Interpreting Graphical Summaries

Question 1

which graphs are quantitative and categorical

Answer 1

quantitative (numerical)

• stem-and-leaf plots
• dotplots
• histograms
• boxplots
• time series plots

qualitative (categorical)

• bar charts
• pie charts

Question 2

important features of a graph

Answer 2

• what is the overall pattern?
• what is the shape and centre of the distribution?

variability: how spread out is the distribution?

• are there any big deviations from this pattern?
• are there any gaps? are there any outliers (which are points that fall well outside the overall pattern)
• number and location of peaks

Question 3

histogram

Answer 3

shapes of histogram:

• unimodal histogram is one that rises to a single peak and then declines
• bimodal histogram has two different peaks (may occur when the data set consists of observations on two quite different kinds of individuals or objects, e.g. male vs female)
• histogram with more than 2 peaks is multimodal
• a histogram is symmetric if the left half is a mirror image of the right half
• a unimodal histogram is positively (right) skewed if the right tail is longer and flatter than the left tail and negatively (left) skewed if the left tail is longer and flatter

Question 4

boxplot

Answer 4

• boxplots are most useful when comparing two or more distributions (whereas stem-and-leaf plots/histograms provide clearer displays of a single distribution)
• box plots can also be used to identify the approximate shape of the distribution of a set of data

5 number summary (max, Q3, median, Q1, min)

Question 5

modified boxplots and outliers

Answer 5

outliers are values that are far removed from the rest of the distribution

common rule: values more than 1.5 x of IQR beyond Q1 or Q3

Question 6

bar chart

Answer 6

a bar chart presents categorical data in the form of bars that provide a visual display of the relative sizes of each category

• are particularly useful to show comparisons where the actual size of the data is important

Question 7

pie chart

Answer 7

pie chart presents categorical data in the form of slices of a pie providing a visual display of what fraction of the whole each category takes up

• are an appropriate means representing relative differences in data

Question 8

stem plot

Answer 8

easy way to put a list of numbers into order while getting a picture of their shape

help determine shape of a data set, identify outliers and locate the center

Question 9

pictogram

Answer 9

pictogram is like a bar graph except it uses pictures related to the topic of the graph

easy to be mislead by pictograms because the eye tends to focus on the area of the picture instead of just the height

Question 10

line graph

Answer 10

example of line graph displayed over time

shows winning times for the men’s 500 meter speed skating 1924-2010

patterns are easy to detect with pictures than they would be scanning a list

Question 11

scatterplot

Answer 11

scatterplots are useful for displaying the relationship between two measurement variables

each dot represents one individual, unless two or more individuals have the same data, in which case only one point is plotted at that location (some software programs replace with a number)

harder to read than line graph, but displays more information, shows outliersk as well as the degree of variability that exists for one variable at each location of the other variable

Question 12

time series plot

Answer 12

time series is simply a record of a variable across time, usually measured at equally spaced intervals

for instance, most economic data used by both governments and businesses are measured monthly

components of time series - long-term trend, seasonal components, irregular cycles and random fluctuations