Statistics 6

What are the most commonly used graphs for categorical data?

bar graph, pareto graph, and pie chart

Manipulating the x-axis (abscissa)

"Cherry-Picking" data Missing data Unequal category widths on the x-axis

What are the most common graphs for numerical data (interval or ratio data)?

Histogram Frequency Polygon Stem and leaf Box Plot Time Series Scatterplot (in another lecture)

bar graph

are a common way to display categorical data and consist of bars that are usually separated from each other. The x-axis usually displays the various categories or levels of the variable of interest, and the y-axis usually displays the frequency, percentage or proportion of each category. However, horizontal bar graphs (x and y swapped) are not uncommon.

box plot or box and whiskers plot

displays a five number summary (Q1, Q2, Q3, IQR and range. It is a very useful graph for examining symmetry and outliers.

.The box plot or box and whisker plot displays the actual data as well as the shape of the data.

false

A bar graph would be useful for displaying raw scores on a test.

false

Stem and leaf diagrams are like histograms, except that they lose the original scores.

false

The X-axis for a bar chart displays numerical data.

false

The X-axis for a histogram displays categorical data.

false

The Y-axis for a pie chart may display frequency, relative frequency or percent.

false

The histogram is commonly used with categorical data.

false

The pareto is a type of bar chart where categories are organized from lowest frequency to highest frequency.

false

The pie chart is useful for presenting numerical data.

false

pareto graph

named after Vilfredo Pareto, is a type of bar chart that contains both bars and a line graph, where individual values are represented in descending order by bars, and the cumulative total is represented by the line.

A bar graph would be useful for displaying letter grades on a test

true

A bar graph would be useful for displaying the number of students majoring in psychology, nursing or social work.

true

A histogram would be useful for displaying the amount of weight patients lost on a diet.

true

times series graph

a line graph of repeated measurements taken over regular time intervals. Time is always shown on the horizontal axis. On time series graphs data points are drawn at regular intervals and the points joined, usually with straight lines. Time series graphs help to show trends or patterns.

Typically, the Y axis should begin at 0.

true

What are some ways in which a graph can be misleading?

Manipulating the Y-axis (ordinate) or Manipulating the x-axis (abscissa)

Misleading graphs not starting at zero on y-axis

Not starting at 0 on the y-axis can exaggerate the differences between or among your categories. There are occasions where not starting at 0 is appropriate.

Manipulating the Y-axis (ordinate)

Omitting the baseline (not starting at 0) on the y-axis Using the wrong scale Failing to use labels

What are the most common graphs for categorical data (nominal and ordinal data)?

Pie Chart Bar Chart Pareto chart

Consider the following score diagram. 1 2 2. 1 3 3 2 4 6 7 4. 2 3 5 6 8 5. 1 3 4 4 5 6 8 6. 3 3 3 5 6 7 8 8 9 9 9 7. 2 2 2 3 3 4 5 5 5 6 6 7 7 7 8. 1 1 1 2 3 3 4 4 5 5 5 6 6 6 6 9. 2 2 2 3 3 4 4 5 5 5 6 6 7

Steam and leaf

What are the most commonly used graphs for numerical data?

The most commonly used graphs for displaying numerical data (interval or ratio) are the histogram, time series, box plot, stem and leaf, and frequency polygon.

histogram graph

a graphical display of data using bars of different heights. It is similar to a bar chart, but a histogram usually groups numbers into ranges and is used to display numerical data rather than categorical data. The bars usually touch one another indicating continuous data, but the lines may be separated to designate discrete data was used.

stem and leaf display

a graphical method of displaying numerical data using the actual data rather than lines or bars. It is particularly useful when your data are not too numerous. A stem and leaf graph is a type table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit).

frequency polygon

a type of frequency distribution graph (percentage or relative frequency can also be displayed on the y axis) that can be used to display numerical data. Unlike a histogram, a frequency polygon uses midpoints for each interval rather than the interval itself. A straight line then connects each set of points. The first graph below shows a frequency polygon superimposed over a histogram.

pie chart

a type of graph used to display categorical data in which a circle is divided into sectors or slices that each represent a proportion of the whole. Sometimes percent and or frequency are displayed with the slices.

The stem and leaf plot is useful for small, categorical data sets.

false

The stem and leaf plot is useful for small, categorical data sets..

false

The stem and leaf plot is useful for very large data sets.

false

The vertical axis, i.e., the Y axis of a graph, is called the abscissa.

false

If the Y-axis on a histogram or bar chart is changed from frequency to relative frequency, the shape of the graph will remain unchanged.

true

If the right whisker is substantially larger than the left whisker in a box and and whisker plot, the data is likely to be positively skewed.

true

Q1, Q2 and Q3 are displayed in box plot.

true

The X-axis for a bar chart displays categorical data.

true

The X-axis for a histogram displays numerical data.

true

The actual raw data can be reconstructed when using a stem and leaf graph.

true

The box in a box plot represents the IQR.

true

The primary function of a frequency distribution is organize and manage large sets of data.

true

The stem and leaf graph displays the actual data as well as the shape of the data.

true

The stem and leaf plot is useful for small, numerical data sets.

true