Chapter 2

Pareto Chart

A bar graph whose bars are drawn in decreasing order of frequency or relative frequency.

Pie Chart

A circle divided into sectors. Each sector represents a category of data. The area of each sector is proportional to the frequency of the category. -Typically used to represent the relative frequency of qualitative data. Can be nominal or ordinal.

Pie Chart (Qualitative Data Sets)

A circle is divided into sectors that represent categories. The area of each sector is proportional to the frequency of each category.

Ogive

A graph that represents the cumulative frequency or cumulative relative frequency for class. It is constructed by plotting points whose x-coordinates are the upper class limits and whose y-coordinates are the cumulative frequencies or cumulative relative relative frequencies of the class.Then line segments are drawn connecting consecutive points. An additional line segment is drawn connecting of the first point to the horizontal axis at a location representing the upper limit of the class that would precede the first class (if it existed).

Histogram

Constructed by drawing rectangles for each class of data. The height of each rectangle is the frequency of the class. The width of each rectangle is the same and the rectangles touch each other.

Classes

Categories in which data are grouped

Bar Graph

Constructed by labeling each category of data on either the horizontal or vertical axis and the frequency or relative frequency of the category on the other axis. Rectangles of equal width are drawn for each category. The height of each rectangle represents the category 's frequency or relative frequency.

Time Series

Data set is composed of quantitative entries taken at regular intervals over a period of time.

Determining the Width

Decide on the number of classes. Generally there should be between 5 and 20 classes. The smaller the data set, the fewer classes you should have. -Determine the Class width by computing Largest Data Value - Smallest Data Value/ # of Classes

Bar Graph or Pareto Chart

A vertical bar graph in which the height of each bar represents frequency or relative frequency -Bars do not touch -If the bars are positioned in order of decreasing height, with the tallest bar positioned at the left, the bar graph is called a Pareto Chart.

Stem-and-leaf plot (Quantitative Data Sets)

Another way to represent quatitative data graphically. In a stem-and-leaf plot, we use digits to the left of the rightmost digit to form the STEM. Each rightmost digit forms a LEAF. -Each number is separated into a stem and leaf -Similar to a histogram -Still contains original data

Dot Plot (Quantitative)

Place each observation horizontally in increasing order and place a dot above the observation each time it is observed. Provide a quick picture of the data.

Choosing the lower class limit of the first class

Choose the smallest observation in the data set or a convenient number slightly lower than the smallest observation in the data set.

Cumulative Frequency Distribution

Displays the aggregate frequency of the category. In other words, for discrete data. It displays the total number of observations less than or equal to the upper class limit of a class.

Cumulative Relative Frequency Distribution

Displays the proportion (or percentage) of observations less than or equal to the category for discrete data and the proportion (percentage) of observations less than or equal to the upper class limit for continuous data.

Dot Plot (Quantitative Data Sets)

Each data entry plotted, using a point, above a horizontal axis.

Paired Data Sets

Each entry in one data set corresponds to one entry in a second data set. -Graph using a scatter plot -The ordered pairs are graphed as points in a coordinate plane -Used to show the relationship between two quantitative variables

Frequency Polygon

Graph that uses points , connected by line segments, to represent the frequencies for the classes. It is constructed by plotting a point above each class midpoint on a horizontal axis at a height equal to the frequency of the class. Next, line segments are drawn connecting each end of the graph with the horizontal axis.

Time-Series Data

If the variable is measured at different points in time.

Frequency Distribution

List each category of data and the number of occurrences for each category of data.

Relative Frequency Distribution

Lists each category of data together with the relative frequency.

Class Width

The difference between the Consecutive lower class limits.

Open Ended

The first class has no lower limit or the last class has no upper class limit.

Uniform Distribution

The frequency of each value of the the variable is evenly spread out across the values of the variables.

Bell Shaped Distribution

The highest frequencies occur in the middle and frequencies tail off to the left and right of the middle.

Upper Class Limit

The largest value within the class.

Relative Frequency

The proportion (or percent) of observations within a category and is found using the formula -Relative Frequency= Frequency/Sum of All Frquencies

Skewed Right

The scale to the right of the peak is longer than the scale to the left of the peak.

Lower Class Limit

The smallest value within the class.

Construction of a Stem-and-Leaf Plot (Quantitative) : Step 1

The stem of a data value will consist of the digits to the left of the right most digit.The leaf of a data value will be the right most digit.

Class Midpoint

The sum of consecutive lower class limits divided by 2

Skewed Left

The tail to the left of the peak is longer the the scale to the right of the peak.

Construction of a Stem-and-Leaf Plot: Step 4

Within each stem, rearrange the leaves in ascending order, title the plot, and include the legend to indicate what the values represent.

Construction of a Stem-and-Leaf Plot: Step 3

Write each leaf corresponding to the stems to the right of the vertical line.

Construction of a Stem-and-Leaf Plot: Step 2

Write the stems in a vertical column in increasing order. Draw a vertical line to the right of the stem.

Time-Series Plot

is obtained by plotting the time in which a variable is measured on the horizontal axis and the corresponding value of the variable. On the vertical axis. Line segments are then drawn connecting the points.