Charts & frequency tables

Discrete data can be shown in several ways. Edexcel expects you to read and draw each of these:

• Pictograms — a symbol stands for a number; watch the key (e.g. ⬤ = 4 people).
• Bar charts — bar height shows frequency; leave gaps between bars.
• Pie charts — the whole circle (360°) is the total; each slice angle = (frequency ÷ total) × 360°.
• Frequency tables — a tally of how many times each value occurs.

Pie chart tip: the angles must add to 360°. To read one back, a slice of angle A represents (A ÷ 360) × total.

Reading a pie chart

Mean, median, mode & range

Four values summarise a list of numbers:

• Median — the middle value when the data is put in order. For n values it is in position (n+1)÷2. With two middles, average them.
• Mode — the most common value (there can be none, one, or several).
• Range — largest − smallest. It measures spread, not average.

Misconception — mean vs median: the mean is dragged towards extreme values (outliers). If a dataset has one huge value, the median is usually the fairer "typical" value.

Your turn — the median

Your turn — the mean

Averages from tables

When data is in a frequency table, don't add the values once each — weight each value by how often it occurs.

Watch out: the total number of matches is Σf = 20, not the number of rows. Divide by the total frequency.

Your turn — mean from a table

Estimated mean of grouped data

With grouped (continuous) data we don't know exact values, so we use the midpoint of each class as a best estimate. The mean is then only an estimate.

Modal class = the class with the highest frequency (here 18 ≤ t < 22). The class containing the median is found from the running total of frequencies.

Your turn — estimated mean

Correlation & line of best fit

A scatter graph shows whether two quantities are related:

• Positive correlation — one goes up as the other goes up (points rise ↗).
• Negative correlation — one goes down as the other goes up (points fall ↘).
• No correlation — points are scattered with no pattern.

Warning: correlation does not prove one thing causes the other, and predictions outside the data range (extrapolation) are unreliable.

Name the correlation

Histograms & frequency density

When class widths are unequal, a normal bar chart misleads the eye. A histogram fixes this: it plots frequency density so that area = frequency.

Misconception: in a histogram the height is NOT the frequency — you must use frequency density, and the area of each bar gives the frequency.

Your turn — frequency density

Cumulative frequency & box plots

Cumulative frequency is a running total. Plot it against the upper class boundary to get an S-shaped curve, then read off key measures:

• Median — read across from ½ of the total (n ÷ 2).
• Lower quartile (LQ) — at ¼ (n ÷ 4); upper quartile (UQ) — at ¾ (3n ÷ 4).
• Interquartile range (IQR) = UQ − LQ — a measure of spread that ignores outliers.

Your turn — interquartile range

Which measure fits?

Tap the statistic that best matches each description.

Comparing two data sets

To compare data properly, Edexcel wants two things mentioned:

• An average — usually the median (or mean) to say which set is generally higher.
• A measure of spread — the range or IQR to say which set is more consistent.

Exam phrasing: "Class A had a higher median (so did better on average), and a smaller IQR (so was more consistent)." Always compare in context. A smaller IQR or range means the data is more consistent.

Reading the comparison

Measuring chance

Every probability lies on a scale from 0 (impossible) to 1 (certain), written as a fraction, decimal or percentage.

P(not A)

Sample space & the sum rule

The sample space is the list of all possible outcomes (e.g. for two dice, a 6×6 grid of 36 outcomes).

Mutually exclusive events cannot happen at the same time (like scoring a 2 or a 5 on one die). For these you add:

Key fact: the probabilities of a full set of mutually exclusive outcomes must sum to 1. So if a spinner lands on red, blue or green with P(red)=0.5, P(blue)=0.2, then P(green) = 1 − 0.5 − 0.2 = 0.3.

Add or multiply?

Decide whether each pair of events is mutually exclusive (you'd add) or independent (you'd multiply). Tap an event, then tap the correct box.

The AND (multiply) rule

Two events are independent if one happening does not change the other (like two separate coin flips). For independent events you multiply:

Misconception: P(A and B) = P(A) × P(B) is only true when the events are independent. If picking without replacement, the second probability changes — that is conditional probability.

Conditional probability

Conditional probability is the chance of B given that A has already happened, written P(B | A). It appears with picking without replacement and on tree diagrams.

Tree diagrams

A tree diagram organises two (or more) stages. Rules: multiply along branches (AND), add between separate paths (OR). Each set of branches from a point must sum to 1.

Venn diagram probability

A Venn diagram sorts outcomes into sets. The overlap is A and B (∩); the whole of both circles is A or B (∪).

Check: 12 + 6 + 8 + 4 = 30 = the whole set (ξ). P(plays football, F) = (12+6)/30 = 18/30 = 3/5.

Relative & expected frequency

Relative frequency (experimental probability) estimates probability from actual trials:

Expected frequency predicts how many times an event should happen:

Term ↔ definition

Tap a term on the left, then its matching definition on the right.

The rules to know

You've covered the whole of 4MA1 Statistics & Probability — representing data, averages, histograms, cumulative frequency & box plots, scatter graphs, and all the probability rules. Press Finish to see your score.