Chapter 5 exercises: Statistical Reasoning and Randomness
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Attempt these tasks before opening the worked answers. Use the chapter experiment notebook, or import NumPy as np and Pandas as pd in your own notebook. Retain your first attempt and explain each correction.
B2-05-E01 · Compare location summaries
Calculate mean and median and explain the influence of 40.
x=np.array([10.,12.,14.,40.])One hint after an attempt
Sort the values before identifying the middle.
B2-05-E02 · Compute a conditional probability
Under a fair-die model, calculate P(result>4 | result is odd).
die=np.arange(1,7)One hint after an attempt
Restrict the outcome space before counting successes.
B2-05-E03 · Separate spread and standard error
Calculate the sample standard deviation and estimated standard error of the mean; state the assumptions for using s/sqrt(n).
x=np.array([4.,6.,8.,10.])One hint after an attempt
Use n−1 for the sample variance, then divide s by sqrt(n).
B2-05-E04 · Original cultural-production challenge: all six tasks
Complete the original challenge: shapes, means, total, slices, threshold selection, logarithms, spread, square roots and a reproducible random comparison.
books=np.array([[120,150,180,210,190],[80,100,120,160,220],[90,130,170,200,250]])
decades=np.array([1970,1980,1990,2000,2010])One hint after an attempt
Check totals by rows, then verify the squared deviations independently.
Reflect and get feedback
Explain one result without looking at the code. Identify one boundary case that would change your method. An optional tutor prompt is: “Here is my attempt at B2-05-E04. Give one hint about the violated assumption; do not give the solution yet.” Then use the worked answers.