NSW Syllabuses

# Mathematics K–10 - Stage 5.3 - Statistics and Probability Single Variable Data Analysis §

## Outcomes

#### A student:

• MA5.3-1WM

uses and interprets formal definitions and generalisations when explaining solutions and/or conjectures

• MA5.3-2WM

generalises mathematical ideas and techniques to analyse and solve problems efficiently

• MA5.3-3WM

uses deductive reasoning in presenting arguments and formal proofs

• MA5.3-18SP

uses standard deviation to analyse data

## Content

• investigate the meaning and calculation of standard deviation using a small set of data
• explain why the standard deviation is calculated using the squares of $$(x-\bar{x})$$ for all data values in a set of data (Communicating, Reasoning)
• find the standard deviation of a set of data using digital technologies
• investigate and describe the effect, if any, on the standard deviation of adding a data value to the set of data, eg adding a data value equivalent to the mean, or adding a data value more or less than one standard deviation from the mean (Problem Solving, Reasoning)
• investigate and describe the effect, if any, on the standard deviation of altering all of the data values in the set of data by operations such as doubling all data values or adding a constant to all data values (Problem Solving, Reasoning)
• use the mean and standard deviation to compare two sets of data
• compare and describe the spread of sets of data with the same mean but different standard deviations (Communicating, Reasoning)
• compare and describe the spread of sets of data with different means by referring to standard deviation (Communicating, Reasoning)

### Background Information

It is intended that students develop a feeling for the concept of standard deviation being a measure of the spread of a symmetrical distribution, but without going into detailed analysis. When using a calculator, the  button or equivalent for standard deviation of a population will suffice.