Statistics & Data Science Learning Path
High School (9–10) Statistics & Data Science
Explore structured statistics & data science courses, solved problems, simulations and Python activities.
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Sampling Variability and Sample Size
Ask forty students how they come to school, then ask forty others. The two answers differ, and neither is wrong. Watch many samples scatter around the truth, and draw the pattern they make. Then find out how fast that scatter shrinks when the sample grows, and why a sample of a thousand works as well for a city as for a country.
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Confidence Intervals for Proportions and Means
A news report says that 52% of people back a new park, plus or minus 3 points. Where do the 3 points come from, and what do they promise? Build an estimate with a margin of error, check when the formula for a proportion can be trusted, and plan the size of a survey. Then run a hundred surveys by simulation and see what a 95% confidence level really means.
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Testing an Idea with Simulation
A coin lands heads 34 times in 50 tosses. Is it fair, or is that just luck? Answer the question by letting a computer toss a fair coin thousands of times, and see how often luck alone does as well. Use the same idea to test a new teaching method by shuffling two groups. Then learn what a p-value is and is not, the two kinds of error, and why a study that runs many tests will nearly always find something.
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Scatter Plots and Correlation
Ten students tell you how long they practise typing and how fast they type. Put each student on a graph as one dot, and a pattern appears. Learn to read that pattern for direction, form and strength, to measure it with the correlation coefficient r, and to spot the cases where r gives the wrong picture.
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The Least-Squares Line
A school canteen sells more cold drinks on hot days. How many should it order for tomorrow, when the forecast says 27 degrees? Draw a straight line through the cloud of points and read off a prediction. Learn which line fits best and why, what its slope and intercept say in words, and how the leftovers, the residuals, tell you when to trust it.
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Correlation and Cause
In a seaside town, the weeks with more ice creams sold are also the weeks with more sunburn. Does ice cream burn the skin? Of course not. Learn to look for the hidden variable behind a correlation, and to see how combining groups can turn a result upside down. Then straighten a curved pattern with a logarithm, and read a claim in the news with care.
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Random Variables and Expected Value
Pick a student at random and ask how many brothers and sisters they have. The answer is a number, and it changes from student to student. Learn to write down the chances of every value, to find the long-run mean that a simulation settles at, and to measure how far the values spread around it. It suits a curious secondary-school student and any adult who wants the ideas behind the formulas.
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Counting Successes: The Binomial Model
Plant ten seeds that each grow with the same chance. How many will come up? Learn when a count of successes follows the binomial model, how to find the chance of each count, and where the counts centre and how widely they spread. A simulation of thousands of packets shows the formula at work. It suits a curious secondary-school student and any adult who wants the ideas behind the formulas.
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The Normal Distribution and Its Areas
Measure the heights of a few hundred people and draw a histogram. A smooth bell shape appears. Learn to describe that bell curve by its mean and standard deviation, and to find the share of values in any range from a z-score. Then judge when the normal model fits a data set and when it does not. Python works out every area. It suits a curious secondary-school student and any adult who wants the ideas behind the formulas.
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Long-Run Chance and the Addition Rule
A made-up record says the school bus was late on 21 of 75 days. Is that a probability? Learn to find a probability from data and from equally likely outcomes, and watch a simulation settle down as the number of tries grows. Then add chances with a Venn diagram, and use the complement when it is easier to count what does not happen.
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Independence, Trees and Streaks
Two alarms guard one door. If each works most of the time, how likely is it that at least one rings? Learn when two chances can be multiplied, draw probability trees for draws with and without replacement, and see why a big population makes the two kinds of draw almost the same. Then meet the gambler's fallacy, and find out by simulation how long the streaks in a random sequence really are.
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Two-Way Tables and Fair Games
A made-up survey asks students two questions and puts the answers in a table. What does the table say about one answer once you know the other? Learn to read a conditional probability straight from a two-way table, to check whether two things are independent, and to work out the expected value of a game. Then run the game a hundred thousand times in Python and see the average land where the rule said.
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