Lecture 2

Graphs for quantitative grouped data

1. histograms

2. polygon

3. relative frequency data

4. cumulative frequency data

Graphs for ungrouped quantitative data

steam and leaf

Graphs for qualitative data

1. pie charts

2. Pareto chart

A frequency histogram

a bar graph that represent the frequency distribution of a data set

properties of frequency histogram

1. the horizontal scale is quantitative and measures the data values

2. the vertical scale measures the frequencies of the classes.

3. consecutive bars must touch

histogram bars must start and end at

class boundary instead of class limits

the y axis of a frequency histogram

the frequency

the x axis of frequency histogram

class boundaries

a frequency polygon

a line graph that emphasizes the continuous change in frequencies

to construct the frequency polygon

1. plot points that represent the midpoint and frequency of each class

2. connect the points in order from left to right

the vertical of the frequency polygon

midpoint

the horizontal axis of frequency polygon

frequency

relative frequency histograms

the same shape and horizontal scale as the corresponding frequency histogram but with relative frequency

the horizontal axis in a relative frequency histogram

class boundaries

the vertical axis in a relative frequency histogram

relative frequency

cumulative frequency graph

a line graph that displays the cumulative frequency of each class at its upper boundary

the other name for cumulative frequency graph

ogive

constructing an Ogive

1. construct a frequency distribution with a cumulative frequency columns

2. plot points that represent the upper class boundaries and their corresponding cumulative frequencies

3. connect the points from left to right

4. the graph should start from the lower boundary of the first class to the upper boundary of the last class

the horizontal axis of an ogive

upper class boundaries

the vertical axis of an ogive

cumulative frequency

stem and leaf graph

similar to a histogram but contains the original data value

advantage of a stem and leaf graph

1. contains the original data values

2. provides an easy way to sort data

pie chart

a circle that is divided into sectors that represents categories.the area is = to the frequency

in order to draw a pie chart

1. calculate the angle for each category

2. draw a circle, mark the center and draw a radius

3. measure and draw the angle foe each category

how to measure the angle

category value (f) / total x 360

pareto chart

vertical bar graph in which the height of each bar represents frequency or relative frequency

features of the pareto chart

1. the tallest bar is positioned at the left

2. there are gaps between the bars