Exam 1: Describing Data With Graphs

A piano teacher gave 33 lessons this month. The level of each student is listed below: where "B" is beginner, "I" is intermediate, and "A" is advanced. Summarize these data in a bar chart, and explain what the chart tells us. B I I I I A B B I B A I A A B B B B B A B B I I B B B B I A B I I

A bar chart in which the bars are ordered from smallest to largest is called a Pareto chart.

A variable that is normally described in words, rather than numerically presented, is a qualitative variable.

A qualitative variable about which observations can be made in only two categories is a bivariate data set.

Water Temperature A limnologist is studying an Alberta lake in October. He records the temperatures in $\degree$ C for surface water taken every other day at noon. The data are as follow: 8.5, 8.1, 7.9, 9.0, 7.7, 7.3, 7.1, 6.8, 9.2, 6.8, 6.3, 7.0, 6.5, 5.7, 5.9, 4.9, 4.2, and 6.9. -Refer to the Water Temperature statement. Would you describe the distribution of the data as symmetric, skewed to the right, or skewed to the left? Explain.

A tabular summary of a categorical data set, which shows the number of observations that fall into each of several collectively exhaustive and mutually exclusive classes, is called a bar chart.

What is a single observation about a specified characteristic of interest called?

Suppose that the largest value in a set of data is 99, and the lowest value is 20. If the resulting frequency distribution is to have five classes of equal width, the class width should be 16.

What are the two graphical techniques most commonly used to present qualitative data?

Twenty-five percent of a sample of 200 professional tennis players indicated that their parents did not play tennis. This is an example of descriptive statistics, rather than inferential statistics.

How is the relative frequency of a class computed?

Kittens in Litters The following data represent the numbers of kittens born in litters for a particular breed of cat: 4, 5, 3, 6, 5, 5, 3, 4, 4, 5, 7, 5, 6, 6, 7, 4, 5, 5, 6, and 6. -Refer to the Kittens in Litters statement. Construct a relative frequency histogram.

Multivariate data result when more than two variables are measured.

Friendly Encounter The Executive Board of a popular online dating website, called Friendly Encounter, wanted to know how to market the site by targeting the age groups most likely to be interested in its product. To find out, a random sample of 250 users was drawn from its database of participants who had been active during the previous month. The users were then categorized into age groups. The average frequency of access per week was recorded for each age group. The result was organized into the following table of data: -Refer to the Friendly Encounter table. Should the Board decide to ignore the 40 & over age group altogether in its next marketing campaign? Explain your conclusion.