# How to Truncate With Stem & Leaf

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A stem and leaf plot is one of many methods that can be used to organize statistical data. A natural way of ordering quantitative data is to organize the raw data from lowest to highest in a histogram-like chart. Stem plots split each number to create the stems and leaves of the data. Stems can be multiple digits but leaves must be single digits. Sometimes, to get the best result, you have to truncate the data. This is easy to do with stem and leaf plots.

Arrange the data set into numerical order. For instance if the values are 21, 44, 9, 58, 36, 27, 4, 19, 42 and 49, reorder them to 4, 9, 19, 21, 27, 36, 42, 44, 49 and 58. Divide each number into a stem value and a leaf value. In this example, the values range from 4 to 58, so the digit in the tens place becomes a stem value and the digits in the units place become leaf values. The stems are 0, 1, 2, 3, 4, and 5 and the stem leaf diagram would be: |0|4 9 |1|9 |2|1 7 |3|6 |4|2 4 9 |5|8

Determine how each data set should be split so that ideally there are 5 to 12 stem numbers (the example above has 6). For instance, if a data set contains values from 303 to 407, you can make the stems from 30 to 40 with single digit leafs. This will give you 11 stem numbers. If a data set contains values from 119 to 863, you should not treat it the same way as the previous data set, as you would have stems from 11 to 86, which is far too many. This is a sign you need to truncate to produce a stem and leaf plot.

Truncate a data set by simply removing one (or more) numbers from the end of the number. In the example above, 119 would become 11 and 863 would become 86. You would then have stems of 1 through 8 and a single digit leaf. Some data sets contain decimal numbers such as 2.48, 3.97, and you can truncate them by removing the final digit so that the result is 2.4 and 3.9.

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#### Tips

• Make sure your stem and leaf plot has a key. Without a key, it is unclear whether |5|8 is 0.58, 5.8, 58, 580, etc.

#### Warnings

• Truncating is different than rounding. Rounding turns 5.49 into 5.5, whereas truncating makes it 5.4.