Topic 05 · 14 lessons

Data & Statistics

Statistics is how we turn a pile of numbers into a clear statement. How tall is a typical ten-year-old? Is a new medicine better than the old one? Will it rain tomorrow? Each question needs data, a sensible summary and an honest sense of uncertainty.

These lessons cover the core tools: averages, spread, charts and probability, and the common traps that make statistics misleading.

Lessons in this topic

5.1Sorting and Grouping ObjectsSorting means putting things into groups using a rule. Once things are sorted, you can count each group and compare them.
5.2Counting with Tally MarksA tally mark is a quick line you draw each time you count one thing. Every fifth mark crosses the first four, so groups of five are easy to count.
5.3Reading Tables and PictogramsA table lists data in rows and columns. A pictogram uses symbols, and the key tells you how many each symbol is worth.
5.4Bar ChartsIn a bar chart the height of each bar shows a count. Read the scale carefully, because bars between two marks need a sensible estimate.
5.5Line GraphsA line graph joins readings taken over time. Rising lines show increases, falling lines show decreases, and steep lines show fast change.
5.6Reading and Drawing Pie ChartsA pie chart shows parts of a whole as slices of a circle. Each slice angle is its share of 360 degrees.
5.7Charts and GraphsA good chart answers a question at a glance. The skill is matching the chart type to the kind of data and the question asked.
5.8Collecting Data and Asking Fair QuestionsGood data starts with a good question. A fair question is clear, has useful answer choices and is asked to a sample that represents everyone.
5.9Frequency Tables and Dot PlotsA frequency table counts how often each value occurs. A dot plot shows the same counts as stacks of dots along a number line.
5.10Mean, Median and ModeThree different answers to the question "what is typical?", each useful in different situations.
5.11Range and OutliersThe range is the largest value minus the smallest. An outlier is a value far from the rest, and it can change the range and the mean a lot.
5.12Chance: Impossible to CertainChance words describe how likely something is, from impossible at one end to certain at the other, with even chance in the middle.
5.13Introduction to ProbabilityProbability puts a number on uncertainty, from 0 for impossible to 1 for certain.
5.14Standard DeviationStandard deviation measures how far values typically sit from the mean. Small means tightly clustered; large means widely spread.

The big ideas

a)A summary loses detail: An average describes a typical value but hides the spread. Always ask what the summary leaves out.
b)Pick the right picture: Bar charts compare categories, line graphs show change over time and scatter plots reveal relationships.
c)Chance has a scale: Probability runs from $0$ (impossible) to $1$ (certain). Everything else sits somewhere in between.
d)Spread matters: Two classes can share the same mean score while one is tightly bunched and the other is all over the place.

Worked example

A fair average

Five friends have $2$ , $3$ , $3$ , $4$ and $18$ pets between them. Which average best describes a typical friend?

Mean: $(2 + 3 + 3 + 4 + 18) \div 5 = 30 \div 5 = 6$ .
Median: the middle value of the ordered list is $3$ .
Mode: the most common value is $3$ .
The value $18$ is an outlier that drags the mean upward. Only one friend has more than $4$ .

Answer: The median ( $3$ ) is the most representative average here.

Where you will meet it

Weather forecasts, opinion polls, sports rankings, medical trials and the recommendations on streaming services are all built on statistical summaries and probability.

The wider field

Data & Statistics also covers these ideas, which build on the lessons above:

Collecting data and surveys
Frequency tables
Sampling and bias
Correlation and regression
Normal distribution
Combined events