Statistics
Frequencies and charts, two-way tables, mean, median and mode, variance and standard deviation, and how changes to the data move them. Statistics is tested in the Mathematics section of the Bocconi Test, which has 24 of the 50 questions (75 minutes in total, 2027/28 format). This guide covers it in 6 lessons, each with the rule that solves it and a diagram.
Absolute and relative frequencies
Relative frequency = count ÷ total, and the shares add up to 100%. Cumulative frequencies answer “at most”. Bar charts show categories, histograms classes of numbers, and a pie slice has angle = share × 360°.
Joint and conditional frequencies
A two-way table counts every combination of two features; the margins hold the totals. “The percentage of X who…” divides by the total of X. Compare groups by their rates, not their counts.
Mean, median and mode
Mean: the sum divided by the count, so sum = n · mean. Median: the middle of the sorted data (the mean of the two middle values when n is even). Mode: the most frequent value. One extreme value pulls the mean but barely moves the median.
Central tendency from a frequency table
The weighted mean is Σ xᵢnᵢ ÷ Σ nᵢ. Groups of different sizes combine through their sums, not by averaging the averages. The median is found with cumulative frequencies; grouped data use the class midpoints.
Variance and standard deviation
Variance is the mean of the squared deviations from the mean; the standard deviation σ is its square root. Shortcut: σ² = mean of the squares − square of the mean. Same mean does not mean same spread.
How changes to the data act
For y = a·x + b, the mean, median and mode become a·(old) + b; the range and σ are multiplied by |a| and ignore b; the variance is multiplied by a². A new value at the mean keeps the mean and lowers the variance.
What is the Bocconi Test format?
Online Bocconi Test for admission in academic year 2027/28, as published by Università Bocconi.
- Questions / time
- 50 / 75 minutes
- Distribution
- 24 mathematics · 11 reading · 6 numerical reasoning · 9 critical thinking
- Scoring
- +1 correct · 0 blank · −0.2 wrong
- Question languages
- English · Italian
- Three-option questions
- Some critical thinking questions have three options; a wrong answer there costs −0.33
- Minimum score
- Below 17 points the test is not considered for selection
- AI degree
- Mathematical and Computing Sciences for Artificial Intelligence also needs at least 11 of 24 points in mathematics
- Law test
- A separate test, 50 questions / 75 minutes: 5 mathematics · 11 reading · 6 numerical reasoning · 18 logic and critical thinking · 10 verbal reasoning; same scoring
Source: Università Bocconi, Online Bocconi Test page (checked October 7, 2026)
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