---
title: "Data & Statistics"
description: "49 topics in Mathematics, in the order they build on each other."
canonical: https://lightmysky.com/learn/mathematics/areas/data-and-statistics
source: https://lightmysky.com/learn/mathematics/areas/data-and-statistics.md
retrieved: 2026-10-19
---

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# Data & Statistics

49 topics in Mathematics, in the order they build on each other.

Page: https://lightmysky.com/learn/mathematics/areas/data-and-statistics

- [Sorting into categories](https://lightmysky.com/learn/mathematics/sorting-into-categories-mt_xppl18avyY): Classify objects into given categories, count the number in each category, and sort the categories by count
- [Data collection and display vocabulary](https://lightmysky.com/learn/mathematics/data-collection-and-display-vocabulary-mt_u5HkSxZECM): Read, write, and use the vocabulary of data collection and display — data, tally, tally chart, frequency, frequency table, survey, pictogram, bar chart, axis/axes, scale, label, category, discrete data, continuous data, line graph, pie chart — and apply these terms when collecting, organising, and presenting data
- [Sorting data into categories](https://lightmysky.com/learn/mathematics/sorting-data-into-categories-mt_ylXdiVRAYv): Organise and represent data with up to three categories by counting objects in each category and sorting categories by quantity
- [Pictograms and tally charts](https://lightmysky.com/learn/mathematics/pictograms-and-tally-charts-mt_c29FaCTNsx): Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables
- [Picture & bar graphs](https://lightmysky.com/learn/mathematics/picture-and-bar-graphs-mt_VhBH8wrFC6): Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories; solve put-together, take-apart, and compare problems using information presented in a bar graph
- [Scaled picture graphs and bar graphs](https://lightmysky.com/learn/mathematics/scaled-picture-graphs-and-bar-graphs-mt_r8XnXwRA6g): Draw a scaled picture graph and a scaled bar graph to represent a data set; solve one- and two-step comparison, sum, and difference problems using bar charts, pictograms, and tables
- [Bar charts and time graphs](https://lightmysky.com/learn/mathematics/bar-charts-and-time-graphs-mt_ChjMU2GDJa): Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs
- [Reading and comparing bar and line graphs](https://lightmysky.com/learn/mathematics/reading-and-comparing-bar-and-line-graphs-mt_H6LlpWgEYS): Solve comparison, sum, and difference problems using information presented in a bar graph
- [Reading tables](https://lightmysky.com/learn/mathematics/reading-tables-mt_Cqm8iy48UI): Complete, read, and interpret information in tables, including timetables
- [Statistical analysis vocabulary](https://lightmysky.com/learn/mathematics/statistical-analysis-vocabulary-mt_fmm-P17Vka): Read, write, and use the vocabulary of statistical analysis (mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation) with an understanding of what each term describes
- [Statistical Questions](https://lightmysky.com/learn/mathematics/statistical-questions-mt_4Ax4JPXJWD): Tell a statistical question from one with a single fixed answer: a statistical question anticipates variability ('How tall are the students in my class?' rather than 'How tall am I?') and is answered by collecting many values
- [Scatter Graphs](https://lightmysky.com/learn/mathematics/scatter-graphs-mt_BdAeZJUOir): Plot bivariate data on a scatter graph with correctly labelled axes and appropriate scales; describe the correlation (positive, negative, none) and draw an estimated line of best fit where appropriate
- [Populations, Samples and Bias](https://lightmysky.com/learn/mathematics/populations-samples-and-bias-mt_c7knRZy3Vt): Tell a population from a sample, judge whether a way of collecting data is fair, and say how a biased sample bends the conclusion.
- [Calculating the mean](https://lightmysky.com/learn/mathematics/calculating-the-mean-mt_Cg8VPguS_V): Calculate and interpret the mean as an average of a data set
- [Two-Way Tables](https://lightmysky.com/learn/mathematics/two-way-tables-mt_oD1Rgg52n3): Construct and read two-way tables that sort the same people by two categories at once (e.g., year group against preferred sport); use row and column totals and relative frequencies to judge whether the two categories are associated
- [Interpreting categorical data](https://lightmysky.com/learn/mathematics/interpreting-categorical-data-mt_1VSfm9yiLn): Interpret categorical data by asking and answering questions about totals, how many in each category, and how many more or less one category has than another
- [Line plots with fractions of a unit](https://lightmysky.com/learn/mathematics/line-plots-with-fractions-of-a-unit-mt_IHipFGTFEY): Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8); use operations on fractions to solve problems involving data in line plots (e.g. redistribute total equally)
- [Pie charts and line graphs](https://lightmysky.com/learn/mathematics/pie-charts-and-line-graphs-mt_bESTSBB0wK): Interpret and construct pie charts and line graphs; use these to solve problems
- [Stratified Sampling](https://lightmysky.com/learn/mathematics/stratified-sampling-mt_CWzOOk0609): Work out how many to take from each group so that a sample matches the proportions in the population, and round the results sensibly.
