Chapters

# Frequency Part 2

In other sections of this guide, we taught you how to calculate the frequency of a data set. Specifically, you learned about the differences between cumulative and relative frequency, as well as how these are usually presented. We also showed you some basic visualizations you can make with data. Here, we’ll show you how to visualize and interpret frequency.

## Row and Column Frequency

As a reminder, the frequency of an observation is **how often** that thing occurs. In order to calculate the frequency of a variable, you simply need to count how many times it occurs, which is also known as the “count.”

Relative frequency is the frequency **relative to the whole**. There are two basic types of relative frequency, which deal with row and column frequencies. These two relative frequencies are best seen through an example. The table below lists the preference of three new soda flavours by gender.

Female | Male | Other Gender | Total | |

Flavour A | 398 | 556 | 146 | 1100 |

Flavour B | 659 | 450 | 91 | 1200 |

Flavour C | 230 | 300 | 470 | 1000 |

Total | 1287 | 1306 | 707 | 3300 |

Simply looking at this table, you may have a hard time understanding which flavour people prefer. A better way of analysing these results may simply be to take the relative frequency by row, which is finding the proportion of each number by the total of its row.

Female | Male | Other Gender | Total | |

Flavour A | 398/1100 = 36% | 556/1100 = 51% | 146/1100 = 13% | 100% |

Flavour B | 659/1200 = 55% | 38% | 8% | 100% |

Flavour C | 230/1000 = 23% | 30% | 47% | 100% |

Looking at the results, we can see the relative frequency of each flavour by gender, or the preference of flavour between genders. Meaning, for flavour A, we can see that more males preferred this flavour. For flavour B, women preferred this flavour over all the other genders, and so on.

However, we can also calculate relative frequency **for columns**, which simply takes the value divided by the column total.

Female | Male | Other Gender | |

Flavour A | 398/1287= 31% | 556/1306= 43% | 146/707= 21% |

Flavour B | 659/1287= 51% | 34% | 13% |

Flavour C | 230/1287= 18% | 23% | 66% |

Total | 100% | 100% | 100% |

As opposed to row relative frequency, the column relative frequency lets us know how the preference of flavour within each gender. For females, 51% preferred flavour B, 43% of males preferred flavour A and 66% of other genders preferred flavour C.

These tell us details about the specifics within each variable, whether it be for flavour type or for gender. Simple frequency will tell us only information about the data set **as a whole**. It is calculated by taking the value and dividing it by the total sample size.

Female | Male | Other Gender | Total | |

Flavour A | 398/3300= 12% | 556/3300=17% | 146/3300= 4% | 33% |

Flavour B | 20% | 14% | 3% | 36% |

Flavour C | 7% | 9% | 14% | 30% |

Total | 39% | 40% | 21% | 100% |

The frequency allows us to understand the preferences of the whole data set. We can interpret and say there were more males than other genders in our data set, at 40%. More people, regardless of gender, preferred flavour B at 36%.

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