## S2 Data

### Definitions

\(\mathbf{Population}\): the total group of individuals or items under consideration.

\(\mathbf{Sample}\): a group of individuals or items chosen from the population.

\(\mathbf{Data}\): the information collected from the sample or population.

\(\mathbf{Statistic}\): a number calculated from the sample data.

\(\mathbf{Parameter}\): a number calculated from the population data.

### Types of data

Data may be either qualitative (categorical) or quantitative (numerical)

\(\mathbf{Qualitative\,Data}\) (classified or labeled).

Data is put into non-numerical categories. Blood type, religion, cause of death, are all examples of qualitative data.

\(\mathbf{Quantitative\,Data}\) (counted or measured).

There are two types of quantitative data.

\(\mathit{Discrete\,Data:}\) data is put into categories depending on its counted number; for example, the number of children in a family.

\(\mathit{Continuous\,Data:}\) data is put into categories depending on its measured size; for example, height.

### Graphical Representation of Data

Qualitative/Categorical data is often represented by means of a bar chart or a pie chart.

Quantitative/Numerical Data is often represented by means of a frequency bar chart called a histogram.

#### Examples

- The table shows the percentage of Australian imports from various countries. This data can be represented on a pie chart so that comparisons are easier.

Country |
Imports % |
---|---|

China | 22 |

Japan | 20 |

South Korea | 8 |

India | 8 |

USA | 5 |

UK | 4 |

New Zealand | 4 |

Others | 29 |

- A group of school students were surveyed to find the number of children in their families. This data can be represented using a histogram.

No. of Children |
Frequency |
---|---|

1 | 13 |

2 | 21 |

3 | 11 |

4 | 4 |

5 | 3 |

6 | 1 |

7 | 1 |

Total |
54 |

### Exercise 1

Label each of the following as either a categorical or numerical variable. For the numerical variables label each as either discrete or continuous.

Hair colour

A persons religion

A persons height

Number of children in a family

The weights of babies born on a particular day

The number of crimes committed in Victoria each week

The distance traveled to work by the employees of a large company

The make of car driven by students at RMIT

Categorical

Categorical

Numerical – continuous

Numerical – discrete

Numerical – continuous

Numerical – discrete

Numerical – continuous

Categorical

### Exercise 3

A group of employees recorded the time that it took them to travel to work on a particular day (see table below). Represent this data using a histogram.

\(\mathbf{Time\:in\:minutes}\) | \(\mathbf{Frequency}\) |
---|---|

0 - < 15 | 2 |

15 - < 30 | 12 |

30 - < 45 | 23 |

45 - < 60 | 9 |

60 - < 75 | 3 |

75 - < 90 | 1 |

\(\mathbf{Total}\) | \(\mathbf{50}\) |

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