Displaying Data

Question 1

how to draw a good graph (4)

Answer 1

• show the data
• make patterns in the data easy to see (avoid unnecessary clutter)
• represent magnitudes honestly (have a baseline)
• draw graphical elements clearly (appropriate font and text size)

Question 2

frequency and frequency distribution (2)

Answer 2

• frequency: number of observations having a particular measurement in a sample
• frequency distribution: number of occurrences for all values in the data

Question 3

relative frequency

Answer 3

• proportion of observations having a given measurement, calculated as the frequency divided by the total number of observations

Question 4

relative frequency distribution

Answer 4

• proportion/fraction of occurrences of each value in a data set

Question 5

frequency table (2)

Answer 5

• text display of the number of occurrences of each category in a data set
• categorical data for one variable

Question 6

bar graph (2)

Answer 6

• uses the height of rectangular bars to display frequency distribution (or relative frequency distribution)
• categorical data for one variable

Question 7

how to make a good bar graph (6)

Answer 7

• the bars must have equal widths to represent magnitude correctly
• baseline of y-axis is at 0
• bars should stand apart, spaces between bars
• nominal data: order categories based on frequency of occurrence
• ordinal data: present values in natural order
• total # of observations (n) in figure legend

Question 8

bar graph vs pie chart (2)

Answer 8

• bar graph is usually better than a pie chart

- more difficult to compare frequencies, supplementary labelling required

Question 9

histogram (3)

Answer 9

• uses area of rectangular bars to display the frequency distribution (or relative frequency distribution)
• data values split into consecutive bins/intervals of equal width
• used for single numerical variable

Question 10

mode

Answer 10

• interval corresponding to the highest peak in the frequency distribution

Question 11

bimodal

Answer 11

• frequency distribution having two distinct peaks

Question 12

symmetric

Answer 12

• frequency distribution having frequencies on the left half of the histogram mirror the frequencies on the right half

Question 13

skewed

Answer 13

• frequency distribution that is not symmetric for a numerical value

Question 14

uniform

Answer 14

• frequency distribution having level frequency distribution (all frequencies are around the same range)

Question 15

outliers

Answer 15

• observation well outside of the range of values of other observations in a data set

Question 16

how to draw a good histogram (6)

Answer 16

• each bar must rise from baseline of 0
• no spaces between each bar
• “left closed” intervals: value 70 falls into the interval 70-72 rather than 68-70
• number of intervals should best show patterns and exceptions in the data
• use readable numbers for breakpoints (0.5 rather than 0.486)
• include total number of individuals in legend

Question 17

contingency table (2)

Answer 17

• used for multiple associated categorical variables

- gives the frequency of occurrence of all combinations of 2+ categorial variables

Question 18

grouped bar graph (3)

Answer 18

• uses height of rectangular bars to display frequency distributions of 2+ categorical variables
• different categories of response variable are indicated by different colours
• bars are grouped by category of the explanatory variable treatment

Question 19

mosaic plot (3)

Answer 19

• area of rectangles to display relative frequency occurrence of all combinations of 2 categorical values
• bar area and height indicate the relative frequencies of the responses
• width of each vertical stack is proportional to the number of observations in that group

Question 19

mosaic plot (3)

Answer 19

• area of rectangles to display relative frequency occurrence of all combinations of 2 categorical values
• bar area and height indicate the relative frequencies of the responses
• width of each vertical stack is proportional to the number of observations in that group

Question 20

scatter plot (3)

Answer 20

• graphical display of two numerical values where each observation is represented as a point on a graph with two axes
• position on x-axis indicates measurement of explanatory variable
• position on y-axis indicates measurement of response variable

Question 21

positive association

Answer 21

• points tend to run from lower left to upper right

Question 22

negative association

Answer 22

• points tend to run from upper left to lower right

Question 23

absent association

Answer 23

• no discernible pattern in points

Question 24

strip chart

Answer 24

- graphical display of a numerical variable and a categorical variable in which each observation is represented as a dot

Question 25

violin plot

Answer 25

- graph that shows approximation of frequency distribution of a numerical variable in each group and its mirror image, association between numerical and categorical

Question 25

violin plot

Answer 25

- graph that shows approximation of frequency distribution of a numerical variable in each group and its mirror image, association between numerical and categorical

Question 26

line graph (2)

Answer 26

- uses dots connected by line segments to display trends over time in a summary measurement, such as mean, or other ordered series - steepness of line segment reflects speed of change between values

Question 27

map

Answer 27

- spatial equivalent of the line graph, using colour gradient to display a numerical response variable at multiple locations on a surface - explanatory variable: location in space

Question 28

how to make a good table (3)

Answer 28

- make patterns in the data easy to see (avoid clutter and arrange values to facilitate pattern detection) - represent magnitudes honestly (intervals of equal width) - draw table elements clearly (labels, units)

Question 29

what graph do you use for categorical data?

Answer 29

- bar graph

Question 30

what graph do you use for numerical data?

Answer 30

- histogram

Question 31

what graph do you use for multiple numerical values? (2)

Answer 31

- scatter plot | - line graph

Question 32

what graph do you use for multiple categorical variables? (3)

Answer 32

- grouped bar graph - mosaic plot - contingency table

Question 33

what graph do you use for one numerical variable and one categorical variable? (4)

Answer 33

- multiple histograms - cumulative frequency diagrams - violin plot/box plot (categorical explanatory, numerical response) - strip chart (categorical explanatory, numerical response)