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Since we've decided that a line plot may not be a useful graph for investigating variation, we must come up with a new representation based on groups of data. One such representation is called a stem and leaf plot. Note 2
Let's look at our data again:
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26 Responses to the Question |
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63 |
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67 |
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79 |
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75 |
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57 |
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72 |
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52 |
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89 |
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39 |
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59 |
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55 |
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68 |
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66 |
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86 |
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70 |
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52 |
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60 |
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64 |
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42 |
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54 |
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56 |
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82 |
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57 |
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65 |
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59 |
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33 |
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Notice that these data consist of two-digit numbers. The smallest data value is 33, the largest is 89, and there are data values in the 30s, 40s, 50s, 60s, 70s, and 80s. It would be reasonable to group the data by tens, and a stem and leaf plot can help us do this.
The first step is to organize the data in groups of 10. Each stem of a stem and leaf plot is determined from the leftmost digit(s) of each number -- in this case, this is the tens digit. For example, the stem of the first data value (63) is 6, and the stem of the data value below it (57) is 5.
To construct the stem and leaf plot, start by listing all possible stems within the range of the data:
The leaf of each data value in a stem and leaf plot is determined from the rightmost digit of each number -- in this case, this is the units digit. For example, the leaf of the first data value (63) is 3, and the leaf of the data value below it (57) is 7.
To construct a stem and leaf plot, go through the data list one value at a time, and record the leaf of each number beside the proper stem. For example, the first data value, 63, has stem 6 and leaf 3:
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26 Responses to the Question |
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63 |
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67 |
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79 |
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75 |
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57 |
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72 |
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52 |
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89 |
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39 |
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59 |
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55 |
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68 |
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66 |
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86 |
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70 |
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52 |
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60 |
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64 |
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42 |
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54 |
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56 |
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82 |
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57 |
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65 |
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59 |
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33 |
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If we move across the top row, the second data value (67) has stem 6 and leaf 7. Put this value next to the first leaf (3) already listed on stem 6. (The leaf entries do not have to be ordered at this time.)
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26 Responses to the Question |
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63 |
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67 |
|
79 |
|
75 |
|
57 |
|
72 |
|
52 |
|
89 |
|
39 |
|
59 |
|
55 |
|
68 |
|
66 |
|
86 |
|
70 |
|
52 |
|
60 |
|
64 |
|
42 |
|
54 |
|
56 |
|
82 |
|
57 |
|
65 |
|
59 |
|
33 |
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The next data value (79) has stem 7 and leaf 9:
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26 Responses to the Question |
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63 |
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67 |
|
79 |
|
75 |
|
57 |
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72 |
|
52 |
|
89 |
|
39 |
|
59 |
|
55 |
|
68 |
|
66 |
|
86 |
|
70 |
|
52 |
|
60 |
|
64 |
|
42 |
|
54 |
|
56 |
|
82 |
|
57 |
|
65 |
|
59 |
|
33 |
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