Tallies and Counts in Statistics

In statistics, the words "tally" and "count" are subtlely different from one another, though both involve dividing statistical data into categories, classes, or bins. Although the words are commonly used interchangeably, tallies rely on organizing data into these classes while counts rely on actually enumerating the amount in each class.

Particularly when constructing a histogram or bar graph, there are times when we distinguish between a tally and a count, so it's important to understand what each of these means when used in statistics, though it's also important to note that there are a few disadvantages to using either of these organizational tools.

Both tally and counting systems result in a loss of some information. When we see that there are three data values in a given class without the source data, it is impossible to know what those three data values were, rather that they fall somewhere in a statistical range dictated by the class name. As a result, a statistician who wants to retain information about the individual data values in a graph would need to use a stem and leaf plot instead.

How to Effectively Use Tally Systems

To perform a tally with a set of data requires one to sort the data. Typically statisticians are confronted with a data set that is not in any type of order at all, so the goal is to sort this data into different categories, classes, or bins.

A tally system is a convenient and efficient way to sort data into these classes. Unlike other methods where statisticians can make mistakes before counting how many data points fall into each class, the tally system reads the data as it is listed and makes a tally mark "|" in the corresponding class.

It is common to group tally marks into fives so that it will be easier to count these markings later. This is sometimes done by making the fifth tally mark as a diagonal slash across the first four. For example, suppose you are trying to break the following data set into the classes 1-2, 3-4, 5-6, 7-8, and 9,10:

• 1, 8, 1, 9, 3, 2, 4, 3, 4, 5, 7, 1, 8, 2, 4, 1, 9, 3, 5, 2, 4, 3, 4, 5, 7, 10

In order to properly tally these figures, we would first write down the classes then place tally marks to the right of the colon each time a number in the data set corresponds to one of the classes, as illustrated below:

• 1-2 : | | | | | | |
• 3-4 : | | | | | | | |
• 5-6 : | | |
• 7-8 : | | | |
• 9-10: | | |

From this tally, one can see the beginnings of a histogram, which can then be used to illustrate and compare the trends of each class appearing in the data set. In order to do this more accurately, one must then refer to a count to enumerate how many of each tally marks exist in each class.

How to Effectively Use Count Systems

A count is different than a tally in that tally systems are no longer rearranging or organizing data, instead they are literally counting the number of occurrences of values that belong to each class in the data set. The easiest way to do this, and indeed why statisticians use them, are by counting the number of tallies in tally systems.

Counting is harder to do with raw data like that found in the set above because one must keep individual track of multiple classes without the use of tally marks — that's why counting is typically the last step in data analytics before adding these values to histograms or bar graphs.

The tally performed above has the following counts. For each line, all that we have to do now is state how many tally marks fall into each class. Each of the following rows of data are arranged Class : Tally : Count:

• 1-2 : | | | | | | | : 7
• 3-4 : | | | | | | | | : 8
• 5-6 : | | | : 3
• 7-8 : | | | | : 4
• 9-10: | | | : 3

With this system of measurements all arranged together, statisticians can then observe the data set from a more logical viewpoint and begin to make assumptions based off of the relationships between each data class.

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