Exam 1: Describing Data With Graphs

Absenteeism A high school band teacher has a record of each student's absence. The results, in days, are 3, 4, 7, 2, 2, 1, 0, 0, 1, 0, 3, 3, 2, 1, 6, 0, 1, 0, 1, 1, 1, 5, 3, 1, 1, 0, 0, 2, 1, 2, 1, 0, 0, and 4. -Refer to the Absenteeism statement. How many students have been absent at most six days?

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. Find the relative frequency of the primary variable of interest.

A local cable system using a sample of 1000 subscribers estimates that 50% of its subscribers watch premium channels at least five times per week. This is an example of inferential statistics, as opposed to descriptive statistics.

When constructing a relative frequency distribution, if the data are discrete, it will always be necessary to develop class boundaries.

Univariate data result when a single variable is measured on a single experimental unit.

If you wish to compare two data sets of different sizes, it is usually a good idea to convert frequency distributions to relative frequency distributions.

The difference between a histogram and a bar chart is that the histogram represents quantitative data while the bar chart represents qualitative data.

The owner of an Italian restaurant would like to see a graphical display of the number of customers that the restaurant serves. The following data are the average number of customers served each day for the past 12 months. Construct and interpret a line graph.

In a sample of 1000 students in a university, 125, or 12.5%, are biology majors. The 12.5% is an example of statistical inference.

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. What proportion of litters has between four and six kittens, inclusive?

Potato Preferences A study was performed to examine preferences for various types of potatoes: mashed, french fries, hash browns, steak fries, and baked. The following data were recorded regarding the preferences of 150 people: -Refer to the Potato Preferences table. Construct a pie chart to describe the data.

Time series data are often graphically depicted on a line chart. A line chart is a plot of the variable of interest over time.

Bar and pie charts are graphical techniques for qualitative data. The former focus the attention on the frequency of the occurrences of the categories; the latter emphasize the percentage of occurrences of each category.

A discrete quantitative variable is one that may assume values only at specific points on an interval of values, with inevitable gaps between them.

Absenteeism A high school band teacher has a record of each student's absence. The results, in days, are 3, 4, 7, 2, 2, 1, 0, 0, 1, 0, 3, 3, 2, 1, 6, 0, 1, 0, 1, 1, 1, 5, 3, 1, 1, 0, 0, 2, 1, 2, 1, 0, 0, and 4. -Refer to the Water Temperature statement. Construct a stem-and-leaf plot to display the distribution of the data.

Social Media The Executive Board of a popular social media website wanted to know which kinds of professional people were accessing their website regularly over a two-month period. To that end, a random sample from its database of active users was collected. The following data were recorded: -Refer to the Social Media table. What is the variable of primary interest? Is it qualitative or quantitative?

When a distribution has more values to the left and tails to the right, then it is considered to be skewed to the left.

Describe the difference between descriptive statistics and inferential statistics, and give an example for each.

If the manager of a grocery store wishes to display the sales trend, which of the following is the most effective type of graph to use?

Lecture Notes The numbers of pages of notes per lecture taken by a student in a beginning statistics course are as follow: 1, 5, 2, 6, 2, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 4, 5, and 6. -Refer to the Lecture Notes statement. Based on your dotplot, what can be said about the shape of the distribution of the data? Why?