Chapter 2: Summarizing Data Using Graphs

Are there spaces between bars in a histogram?

No, there are no spaces.

What are the two major types of variables?

Numerical (or quantitative) and Categorical (or qualitative).

What is the center of a graph?

The center of a graph is the middle and numeric methods are normally used to describe it.

What is the table that accompanies a histogram called?

A frequency table.

Can you take the average of a categorical variable?

No

Are histograms and bar graphs the same thing?

No, histograms are for quantitative data while bar graphs are for qualitative data.

Based on the number of peaks, what are the different ways we can describe the shape of a graph?

A unimodal graph has one peak, a bimodal graph has two peaks, and a multimodal graph has three or more peaks.

What is a variable?

A variable is a characteristic or attribute that we are interested in.

What is the definition of an outlier?

An outlier is a data point that is far from the rest of the data.

What are deviations from the data called?

Deviations from the data are called outliers.

Numerical variables can be either discrete or continuous. What is the difference between discrete and continuous variables?

Discrete variables are finite or are countable (e.g. the number of students in a class). Continuous variables consist of intervals (e.g. the results of rolling 2 dice)

What is frequency distribution?

Frequency distribution consists of the frequency or count of the number of observations in each class.

What is a histogram?

Histograms show the distribution of a quantitative variable by using bars.

Should you delete outliers?

NEVER delete outliers just because they are outliers or make the data harder to analyze. Sometimes outliers are miss-copied or that data are taken in error. In those cases, outliers may be deleted. However, an outlier can provide you with insight into your data and can suggest ideas for new studies.

What is relative frequency?

Relative frequency is the measured frequency divided by the total number of data points.

We can classify datasets based on the number of variables they contain, what are these classifications called?

Single observations are called univariate. Two observations are called bivariate. Three or more observations are called multivariate.

What are the different peak shapes for a unimodal histogram?

The different peak shapes are symmetric, positively skewed, and negatively skewed.

For discrete data sets, we can have a bin for each number. However, it is not clear how many classes or bins we should generate for the x-axis of the graph. As a rule of thumb, approximately how many classes should there be?

The number of classes should be approximately equal to the square root of the number of observations (But the number of classes should never exceed 30).

What is the right side of a positively skewed peak called (the longer line)?

The tail, and the situation can also be called right tailed. A negatively skewed shape can be called left tailed.

What is the variability of a graph?

The variability of a graph tells us how spread out the data is.

(True/False) In inference, it is very important that each population should be unimodal.

True

(True/False) The number of classes or bins affects the shape of the histogram.

True

(True/False) You should always graph your data so that you have a feel for what the data looks like.

True

(True/False) You should always look at the histogram to be sure that the graph is appropriate for your situation no matter how many classes that there are.

True

What do we look at to explain the pattern of a graph of data?

We look at the shape, the center, and the variability.

What do we look for in any graph of data?

We look for the overall pattern and for striking deviations.

How do we separate categorical variables?

We separate the variables into different categories called bins or classes. We also can separate numerical variables into the same thing, in this case, it would be groups of numbers.

What about the shape of a graph will we be concerned about?

Whether the shape is symmetric or not.

Are there spaces between bars in a bar graph?

Yes, there are spaces.