# 11.2.3 Constructing Your Own Tables

Sometimes, you may need to summarize a set of data and construct a table yourself. The first step is to decide how to sort the data into categories to stress the points you wish to make. For example, you may have collected data from a group of people that included their age.

Should you divide this into “under 25,” “25–40,” and “over 40,” perhaps? Your choice of category would depend on the kind of data that you have and what you want to show.

If you are counting the data elements yourself rather than using data that are already tabulated, you may want to employ some strategies to save time and minimize the chances for error. If you have a lot of data, for instance, you may find it useful to use a tally chart.

If you are unsure what a tally chart is or how to construct one take a look at this pencast (click on “View document”).

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First draw up a blank table with the row and column headings. Then, for each data value, put a vertical mark in the cell to which it belongs. When you have counted the item, you may find it helpful to cross it off your list, so that you know which item you are up to: It is easy to lose track! When you get to the fifth value in the cell, draw a diagonal line across the previous four marks (instead of a new vertical mark), making a “gate” like this: . This will make it easier to total the number in each cell, as you can add groups of five together quickly.

When you have completed the tally chart, check that the total number of tally marks agrees with the number of items on your data list.

For example, suppose you have volunteered to collect the lunch preferences for your colleagues at work. There is a choice of cheese (C) sandwich, ham (H) sandwich, or salad (S). Your colleagues have expressed their preferences as follows:

H S C H H C C H S C H H

The tallies for the lunch order would look like this:

You will need four cheese sandwiches, six ham sandwiches, and two salads.

There are different ways of drawing up a tally table. A statistician named John Tukey suggested using a square symbol, putting one dot in each corner for the first four items of data, then a side for each of the next four items and finally a diagonal line for each of the last two items. This symbol then represented ten data items.

Tukey felt that this symbol was easier to read and add up than the gate symbol. What do you think? Your answer will probably depend upon what you have used in the past!

## Activity: More About Tourists

Imagine you are the manager of a small Irish hotel that has guests of different ages and nationalities. You would like to know what kinds of guests visit your hotel, so you decide to summarize this information in a table.

You decide to divide the ages into groups: child (under 16), adult (16–60), and senior (over 60); and the nationalities into the categories Irish (Ir), British (B), Mainland European (E) and the Rest of the World (W).

From the room bookings the following data were collected. This is of the form 16E, where the number represents the age (16) and the letter represents the category (E), so 16E represents a 16-year-old guest from Mainland Europe.

16E | 7B | 24Ir | 26Ir | 46Ir | 43Ir | 5Ir |

50W | 55W | 13Ir | 13B | 15Ir | 61B | 8Ir |

37W | 48E | 8Ir | 62B | 49E | 6W | 55Ir |

11Ir | 9Ir | 12B | 62W | 65B | 65B | 67Ir |

13W | 12W | 54B | 72Ir | 61Ir | 48B | 61W |

15B | 62Ir | 67E | 10W | 27B | 12Ir | 31B |

35W | 8W | 42B | 43B | 15W |

Construct a blank table with a title, the source of the data and column and row headings corresponding to the categories above. Use a tally to determine the number of guests in each age group and each category in your table first. Then from the tally chart, construct the final table.

The data probably looks quite confusing—take your time and work methodically through the data to make sure you don’t miss any!

The title, column and row headings should make it clear to the reader what information is contained in the table—so think carefully about these.

### Answer

The final table should look something like the table below. You may have put the rows and columns the other way round.

#### Origin and Age Categories of Hotel Guests

Child | Adult | Senior | Total | |
---|---|---|---|---|

Irish
| 8 | 5 | 4 | 17 |

British
| 4 | 6 | 4 | 14 |

Mainland European
| 0 | 3 | 1 | 4 |

Rest of the world
| 6 | 4 | 2 | 12 |

Total
| 18 | 18 | 11 | 47 |

You can work out the total number of visitors either by adding together the numbers of children, adults and seniors , or by adding the numbers of Irish, British, Mainland European and “Rest of the world” visitors . These two totals should agree, so it is useful to work out both as a check.

Do you think that there is any other information that would be useful to include with this table? For example how old is a child or a senior?

11.2.2 Representing Data in Tables