week 3 - visualisation

Question 1

Showing Data for A Variable - Relative Freq.

Answer 1

• proportion of observations having a given measurement
• Calc. freq/total number of observations
• Proportion of occurrences of each value in the data set.
• Describes the fraction of occurrences of each value of a variable.

Question 2

Showing Data for A Variable - Freq. Table & Bar Graph (Categorical)

Answer 2

• Freq. table = text display of the # of occurrences of each category in the data set.
• Bar graph uses height of rectangular bars to visualize the freq of occurrence of each category.

Question 3

Showing Data for A Variable - Making a Good Bar Graph

Answer 3

• Illustrating freqs in each group.
• Eye compares the areas of the bars → must be equal width
• Categorical variable = nominal → order by freq. of occurrence
• Ordinal categorical variable → order naturally
• Bars should be separate

Question 4

Showing Data for A Variable - Pie Charts

Answer 4

• Used to display freq. of categorical variables
• Uses colour wedges around circumference of circle to rep freq.
• Eye = more difficulty comparing freq. of diff. groups
• Hard to compare 2+ pie charts side-by-side

Question 5

Showing Data for A Variable - Histograms

Answer 5

• Shows data for single numerical variable
• Histogram uses the area of rectangular bars to display freq.
• Splits data values into intervals/bins of equal width
• Freq. of observations falling into each bin = displayed.

Question 6

Showing Data for A Variable - Describing Histogram Shape

Answer 6

• Reveals the shape of a freq dist.
• Any interval of the freq dist that = noticeably more freq than surrounding intervals = peak.
• Mode = highest peak.
• Bell-shaped freq dist = 1 peak in the center of the range of observations.
• A freq dist w/ 2 peaks = bimodal
• Frequency dist = symmetric → left = right
• If a freq dist = not symmetric → skewed.
• Left skew = -ve
• Right skew = +ve

Question 7

Showing Data for A Variable - Outliers

Answer 7

• Extreme data points lying well away from the rest of the dataset
• Result from mistakes in recording the data → can be removed
• May rep real observations from nature → leave in

Question 8

Showing Data for A Variable - Making a Good Histogram

Answer 8

• Choice of interval = affect conclusions
• Each bar must start from 0 → area = proportional to freq.
• No space betw. bars
• No strict rules on # of bars

Question 9

Showing Assoc. Betw. 2 Variables & Diffs Betw. Groups - Categorical Variables

Answer 9

• 2 categorical variables = associated → relative freqs for 1 variable = differ among categories of the other variable.
• To reveal such assoc → use a contingency table/mosaic plot/ grouped bar graph.
• Contingency table = freq table for 2+ categorical variables b/c shows how the freqs of categories in a response variable
• Cell = 1 combo of categories of row & column variables
• Explanatory = column
• Response = row

Question 10

Showing Assoc. Betw. 2 Variables & Diffs Betw. Groups - Grouped Bar Graph

Answer 10

• Uses heights of rectables to graph the freq. of occurrence of all combos to 2+ categorical variables
• Includes diff categories for response variables = repped by diff colours

Question 11

Showing Assoc. Betw. 2 Variables & Diffs Betw. Groups - Mosaic Plots

Answer 11

• Treatment groups = stacked on top of each other
• Bar area & height = relative freq of response
• Easier to see assoc. betw variables
• Assoc. = vertical position at which colours meet = differ betw stacks
• No assoc. = meeting point = be the same
• Width = proportional to # of observations in that group
• Only provides relative freqs not absolute freq

Question 12

Showing Assoc. Betw. 2 Variables & Diffs Betw. Groups - Scatter Plots

Answer 12

• Assoc betw numerical variables
• Can +ve or -ve or 0 correlations

Question 13

Showing Assoc. Betw. 2 Variables & Diffs Betw. Groups - Strip Plots

Answer 13

• Assoc betw a numerical & categorical variables
• Explan variable = categorical
• Need to spread/jitter points along horizontal axis to reduce overlap → points = easier to see
• Each observations reps a dot

Question 14

Showing Assoc. Betw. 2 Variables & Diffs Betw. Groups - Violin Plots

Answer 14

• Uses compact visual summary
• Approxs the freq dist for each group (sim to histogram)
• Dist = smoothed & shown w/ mirror image
• Central dot = mean

Question 15

Showing Assoc. Betw. 2 Variables & Diffs Betw. Groups - Multi Histograms

Answer 15

• Histogram for each group
• Each plot must be stacked above one another → easier to compare
• Use same scale for each

Question 16

Showing Trends in Space & Time - Line Graph

Answer 16

• Uses dots connected by lines to display trends over time
• Help show temp pattern easily
• Steepness reps changes between one point to the next
• Area under two points = proportional to total number during that time

Question 17

Showing Trends in Space & Time - Maps

Answer 17

• Spatial equiv of line graph
• Uses colour gradient to rep numerical response @ multi locations on surface
• Explan variable = space, political/geographical boundaries
• Used to show measurements @ locations