, and the frequencies are displayed by heights of bars, which are arranged in order from highest to lowest Categorical and not discrete data

Notes on Ogives

Used to visually represent how values are below a certain upper class boundary Can show whether the data values increase rapidly or slowly by the steepness of the line between two or more points

Categorical frequency distribution

Used when data can be placed into specific categories E.g., majors in college Class = major; frequency = number; percent = proportion

Grouped frequency distribution

Used when range of data is large, data must be grouped into classes that are more than one unit in width *Between 5-20 classes *Mutually exclusive classes *Continuous classes *Exhaustive classes *Equal width of classes

Ungrouped frequency distribution

WHen each class is only one unit wide Class = 1; limit = .5 - 1.5 Class = 2; limit = 1.5 - 2.5 Class = 3; limit = 2.5 - 3.5 *Not really grouped - needed for histogram

Notes on stem & leaf plots

When analyzing look for peaks or gaps in the distribution; is the distribution symmetric or skewed Back to back stem & leaf plot can be created to compare two data sets using the same digits as stems