- [Sampling Methods and Their Trade-offs](https://lightmysky.com/learn/mathematics/sampling-methods-and-their-trade-offs-mt_aSsRQvnKa6): Compare simple random, systematic, stratified, quota and opportunity sampling by what each costs to run and what bias each risks, and describe the sampling frame a method needs.
- [Frequency tables, bar charts and pie charts](https://lightmysky.com/learn/mathematics/frequency-tables-bar-charts-and-pie-charts-mt_eKJG-0eC6D): Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type
- [Comparing data sets with averages and range](https://lightmysky.com/learn/mathematics/comparing-data-sets-with-averages-and-range-mt_XSXnTQoQ4l): Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers
- [Scatter Graphs & Correlation](https://lightmysky.com/learn/mathematics/scatter-graphs-and-correlation-mt_8atyuvPUZc): Describe simple mathematical relationships between two variables using scatter graphs, identify positive, negative, or no correlation, and use a line of best fit to make predictions
- [Averages from frequency tables](https://lightmysky.com/learn/mathematics/averages-from-frequency-tables-mt_5WF_Rhdb1X): Find the mean, median, mode and range from a frequency table by working with the counts instead of listing every value.
- [Estimating the mean from grouped data](https://lightmysky.com/learn/mathematics/estimating-the-mean-from-grouped-data-mt_3PHP7NLZAw): Estimate a mean from grouped data using class midpoints, say why the answer is only an estimate, and identify the modal class and the class holding the median.
- [Lines of Best Fit: Prediction and Its Limits](https://lightmysky.com/learn/mathematics/lines-of-best-fit-prediction-and-its-limits-mt_CnYCx1a0j5): Use a line of best fit to predict inside the range of the data, say why predicting far outside it is unsafe, and separate correlation from cause.
- [Quartiles and the Interquartile Range](https://lightmysky.com/learn/mathematics/quartiles-and-the-interquartile-range-mt_vN10d1I9dA): Find the median, the quartiles and the interquartile range of a data set, and use the interquartile range to compare how spread out two sets are.
- [Box Plots and Comparing Distributions](https://lightmysky.com/learn/mathematics/box-plots-and-comparing-distributions-mt_G_SnfEllzQ): Draw a box plot from a five-figure summary, and compare two distributions by their medians and their spread in words about the situation.
- [Cumulative Frequency Curves](https://lightmysky.com/learn/mathematics/cumulative-frequency-curves-mt_5U70qgbnST): Build a cumulative frequency table from grouped data, plot the curve at the upper bound of each class, and read off the median, the quartiles and how many lie above a value.
- [Histograms and Frequency Density](https://lightmysky.com/learn/mathematics/histograms-and-frequency-density-mt_0QAOgzD-Qw): Draw and read histograms where the classes have different widths, using frequency density so that area, not height, shows the frequency.
- [Standard deviation and variance](https://lightmysky.com/learn/mathematics/standard-deviation-and-variance-mt_eNpow5tIX2): Measure spread by how far the values sit from the mean on average, using squared deviations so that distances on both sides count. Compare data sets by mean and standard deviation together.
- [Sampling Distributions and the Central Limit Theorem](https://lightmysky.com/learn/mathematics/sampling-distributions-and-the-central-limit-theorem-mt_nugaEeUSii): For independent observations from one population with finite mean and finite positive variance, sample means centre on the population mean and have standard error σ / √n. Their standardised distribution approaches a standard normal one as n grows.
- [Setting Up a Hypothesis Test](https://lightmysky.com/learn/mathematics/setting-up-a-hypothesis-test-mt_JmpLNHK0Nf): State a null and an alternative hypothesis about a population, fix a significance level before looking at the data, and decide in advance what result would count as surprising enough to reject the null.
- [Testing a Binomial Proportion](https://lightmysky.com/learn/mathematics/testing-a-binomial-proportion-mt_ZJ8MTLYYKE): Test a claim about a proportion by finding the probability of a result at least as extreme under the null model, comparing it with the significance level, and writing the conclusion in the words of the situation.
