Ch. 4

Box Plot

A graphical display based on five statistics: the minimum value, Q1 (the first quartile), Q2 (the median), Q3 (the third quartile), and the maximum value.

Pearson's Coefficient of Skewness

A measure of the degree of skewness. sk = the coefficient of skewness X Bar = the mean s = the standard deviation

A dot plot is best applied when _____________________.

A single variable is summarized

Stem-and-Leaf Display

A statistical technique for displaying a set of data. Each numerical value is divided into two parts: the leading digit(s) becomes the stem, and the trailing digits the leaf. The stems are located along the main vertical axis and the leaf for each observation along the horizontal axis. Example: the number 15 has a stem value of 1 and a leaf value 5. 231 has a stem of 23 and a leaf of 1.

Contingency Table

A table used to classify sample observations according to two or more identifiable characteristics.

Scatter Diagram

A graph in which paired data values are plotted on an X,Y Axis.

Bivariate Data

A collection of paired data values

Dot Plot

A graph for displaying a set of data. Each numerical value is represented by a dot placed above a horizontal number line.

Steps to follow in developing a dot plot graph are:

1. Sort the data from smallest to largest. 2. Draw and label a number line. 3. Place a dot for each observation.

Characteristics of the coefficient of skewness are:

1. The coefficient of skewness, designated sk, measures the amount of skewness and may range from -3.0 to +3.0 2. A value near -3, such as -2.57, indicates considerable negative skewness. 3. A value such as 1.63 indicates moderate positive skewness. 4. A value of 0, which will occur when the mean and median are equal, indicates the distribution is symmetrical and that there is no skewness.

Percentiles divide a distribution into _____________.

100 equal parts

The median of a sample will always equal the ________.

50th percentile

A dot plot is an easy way to represent the relationship between two variables.

False

The 25th percentile is referred to as the ________.

First quartile

Percentile Example Problem:

If you had a set of data with 49 observations in ordered array and wanted to locate the 78th percentile, then let P = 78 and n = 49 so Lp = (49+1)(78/100) Thus, you would locate the 39th observation. If you wanted to locate the 6th decile, then let P = 60 and Lp = (49+1)(60/100) Thus, you would locate the 30th observation. *(6th decile equals the 60 percentile)

Percentile Example Problem:

If you were told tha tyour Scholastic Aptitude Test score was in the 9th decile, yo ucould assume that 90 percent of those taking the test had a lower score than yours and that 10 percent ahd a higher score. A grade point average in the 55th percentile means that 55 percent of students have a lower GPA than yours and that 45 percent have a higher GPA. The procedure for finding the quartile, decile, and percentile for ungrouped data is to order the data from smallest to largest. Then use the formula: Lp = (n + 1)(P/100) Lp = location of the desired percentile n = number of observations P = the desired percentile

Interquartile Range

The difference between the third quartile, Q3, and the first quartile, Q1. It is the range of the middle 50% of the data values.

First Quartile

The point below which 1/4 or 25% of the ranked data values lie. (It is designated Q1)

Third Quartile

The point below which 3/4 or 75% of the ranked data values lie. (It is designated Q3)

What does the interquartile range describe?

The range of the middle 50% of the observations

The 75th percentile is referred to as the ________.

Third quartile

A dot plot can be used to show _________________.

the distribution for a quantitative variable