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Graphical statistical representations

Of course, in addition to purely mathematical calculations, there are also many graphical representations of statistics in the statistics, which represent the data purely visually and allow for various analyzes, depending on the set goals. Different types of charts are becoming more common for visualization of end results. But before we get to the end results, for most analysts, the trend, the dynamics, the range distribution and other parameters is important. Here is an example of preliminary preparation of the final results – easy enough to implement – Stem and Leaf diagram in statistics.

The stem and leaf diagrams can be used at the same time to analyze data and present it. This is a way to show their values ​​and their relationship to other data.

A stem – leaf is a method of representing the frequency with which certain groups of values ​​appear. You can make a frequency distribution table or histogram for the values, or you can use the stem-leaf diagram and let the numbers show almost the same information.

To make a stem-and-leaf plot, create the “stem” by listing the largest place-value digits to the left of a vertical line. The remaining digits will be written to the right of the vertical line to create the “leaves”. We know, that sounds pretty abstract. This plot is better explained using an example, so let’s dive into one.

You have obtained the following results at the matriculums after grade 7:

91, 95, 53, 68, 79, 84, 87, 72, 71, 69, 65, 89, 84, 83, 72

Or transferred to the six-point system:

From 44 to 57 points – 4.00-4.5

From 58 to 71 points – 4,5-5

From 72 to 85 points – 5 – 5.5

From 86 to 99 points – 5.5 – 5.99

And 100 points – full 6 you can safely present the data in the performance report as follows:


The conversion ranges are wide enough, you are a responsible teacher and you want to increase your academic performance next year, so you need a slightly different approach.

The largest place value that all the data have in common is the tens place. These digits will be our stems. We list these from least to greatest. Some people arrange them from greatest to least, but the conclusions are actually important, not the order of the numbers.



stem leaf

On the left side of the table, in a column in ascending order, we record the decimals. In the right part in random order the units, corresponding to the decimal. In other words, every number has a “stem” – the senior figure and the “leaf” – the junior one.


stem leaf
5 3
6 8 9 5
7 9 2 1 2
8 4 7 9 4 3
9 1 5

Now rearrange the numbers so that each row is in numerical order (least to greatest).



stem leaf
5 3
6 5 8 9
7 1 2 2 9
8 3 4 4 7 9
9 1 5

Once the raw data is recorded in this form, you are given a clear and easy-to-evaluate table in which the raw data is sorted and it is easy to see the distribution of the data as well as the area with the most commonly obtained test results as well as the final values ​​- both the weakest and highest. Overall, the test scores are more than good considering your school average. But it is a matter of proper individual educational approach to the person with the lowest score for increasing his or her success rate.

If you are interested in, calculate the mean of the grade and the median for these values.

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