Intro To Stats (Ch 2. Practice Problems)

Why should the number of classes in a frequency distribution be between 5 and​ 20?

If the number of classes in a frequency distribution is not between 5 and​ 20, it may be difficult to detect any patterns.

What is the difference between class limits and class​ boundaries?

Class limits are the least and greatest numbers that can belong to the class. Class boundaries are the numbers that separate classes without forming gaps between them. For integer​ data, the corresponding class limits and class boundaries differ by 0.5.

Frequency Distribution

 A table that shows class or intervals of data entries with a count of a number of entries in each class.

Frequency F

The number of data entries in a class.

Range

The difference between maximum and minimum data entries.

Class Limits

The least and the greatest number that can belong in a class.

Class Width

The distance between lower (or upper limits) of consecutive classes.

Relative Frequency

The portion or percentage of the data that falls in the class. (Class Frequency)/(Sample Size).

Cumulative Frequency

The sum of frequencies of that class and all previous classes.

Midpoint of A Class

The sum of the lower and upper limits of the classes divided by two.

Class Boundaries

The numbers that separate classes without forming gaps between them.

How to construct a frequency distribution?

1. Decide on the number of classes (between 5 and 20). 

2. Find the class width as follows: 

   • Divide the range by the number of classes.

   • Round up to the next convenient number.

3. Find the class limits.

4. Make a tally mark for each data entry in the class.

5. Count the tallies to find the frequency F for each class.

A frequency histogram

A _____ is a bar graph that represents the frequency distribution of a data set.

frequency polygon

To construct a _____ use the same horizontal and vertical scales that were used in the histogram. Plot points that represent the midpoint and the frequency of each class and connect the points in order from left to right. Because the graph should begin and end on the horizontal axis. Extend the left side to class width before the first class midpoint and extend the right side to one class width after the last midpoint.

relative frequency histogram

A ____ has the same horizontal scale as the corresponding frequency distribution. The difference is that the vertical scale measures the relative frequencies, not the frequency.

Name some ways to display quantitative data graphically.

Stem-and-lead plots, Scatter Plots, Time Series Plots, Histograms.

Name some ways to display qualitative data graphically. Select all that apply.

Pie Charts, Bar Graphs, Pareto Charts.

What is an advantage of using a​ stem-and-leaf plot instead of a​ histogram?

Stem-and-leaf plots contain original data values where histograms do not.

What is a disadvantage of using a stem-and-leaf plot instead of a histogram?

Histograms easily organize data of all sizes where​ stem-and-leaf plots do not.

How is a Pareto chart different from a standard vertical bar​ graph?

The bars are positioned in order of decreasing height with the tallest bar on the left.

Pie Chart

A circle that is divided into sectors that represent categories. The area of each sector is proportional to the frequency of each category.

Stem & Leaf Plot

In a ____ each number is separated into a stem and a leaf.

Pareto Chart

A ____  is a vertical bar graph in which the height of each bar represents frequency or relative frequency. The bars are positioned in order of decreasing height, with the tallest bar positioned on the left.

time series, time series chart

A data set that is composed of quantitative entries taking regular intervals over a period of time is called a ____ we use a _____ to graph time series.