# How do you make a stem-and-leaf diagram for this data: 27, 19, 35, 28, 25, 16, 40, 39, 32, 29, 31

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A stem-and-leaf diagram was created by John Tukey and is used to summarize data without making any change in the data points being used. Here a column called stem is created with the first digit of the elements of the data. The final digit of each data point is written beside the corresponding first digit and arranged in ascending order. For the data points you have provided: 27, 19, 35, 28, 25, 16, 40, 39, 32, 29, 31 the stem-and-leaf diagram is:

Stem | Leaves

1 | 6 9

2 | 5 7 8 9

3 | 1 2 5 9

4 | 0

The purpose of the stem and leaf diagram to make the data visually reprenting. We can have the knowlege of spread , centre and shape and out line of of variation.

The representation contains the stem which are usually the leading ( ot the digits in highest pklace ) and the trailing digits are treated as on the leaf).

Example : In the given data if you rearang the data could be classified as:

10 to 19 group : 16,19

20 to 29 proup: 25, 27, 28,29

30 to 39 group: 31, 32 , 35, 39

40 to 49: 40.

We can represent the 10 to 16, in 10 to 19 group as below:

We show 16 and 19 in the stem 1 , as 1 is the leading digit in 16 and 19. The 6 in 16 and 9 in 19 wil be in leaf.

Similarl we write other groups . The stem and leaf representation of the given data is as below:

Stem : leaf

1 : 6 , 9

2 : 5 , 7 , 8 , 9

3 : 1 , 2 , 5 , 9

4 : 0

The representation also helps identify the quartiles , median easily.

Stem and leaf diagram is a semi-graphical representation of any set of data or value of a variable in which the data is first sorted serially in ascending order and then represented in rows, with each row representing the first most significant digit. For each entry in the data, the digits following his most significant digits are written in the corresponding row in ascending order.

Thus sorting the given data in ascending order we get:

16, 19, 25, 27, 28, 29, 31, 32, 35, 39, 40

This set of data has numbers with first significant digit ranging from 1 to 4.

Thus the stem and leaf diagram will have four corresponding rows. The complete diagram will the look as shown below.

Stem Leaves

1 6 9

2 5 7 8 9

3 1 2 5 9

4 0