# Number in Statistics

*Keywords:*

AO elaboration and other teaching resources

These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (see Related Resources) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10 to 15 minute activity.

find the midpoint between two numbers

find the mean of two numbers

find the mean in a group of related numbers

Addition and subtraction, AM (Stage 7)

### Prior Knowledge

Add two and three digit numbers

### Background

The mean is a very important concept in many disciplines. In physics it is the understanding behind the centre of gravity as “moments about the origin” in 1, 2 and 3 dimensional bodies and indeed the definition of E(X) is this exact equation. In statistics the mean represents many other numbers in a very democratic fashion. The moving means of time series data link to graphing and trends. The mean is often confused with average. An average is a number that will represent others as a typical value of which mean, mode, and median are all examples. The median estimates the mean and in certain circumstances is a very good estimator. These exercises develop an understanding of the mean, and uses number and geometrical properties to calculate the mean.

### Comments on the Exercises

**Exercise 1
**Asks students to use different methods to find the number exactly midway between two numbers.

**Exercise 2**

Asks students to find the number exactly halfway between two numbers.

**Exercise 3**

Asks students to find the mean using addition and subtraction methods. For example, 6 + 9 = 15, 15 ÷ 2 = 7.5, and 9 - 6 = 3, 3 ÷ 2 = 1.5, 9 - 1.5 = 7.5.

**Exercise 4**

Asks students to explore the concept of the midpoint or mean using a balance beam model.

**Exercise 5
**Asks students to use the balance beam model to balance two weights against one weight.

**Exercise 6**

Asks students to use the balance beam model to balance more than two weights against multiple weights.

**Exercises 7, 8 and 9**

Asks students to find the mean of a regularly spread sequence of numbers e.g. 4, 8, 12, 16, 20.

Attachment | Size |
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NumberInStatisticsSheet.pdf | 29.92 KB |

NumberInStatisticsSheet.doc | 107.5 KB |