Construct an ordered stem-and-leaf diagram
Stem and Leaf diagrams, also known as a leaf plot, are a basic tool for displaying data.
They help us to order the data, and easily turn it into something that starts to look like a picture. We can use it to group data together and start to quickly make sense of data, compared to just having it in a long list.
From stem and leaf diagrams it is possible to calculate the mean, median, mode and range.
The following are the heights (in cm) of 25 people:
166, 154, 142, 147, 164, 173, 178, 156, 158, 171, 182, 165, 145, 150, 153, 149, 154, 143, 151, 164, 157, 149, 164, 141, 155
Looking at the data like this would make it quite difficult to find out the median, mode and range. We can use a stem and leaf diagram to help make data easier to understand.
To make things easier for us, we can sort the data in ascending order:
141, 142, 143, 145, 147, 149, 149, 150, 151, 153, 154, 154, 155, 156, 157, 158, 164, 164,
164, 165, 166, 171, 173, 178, 182
From the name of the diagram, we are going to split the numbers into 'stems' and 'leaves'. For example, for the number 142. We could take 14 to be our stem and 2 to be our leaf.
So our stem and leaf diagram will look like this:
|Key:17|3 means 173|
Now it is easier to see what the median, mode and range for our set of data
The median is the middle number. If there are n numbers, the median will be the (n+1)/2 th value. So the position of the median for this set of data will be (25+1) /2 = 13. Which looking at the diagram (counting from 141) is 155.
The mode is the value that occurs most often. In this case it is 164. We can see clearly from the diagram that 164 is shown 3 times, whereas 149 and 154 occur only twice.
The range is the difference between the highest and lowest number. Here it is 182-141 = 41.
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