The majority of the content on this page is copy-pasted from the textbook.
Frequency Distributions
A distribution shows the frequency or likelihood of various values occurring in a data set.
The class width of a given frequency distribution is the difference between the lower limits of the consecutive classes.
A frequency distribution is a summary technique that organizes data into classes and provides in tabular form a list of the classes along with the number of observations in each class.
The relative frequency of any class is the number of observations in the class divided by the total number of observations:
The cumulative frequency is the sum of the frequency of a particular class and all preceding classes.
The cumulative relative frequency is the proportion of observations in a particular class and all preceding classes.
Displaying Qualitative Data Graphically
The bar chart is a simple graphical display in which the length of each bar corresponds to the number of observations in a category.
The Pareto chart is a bar graph whose bars are arranged in decreasing order of frequency.
A pie chart (or circle graph) is a graph used to display categorical data as slices of a circle. The size of each slice is proportional to the amount or frequency in each category. The proportion of the total that each slice represents is often displayed as a percentage on the chart. These percentages should total 100%.
Displaying Quantitative Data Graphically
A histogram is a graphical representation of a frequency or relative frequency distribution. The horizontal scale corresponds to classes of quantitative data values and the vertical scale corresponds to the frequency or relative frequency of each class.
If you split the histogram of a distribution down the center, and the left and right sides of the histogram are approximately mirror images of one another, the distribution is said to be symmetric.
A skewed distribution is a nonsymmetric (or asymmetric) distribution that extends more to one side than the other. The distribution is said to be skewed to the right (or positively skewed) if the tail to the right of the peak of the distribution is longer than the tail to the left of the peak. The distribution is said to be skewed to the left (or negatively skewed) if the tail to the left of the peak of the distribution is longer than the tail to the right of the peak.
The stem-and-leaf plot is a graph representing quantitative data that separates each data value into two parts: the stem and the leaf.
Analyzing Graphs
It is often useful to transform data by replacing a variable in the data set by a function of that variable so that the distribution is easier to work with or interpret. For example, if the data set contains a variable x, we can transform the distribution of the data by replacing x with some function of x, such as the square root of x or the logarithm of x. We often refer to these types of changes as normalizing the data.
One type of graph commonly used in the media is a pictograph which is a bar graph that uses pictures of objects in place of the bars. It is often used because it is visually appealing and simple to understand.