Question

Stem 3, 2, 1, 0    Leaf 177, 3444, 4699, 089 a. How many observations were in the original data​ set? b. In the bottom row of the​ stem-and-leaf display, identify the​ stem, the​ leaves, and the numbers in the original data set represented by this stem and its leaves. c.​ Re-create all the numbers in the data set and construct a dot plot.

Answer 1

A stem plot is used to represent data of samples with small range and small number of data points.

The stem of the plot represents the initials of the value except the units place while the leaves represent the units place. The stems have only one value while the leaves contain several values.

For example, the first row of the given stem plot represents the following data - 31,37,37.

Note that the value 37 is repeated 2times and 31 repeated 21times

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Based on the understanding above we can now answer the following questions -

a)

The number of observations would be same as the number of total leaves because the leaves represent the unit place of all the numbers. For example there are 3 leaves in the stem of 3 so there are 3 values (31,37,37.).

So, total number of observations = total number of leaves = 3+4+4+3 = 14

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b)

The left hand side represents the stem while those on right represent the leaves.

So, in the last row,

Stem = 0

Leaves = 0,8,9

Number of original data set represented by this stem and its leaves = number of leaves in this stem = 3

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c)

So, the sample data can be represented

31
37
37
23
24
24
24
14
16
19
19
0
8
9

#Dot plot