Statistics - June 2006, Stage 4&5

Problems

problem icon

Substitution Cipher

Stage: 3 and 4 Challenge Level: Challenge Level:1

Find the frequency distribution for ordinary English, and use it to help you crack the code.

problem icon

The Mean Problem

Stage: 4 Challenge Level: Challenge Level:1

There are four unknown numbers. The mean of the first two numbers is 4, and the mean of the first three numbers is 9. The mean of all four numbers is 15. If one of the four numbers was 2, what were. . . .

problem icon

The Rescaled Map

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

We use statistics to give ourselves an informed view on a subject of interest. This problem explores how to scale countries on a map to represent characteristics other than land area.

problem icon

PDF

Stage: 5 Challenge Level: Challenge Level:1

Given a probability density function find the mean, median and mode of the distribution.

problem icon

Maximum Scattering

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?

problem icon

Over-booking

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2012. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.