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Units, Constants and Useful Formulas

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Stem Plots, Histograms and Ogives
---------------------------------

A:  5.8  5.9  6.1  6.2  6.8  7.3  7.4  7.6  7.7
8.1  8.1  8.2  8.8  9.2

B:  5.0  5.7  7.2  7.3  7.5  7.8  8.1  8.1 8.7
8.9  9.2

Leaf |Stem | Leaf
---------------------
0 7 |  5  | 8 9
|  6  | 1 2 8
2 3 5 8 |  7  | 3 4 6 7
1 1 7 9 |  8  | 1 1 2 8
2 |  9  | 2

Histograms and Ogives
---------------------

Consider the integer data:

02, 07, 16, 21, 31, 03, 08, 17, 21, 55
03, 13, 18, 22, 55, 04, 14, 19, 25, 57
06, 15, 20, 29, 58

Range:  2 .... 58

Class Width:

6 classes.

Class Width = Rounded up[(58 - 2)/# of classes]

= Rounded up(56/6)

= 10

Class Limits and Bpundaries

Limits   Boundaries  Freq.  Rel.   Cum.  Cum. Rel.
Freq.  Freq. Freq.
------  -----------  ----   -----  ----- ---------
02 - 11  1.5 - 11.5     5    0.20    5     0.20
12 - 21  11.5 - 21.5    5    0.20   10     0.40
22 - 31  21.5 - 31.5    6    0.24   16     0.64
32 - 41  31.5 - 41.5    1    0.04   17     0.68
42 - 51  41.5 - 51.5    0    0.00   17     0.68
52 - 61  51.5 - 61.5    8    0.32   25     1.00

The Ogive is the plot of Cumulative Relative Frequency (y)
versus class boundaries (x).

Stem and leaf plots preseve the actual data values while
Histograms do not.