### Beyond AP Statistics

#### Probability Basics

#### Small Samples

#### Distributions

#### Power

### Beyond AP Statistics

#### Probability Basics

#### Small Samples

#### Distributions

#### Power

# One-Way Tables

A one-way table is the tabular equivalent of a bar chart. Like a bar chart, a one-way table displays categorical data in the form of frequency counts and/or relative frequencies.

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A one-way table is distinguished from a two-way table (described in the
next lesson);
because the data entries in a one-way table
refer to *one* variable, whereas the data entries in a two-way
table refer to *two* variables.

## Frequency Tables

When a one-way table shows frequency counts for a particular
category of a categorical variable, it is called a
**frequency table**.

Below, the bar chart and the frequency table display the same data. Both show frequency counts, representing travel choices of 10 travel agency clients.

Choice | Frequency |
---|---|

USA | 5 |

Europe | 3 |

Asia | 2 |

## Relative Frequency Tables

When a one-way table shows relative frequencies (i.e., percentages or proportions)
for particular
categories of a categorical variable, it is called a
**relative frequency table**.

Each of the tables below summarizes data from the bar chart above. Both tables are relative frequency tables. One table shows relative frequencies as a proportion, and the other table shows relative frequencies as a percentage.

Choice | Proportion |
---|---|

USA | 0.5 |

Europe | 0.3 |

Asia | 0.2 |

Choice | Percentage |
---|---|

USA | 50 |

Europe | 30 |

Asia | 20 |

## Test Your Understanding

**Problem**

Twenty first graders were asked which color they liked best - red, green, or blue. Their responses appear below.

red, green, green, blue, red, blue, red, red, blue, red

red, blue, red, red, blue, red, blue, green, green, red

Which of the following one-way tables correctly summarizes responses from the first graders?

Table I

Choice | Frequency |
---|---|

Red | 0.5 |

Green | 0.2 |

Blue | 0.3 |

Table II

Choice | Proportion |
---|---|

Red | 50 |

Green | 20 |

Blue | 30 |

Table III

Choice | Percentage |
---|---|

Red | 10 |

Green | 4 |

Blue | 6 |

(A) Table I only

(B) Table II only

(C) Table III only

(D) None of the above.

(E) All of the above.

**Solution**

The correct answer is (D). None of the frequency tables is labeled correctly. Table I shows proportions, but the label says "Frequency". Table II shows percentages, but the label says "Proportion". And finally, Table III shows frequencies, but the label says "Percentage".

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