Chapter 4 Displaying Quantitative Data

Quantitative variables Quantitative variables- record measurements or amounts of something. Must have units or a variable in which the numbers act as numerical values

Types of Displays Histogram Stem and Leaf Displays Dotplots

Histogram A histogram uses adjacent bars to show the distribution of values in a quantitative variable. Looks very similar to a bar graph but there are differences. The horizontal axis is continuous not just labeled.

An example The histogram shown below gives the number of children visited a particular zoo..

Histogram A histogram is more convenient than a dot-plot or a stem and leaf plot because you don't have to represent each data point. However, you don't get to see the value of each data point. So a table of data and summary statistics would help people interpret the data.

Be Careful A histogram gives the number of data points that fall into equal intervals. Care must be taken in choosing the intervals because it can affect the shape of the graph and misrepresent the true data.

1 st graph The first graph is uses intervals of size 10 yielding the intervals 40-50, 50-60, etc. In this case, Yemen had a life expectancy of 50 and was placed in the column. Usually, borderline values are placed in the higher column.

2 nd Graph In the second graph, the intervals are , 45-50, 50-55, etc. This affects the shape of the graph.

Stem and Leaf Displays Shows quantitative data values in a way that sketches the distribution of the data. The stem-and-leaf plot below shows the number of students enrolled in a dance class in the past 12 years. The number of students are 81, 84, 85, 86, 93, 94, 97, 100, 102, 103, 110, and 111.

Dotplot Graphs a dot for each case against a single axis Graph the following number 5, 5,5,5,5,5,5,10,10,10,10,10 etc

Dotplot with two sets of data Example

Shape To describe the shape of a distribution, look for Symmetry versus skewness Single versus multiple modes

Symmetrical A distribution is symmetric if the two halves on either side of the center look approximately like the mirror images of each other.

Symmetrical Symmetrical Histogram

Dotplot Dots are mirrored images

Stem and leaf Example

Skewed A distribution is skewed if it is not symmetric and one tail stretched out further than the other. Skewed left- when the longer tail stretches to the left. Skewed right-when the longer tail stretched to the right

Examples Skewed right

Skewed left Left

All three Examples

Funny example stics/ymmsum99/ymm111.htm

Center A value that attempts the impossible by summarizing the entire distribution with a single number, a “typical” value

Spread A numerical summary of how tightly the values are clustered around the center

Mode

Unimodal

Uniform

Symmetrical

Tails

Outloiers

Timeplots

Skewness To the right

Skewness To the left