Statistics & Probability

What this covers

• Telling statistical questions from ones with a single answer, and describing a data set by centre, spread and overall shape
• Calculating and choosing between mean, median, mode, range, interquartile range and mean absolute deviation, including how each responds to an outlier
• Building and reading dot plots, histograms and box plots, including choosing bin widths and finding the five-number summary
• Using random samples to make inferences about a population, and comparing two populations using the difference in medians or means relative to spread
• Finding theoretical probability of a simple event, expressing it as a fraction, decimal and percent, and predicting relative frequency over many trials
• Listing sample spaces for compound events with organised lists, tables and tree diagrams, and running simulations to estimate probabilities

Where learners get stuck

Treating the mean as always the best measure of centre

Students learn 'average' as a single procedure long before they meet skewed data. When one very large value pulls the mean away from most of the data, they trust the calculation over the picture. Working through the same data set with and without the outlier, and looking at the dot plot alongside both statistics, makes the choice concrete.

Reading a box plot as if the four sections contain different amounts of data because they are different widths

Every other graph they have met uses length to show quantity, so a long whisker reads as 'more data here'. In a box plot each section holds about 25% of the values, and a long section means those values are spread out. Rebuilding a box plot from the original dot plot is usually what fixes this.

Expecting a probability of 1/2 to produce exactly 5 heads in 10 flips, or believing a run of heads makes tails 'due'

Probability is introduced as a fraction, which feels like a promise about a specific set of trials. Students also carry an everyday sense of fairness into independent events. Simulating 10, 50 and 200 trials and watching the relative frequency settle down shows what the number actually predicts.

What a session looks like

Sessions run as spoken back-and-forth. Evelyn poses a data set or a chance situation, asks the student to talk through what they notice before calculating, and pushes for the reasoning behind each choice: why median here, why this bin width, why a tree diagram rather than a list. Because it is voice-based, work involving graphs is handled by describing values, quartiles and shapes out loud, with the student sketching on their own paper. Wrong answers are followed up with a question rather than a correction, and a session often ends with the student summarising a data set in one or two sentences of plain English.

Helpful to know first

• Fluency with fractions, decimals and percents, including converting between them
• Adding, subtracting, multiplying and dividing multi-digit numbers and decimals
• Plotting and reading values on a number line, including ordering a list of numbers
• Basic familiarity with ratios and part-to-whole comparisons

Questions

What statistics does my child need to know before high school?

By the end of grade 8 students are generally expected to summarise a data set with mean, median, IQR and mean absolute deviation, build and interpret dot plots, histograms and box plots, use random samples to draw conclusions about a population, compare two data sets, and find probabilities of simple and compound events including with tree diagrams and simulations.

Why does my child get the right mean but the wrong median?

Almost always because the data was not put in order first, or because they missed the two-middle-values rule when the count is even. It is a procedural habit rather than a gap in understanding, and it is fixed by ordering the list out loud every time before finding the middle.

Is probability at this level the same as the probability taught in high school?

It is the foundation of it. Grades 6-8 focus on sample spaces, theoretical versus experimental probability, and compound events using lists, tables and tree diagrams. Formal conditional probability, permutations and combinations, and probability distributions come later.

Can this be tutored by voice if the topic involves graphs?

Yes, with the student working on paper. Evelyn describes data sets and asks the student to read back values, quartiles, bin counts and shape descriptions. Much of the difficulty at this level is in interpretation and choice of measure, which is verbal work.