Frequency Tables

A frequency table shows how many times each answer or value turns up in a set of data. The frequency is that number of times. If 7 pupils in a class have a dog, the frequency for dog is 7.

Adding all the frequencies gives the total frequency: how many people or things there are altogether. A table with frequencies 7, 10 and 3 is about 7 + 10 + 3 = 20 pupils.

In the exam you are often given a list of data and asked to complete a frequency table, for 2 marks, then to write down the mode, for 1 mark. Other questions ask you to read a total or a difference from a table, find a missing frequency, sort data into class intervals, or write down the modal class, usually for 1 or 2 marks each. Working out the mean or the median from a table is in separate notes.

A tally is a quick way to count. Draw one stroke for each item. The fifth stroke goes across the four before it, making a group of five. Groups of five are quick to count.

Count a tally in fives, then add the strokes left over. Here two groups of five and three more strokes make 13

To fill in a table from a list, go through the list once, in order. For each item, put a tally mark in its row and cross the item off the list. Then nothing is missed and nothing is counted twice.

Write each frequency as a number in the frequency column; the tally marks stay in the tally column. If an answer never turns up, its frequency is 0. Finally, check that the frequencies add up to the number of items in the list.

To find how many people or things the table is about, add the frequency column. Don't add the first column: that holds the answers or values, not how many.

"How many more" means subtract. If 12 chose red and 7 chose blue, then 12 - 7 = 5 more chose red. Read the words carefully: "at least 2" includes 2, but "more than 2" does not.

The mode is the answer or value with the highest frequency. The question may say modal, or "the most common". Write down the answer or value from the first column, not the frequency.

A frequency over the total frequency gives a fraction of the group. If 6 out of 24 pupils chose drama, then \frac{6}{24} = \frac{1}{4} of the pupils chose drama. This is also the probability that a pupil picked at random chose drama.

If two tables record the same thing for two groups, add the matching frequencies to make one table for everyone. Then add up the new frequencies for the new total.

When data has lots of different values, such as times or lengths, it is put into groups called class intervals. A grouped frequency table gives the frequency of each class.

Class intervals are written with inequalities. Here t is a time in minutes:

10 < t \le 20

This means t is more than 10 and less than or equal to 20. So 20 is in this class, but 10 is not.

A value on a boundary goes in the class where the sign beside that value has the "or equal to" line under it, \le. With these classes, a time of exactly 10 minutes goes in 0 < t \le 10

Some tables write the classes the other way round, such as 10 \le t < 20. Then 10 is in the class and 20 is not. Either way, the classes must not overlap, so every value goes in exactly one class.

The modal class is the class interval with the highest frequency. Write down the interval itself, such as 5 < t \le 10, not its frequency.

A grouped table doesn't show the exact values. You can count how many are more than 10 when 10 is a class boundary. You can't say exactly how many are more than 12, because 12 is inside a class.

A data collection sheet is a table you draw before you collect data. It has a column for the possible answers, a column for the tally and a column for the frequency.

This sheet is for counting vehicles passing a school. The Other row gives every vehicle somewhere to go, such as a motorbike or a tractor.

• Every possible answer needs a row. Add an "Other" row if you can't list them all.
• For numbers, use class intervals that don't overlap and leave no gaps, such as 0 \le t < 30, 30 \le t < 60, 60 \le t < 90
• Make the classes cover every value that could come up, for example with a last row for "90 or more".

A question may show a sheet and ask what is wrong with it. Look for classes that overlap, such as 0 to 10 and 10 to 20, which both include 10, for gaps between classes, and for answers that have nowhere to go.

If you know the total frequency, add the frequencies you know and subtract from the total. A table about 30 pupils with known frequencies 12 and 9 has 30 - 21 = 9 in the missing row.

Sometimes you are given a fact instead of the total, such as a percentage, or "twice as many chose tea as coffee". Use the fact to find the total or the missing number, then check that everything adds up.

A frequency counts people or things, so it must be a whole number. If you get a decimal, look again at your method.

• Mixing up the tally and frequency columns. Tally marks go in the tally column; the frequency is the number they make, not a fraction such as \frac{9}{20}
• Missing an item or counting one twice. Cross off each item as you tally it, then check the frequencies add up to the number of items.
• Tally marks that don't match the frequency. Count the tally in fives and check it against the number beside it.
• Giving the highest frequency as the mode. The mode is the answer or value with the highest frequency, not the frequency itself.
• Putting a boundary value in the wrong class. In 10 < t \le 20, the value 20 is in the class but 10 is not.
• Adding the wrong column for a total. The number of people is the total of the frequency column, not the first column.