# Binostat and the Normal Distribution

**Binostat allows students to experiment and gain a visualisation of the normal distribution. **

**The list below contains a collection of related materials for use in the classroom.**

### Binostat demonstration

If you don't have a Binostat this 33 second YouTube video demonstrates how one works. What happens to the balls as they are fed in? What shpe do you think will be made once they are all at rest?

### How Risky Is Life?

The Bowland Maths classroom project “How Risky is Life”, exploring the mis-match between our expectations and the realities of risk could be a good introduction to this topic, exploring a wide variety of statistical skills.

### Understanding Mean, Median, Mode and Range S4

In this DfE Standards Unit resource, students learn to understand the terms: mean, median, mode, range and explore the relationships between these measures and their relationship to the shape of a distribution. Students will have met the terms mean, median, mode and

range but they may not have a clear understanding of their meaning and the relationships between them. One purpose of this session is to expose and discuss any misconceptions. (GCSE Grades A - F)

### Interpreting Bar Charts, Pie Charts, Box and Whisker Plots S5

In this resource from the DfE Standards Unit, students will learn to understand and interpret bar charts, pie charts, and box and whisker plots. This session is in two linked parts. The first is matching pie charts to bar charts and secondly matching box and whisker plots to bar charts. Each part of the session starts with a whole group discussion to compare the newly-introduced type of representation, looking at its advantages, disadvantages and practical applications. Students then work in pairs. No prior knowledge is assumed, though it is helpful if students have encountered some of these ideas before. (GCSE Grades A-D)

### Normal Distribution

This interactive excel file contains a series of normal distribution curves to investigate.

The first sheet displays the standard normal curve. The mean and variance can be adjusted and compared to the original graph in order to show the effect this has on the shape of the curve.

The second sheet calculates the area under a standard normal distribution curve. The value of the upper limit, z, can be adjusted to explore how this effects the area. The following sheet calculates the area under the curve bounded between adjustable limits, z1 and z2. The final interactive sheet calculates the area of the two tails under the normal distribution curve.

The final sheet contains six questions based on the normal distribution Z ~ N (0, 12). The solutions and graphs can be revealed, and a set of six new questions created.

### The Normal Distribution: Adding Two Normal Distributions

In this activity students use the spreadsheet to simulate the generation of two normal distributions, each with different means and standard deviations. The spreadsheet models what happens when the two distributions are added together in order to explore whether the result is also normally distributed.

### The Normal Distribution: Parameter Gaps

In this activity students are set the challenge of finding missing values such that the mean and variance of a Poisson distribution, a Binomial distribution and a normal distribution makes sense. The solution sheet contains three possible solutions.

### The Normal Distribution: the Coffee Problem

In this activity, students are posed the problem of how a coffee machine should be adjusted to meet certain criteria by either adjusting the mean value of the coffee produced or adjusting the standard deviation. The presentation ends showing the solution to the problem.

### Sampling and Hypothesis Testing using the Normal Distribution: Generating Random Numbers

In this activity students are asked to challenge assumptions made surrounding the selection of random numbers. For simple random sampling every member of the population requires an equal chance of being chosen. Students are required to use this spreadsheet to investigate for numbers up to 30.

### Sampling and Hypothesis Testing using the Normal Distribution: Sample Mean Gap-Filler

In this activity, students are given a variety of normal distributions each containing missing numbers. Students are required to fit the given numbers into the correct place. This puzzle is designed to test students’ understanding of the mean and variance of the sample mean for a Normal distribution. A certain amount of number theory is required to find the unique answer. The resource contains an answer sheet and a set of teacher notes.

### Alex Bellos 'Alex's Adventures in Numberand'

Alex Bellos explores the idea of natural variation by looking at the weights of baguettes (an experiment that would be ideal to carry out in the classroom with a simple set of scales) in ‘Alex’s Adventures in Numberland (Chapter 10). His interpretation of his results (and an interesting historical aside) (p. 353-354) could be shared with the class in order to bring into context their own findings.