Oscar Bonilla

Oscar Bonilla

Oscar Bonilla

This is a way to visualize the distribution of a dataset using the original values.

The first or first digits from left to right represent the stem and the last digit represents the sheet, this stem and this leaf are separated by a vertical line.

To understand better observe the following example:

Temperature data are available in degrees Fahrenheit in a chemistry experiment of -42º, -12º, 5º, 8º, 9º, 23º , 24º, 25º, 26º, 60º, 27º and 111º.

They are requested to be presented on a stem-leaf diagram.

The data must be sorted from minor to major, a vertical line is made to separate the stem from the leaf and finally the data is entered starting with the negative and ending with the positive ones.

In this case the stems have tens and hundreds and leaves the unit.

The next histogram was created with the previous values, note the similarity as to the distribution of the set of data where the difference lies in the position of the observed values, in the histogram the frequencies (leaves) and the X axis (the stems) are observed on the Y axis.

There is a small difference since the histogram has 7 classes and in the stem and leaf diagram there are 6 classes but this is defined by the user in the histogram so it should not be a problem.

One advantage of making a stem and leaf diagram is to be able to obtain the original values ​​by applying scientific notation.

The above is to visualize the data as a stem-chart.hands multiplied by a base 10 and raised to an exponent "a". Note that a vertical line is no longer used to separate the stem and leaf diagram, but to use a "dot".

In the above example, the stem I leaf, -4 I 2 needs to be displayed as a stem-leaf -4.2 and then multiplied by 10 to the exponent 1 and thereby obtain the original value -42.

Performing the above multiplication forces the decimal point to move a position to the right, thus achieving the value -42.0.

Same situation occurs on stem l leaf 11 1 which, when viewed as a stem. 11.1, and being multiplied by 10 to exponent 1, this decimal point is shifted to the right, generating this the original value 111.0.

Caution: if the deciduous decimal point is shifted to the left, resulting in a -0.42 and -1.11 respec- tively, the decimal point is multiplied by a base 10 and the values ​​are incorrect

The Minitab program for statistical purposes is one of the few that generate a stem and leaf diagram, this link describes it if you want to know more.

Example
To make a stem and leaf diagram in Minitab you must do the following:

With Microsoft Excel data is tabulated by obtaining the following database .

Or you can download the database already in Minitab with extension.MTV Download it .

, you will need to copy and paste the data from an Excel sheet into a Minitab worksheet.

Then in Minitab locate the "graphic" tab and the "stem and leaf" option.

When doing this, open the stem and leaf window in it it is necessary to select with a click the variable that you want to analyze, the next step is to left click the "Select" button and finally click the accept button.

The result is the following stem and leaf diagram: / p>

The generated diagram shows on the right side the leaf (one digit for each observation), in the center to the stem and in the left side the counts with intervals of 5 units.

This generates 12 groups distanced as follows (120-124), (125-129), (130-134), (135-139), (140-144), (145-149), (150-154), (155 -159), (160-164), (165-169), (170-174) and (175-179).

The diagram shows on the left side a count in parentheses this indicates that is where the median divides the data set into 2 groups.

The counts are cumulative from above to the middle and down to the middle generating a total count of 250 (71 + 60 + 119).

The next histogram was created to compare it with the result of the stem-leaf diagram of the stem-leaf database (the one that was given to download).

To obtain this histogram we used the statistical software Infostat, with the following restrictions:

10 classes, class intervals of 5 units, a range of 57 tomatoes / plants, lower class limit of 123 tomatoes / plant and upper limit of

On the "X" axis is a minimum of 123 and maximum of 177, with 12 divisions.

The "Y" axis are absolute frequencies with a minimum of 0 and a maximum of 60 with 12 divisions.

When comparing the stem and leaf with the histogram generated and the restrictions described above, we can see the similarity between the two in terms of the distribution of the set of data.

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