Exploratory Analysis and an Honest Chart
Before modelling anything, look: distributions, outliers, relationships between pairs. Then the chart that reports it has to make the truth easy to read, which rules out a truncated axis, a misleading area, and a colour scale nobody can order.
What a learner can do afterwards
- Choose the chart that suits a distribution, a comparison and a relationship
- Redraw a chart with a truncated axis and say what changed in the reader's impression
- Say what an outlier in an exploratory plot should prompt before it is removed
1 · Read
Before modelling anything, you look: shapes of distributions, strange points, and how pairs move together. A long tail on one side is called skew, and it is named after the side the tail points to. A scatterplot comes before any correlation number, because numbers alone hide shape.
You plot hours of practice against quiz score, one dot per student. The cloud slopes upward with one far dot. You check that student first instead of deleting the dot. If the check proves an error, like a broken sensor, you may remove it and write down why.
Match the chart to the job: a histogram or box plot for a distribution, a bar chart for a comparison, a scatterplot for how two numbers move together, and a line chart for change over time. In a relative frequency histogram each bar shows the fraction of the sample in its bin, so the bars add up to 1. A pie shows one set as fractions of a whole. Categories, like pet types, go in a bar chart, a pie or a frequency table, while a histogram bins measured numbers into ranges. Correlation needs two numbers per item, like height and weight.
A truncated axis stretches small gaps into big drama, so start bars at zero. When you redraw it honestly, say what the first version made the reader believe.
A frequency table lists each value with how often it happened. To find the mean, multiply each value by its frequency, add the products, and divide by the total of the frequencies, not by the number of rows. Say 3 homes have 0 pets, 2 have 1 pet, 2 have 2 pets and 1 has 4 pets. The products are 0, 2, 4 and 4, which make 10 pets across 3 + 2 + 2 + 1 = 8 homes, so the mean is 10 / 8 = 1.25 pets per home.
Plot first, match the chart to the question, start bars at zero, and question outliers before you touch them.
Practice items adapted from WeBWorK Open Problem Library problems by University of British Columbia contributors; Djun Kim (University of BC); Doug Torrance (Piedmont) (CC BY-NC-SA 3.0). Reading summaries adapted from wikiHow articles (How to Create a Graph in Excel: Beginner's Tutorial); license not recorded.
2 · Watch
به انگلیسیTake it off screen
Where it sits
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.