- [Correlation and the Product-Moment Coefficient](https://lightmysky.com/learn/mathematics/correlation-and-the-product-moment-coefficient-mt_Rs_Z0P7ELJ): Summarise the strength and direction of a linear relationship in one number between -1 and 1, judge it against a critical value for the sample size, and keep it apart from any claim about cause.
- [The Regression Line and Making Predictions](https://lightmysky.com/learn/mathematics/the-regression-line-and-making-predictions-mt_tsjctRmkyE): Fit the least-squares line through the data, read its gradient and intercept in the units of the problem, and predict only inside the range the data covers.
- [The Law of Large Numbers and the Central Limit Theorem](https://lightmysky.com/learn/mathematics/the-law-of-large-numbers-and-the-central-limit-theorem-mt_NknG3L5rQp): Averages settle on the population mean as samples grow, and their distribution approaches a normal one whatever the population looked like. The two results are what makes inference possible at all.
- [Point Estimation: Bias, Variance and Consistency](https://lightmysky.com/learn/mathematics/point-estimation-bias-variance-and-consistency-mt_I374r2UU_i): An estimator is a random variable computed from a sample. Judge it by whether it is centred on the truth, how much it varies, and whether it settles down as the sample grows.
- [Maximum Likelihood Estimation](https://lightmysky.com/learn/mathematics/maximum-likelihood-estimation-mt_ZRTrcy7-KV): Write the probability of the observed data as a function of the unknown parameter and choose the parameter that makes the data most likely. Logs turn the product into a sum you can differentiate.
- [Confidence Intervals for Means and Proportions](https://lightmysky.com/learn/mathematics/confidence-intervals-for-means-and-proportions-mt_Pg2fPDW1sn): Turn the sampling distribution around to produce an interval and a stated coverage. The t-distribution replaces the normal when the population standard deviation is estimated.
- [Hypothesis Tests for a Mean with the t-Distribution](https://lightmysky.com/learn/mathematics/hypothesis-tests-for-a-mean-with-the-t-distribution-mt_ig2o39hAwh): Test a population mean using a one-sample t statistic when the population standard deviation is unknown. Check the sampling model, use the planned tails and degrees of freedom, and interpret the p-value assuming the null hypothesis.
- [Errors, Power and the Design of a Test](https://lightmysky.com/learn/mathematics/errors-power-and-the-design-of-a-test-mt_D7ZXbvSD0l): A Type I error rejects a true null hypothesis. A Type II error fails to reject a false null. Power is the probability of rejecting the null for a specified real effect, and depends on the test, significance level, variability and sample size.
- [Comparing Two Populations](https://lightmysky.com/learn/mathematics/comparing-two-populations-mt_v34rZkMfqr): Two means or two proportions, with the paired design treated separately because pairing removes a source of variation rather than adding a group.
- [Chi-Square Tests for Categorical Data](https://lightmysky.com/learn/mathematics/chi-square-tests-for-categorical-data-mt_yxc87pzaXX): Compare observed counts with the counts a model predicts. The same statistic serves goodness of fit, independence and homogeneity, with the degrees of freedom telling them apart.
- [One-Way Analysis of Variance](https://lightmysky.com/learn/mathematics/one-way-analysis-of-variance-mt_WYGK3Ktnqz): Compare several group means at once by splitting the total variation into a between-groups and a within-groups part. The F ratio asks whether the split is more lopsided than chance allows.
- [Simple Linear Regression and Inference on the Slope](https://lightmysky.com/learn/mathematics/simple-linear-regression-and-inference-on-the-slope-mt_W2huNTKsMj): State regression as a model with an error term, estimate its slope by least squares, then test and bound that slope. Residual plots are the check on whether the model was reasonable.
- [Multiple Regression and Model Diagnostics](https://lightmysky.com/learn/mathematics/multiple-regression-and-model-diagnostics-mt_TUx1tDF0jv): Several predictors at once, where a coefficient reads as the effect of one variable with the others held fixed. Correlated predictors, influential points and overfitting are the standing hazards.
- [How a Chart Can Mislead](https://lightmysky.com/learn/mathematics/how-a-chart-can-mislead-mt_z7yMoRWipf): The same numbers can be drawn to argue opposite things. A vertical axis that does not start at zero, a broken scale, unequal category widths, a 3-D effect, or a picture whose area grows faster than its height all change what a reader sees without changing a single value.
- [Who Was Asked: Samples and the People Left Out](https://lightmysky.com/learn/mathematics/who-was-asked-samples-and-the-people-left-out-mt_NQju6n-CKb): A statistic is about the people who answered, not the people you care about. Covers the difference between a population and a sample, why the method of asking decides who is missing, and how a poll of a self-selected group can be precisely wrong.