CHAPTER 2 Graphical Descriptions of Data

SECTION 2.1 Frequency Distributions

 After collecting the data, we need to organize the data. This chapter will describe different ways to organize the data.

ORDERED ARRAY  Arranging data from least to greatest or vice versa.

VOCABULARY

TWO TYPES OF FREQUENCY DISTRIBUTIONS Grouped  Classes are ranges of possible values Ungrouped  Each class represents a single value

STEPS TO CREATE A FREQUENCY DISTRIBUTION  Step 1: Determine the number of classes.  Normally between 5 and 20, but the classes will be suggested in this lesson.  Step 2: Choose an appropriate class width.  Find the range, then round up. The class width is the difference between lower limits.  Step 3: Find the class limits.  The lower limit is the smallest number that can belong to the class.  The upper limit is the largest number that can belong to the class.  Step 4: Determine the frequency of each class.  Make a tally mark for each piece of data in the appropriate class, then count the tally marks to find the total frequency for each class.

EXAMPLE Note: Round in increments of 50 for large data values. Used rounded number for smaller data values.

CLASS BOUNDARIES

CLASS MIDPOINTS

RELATIVE FREQUENCY  Relative frequency is the percentage of the data that falls in a particular class.  Sample size is the total amount of data values.

CUMULATIVE FREQUENCY  Cumulative frequency is the sum of the frequency for a given class and the frequencies of all previous classes.  The cumulative frequency of the last class should equal the sample size.

PRACTICE PROBLEM

SOLUTION

SECTION 2.2A Graphical Displays of Data: Pie Charts and Bar Graphs

PIE CHART

PARETO CHART  A bar graph that puts the data in descending order.

SIDE-BY-SIDE BAR GRAPH  Represents two sets of data, with bars next to each other.

STACKED BAR GRAPH  Represents two sets of data by stacking the bars.

SECTION 2.2B Graphical Displays of Data: Histograms, Polygons, and Stem and Leaf Plots

RELATIVE FREQUENCY HISTOGRAM  Similar to the histogram, except the height of the bars is the relative frequency instead of the frequency.

HOW TO CREATE A FREQUENCY POLYGON  Step 1: Mark the class boundaries on the x-axis and the frequencies on the y-axis. There will be two extra classes, one on the lower end and one on the upper end, both with a frequency of 0.

 Step 2: Add the midpoint to the x-axis, then plot a point at the frequency right above the midpoint.  Step 3: Join each point with a line segment.

OGIVE (“OH-JIVE”)  An ogive is a line graph that uses the boundaries and the cumulative frequency of the data.

OR

DOT PLOT  Similar to the stem and leaf other than it is a number line with dots representing the leaves.

SECTION 2.3 Analyzing Graphs

 Time-Series Graph – a picture of how data changes over time and has a variable of time as the horizontal axis.

 Cross-Sectional Graph – a picture of the data at a given moment in time. Neither axis will have a variable of time