Ch 2. Frequency Distributions and Graphs PDF

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Ch 2. Frequency Distributions and Graphs...

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Chapter 2 – Frequency Distributions and Graphs 2-1 Organizing Data Frequency tables or frequency distributions: list categories (or classes) along with the number of scores that fall into each category. Ex. 1: Harvey is looking over employee productivity for his department. A new technician has worked for 20 weeks. The following is the technician’s weekly productivity in terms of well samples tested. 8 9 14 12 12 13 16 16 17 20 24 22 22 13 22 29 26 28 25 18 Make a frequency table. Samples tested 6-9 10-13 14-17 18-21 22-25 26-29 Total

Frequency 2 4 4 2 5 3 20

Note that there are several guidelines to be followed: 1. The class limits do NOT overlap (ie, 6 to 9 and 10 to 13 NOT 6 to 9 and 9 to 12). This makes sure that every number falls into only one class. 2. No classes are skipped, even if the frequency is zero. 3. All classes are the same width. (In this case, they are each four samples apart. This is determined by taking the difference between two consecutive upper boundaries, or between two consecutive lower boundaries.) 4. Use between 5 and 20 classes. There are also several terms used with frequency tables: The following definitions include examples for the table above. Lower class limits – the smallest numbers that actually belong to the classes. ex: 6,10, 14, 18, 22, … Upper class limits – the largest numbers that actually belong to the classes. ex: 9, 13, 17, 21, … Class boundaries – the numbers used to separate classes; the half-way point is used to eliminate gaps created by the class limits. ex: (5.5) 9.5, 13.5, 17.5, 21.5, …29.5 Class Marks – the midpoints of the classes; the average of the upper and lower limits. ex: 7.5, 11.5,15.5 …

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Ex. 2: The following table shows projected depth in metres of new gas well licenses issued in Alberta from May 17, 2012 to June 26, 2012, according to Accumap. 795 906 997 1731 1850 2923 3545 3852 4133 796 907 998 1772 1850 3015 3620 3870 4172 813 913 1016 1850 1850 3055 3627 3883 4185 822 914 1021 1850 1850 3150 3645 3900 4190.9 840.3 916 1043 1850 1850 3185 3653.4 3900 4200 856 923 1057 1850 1850 3240 3660 3943 4207 868 934 1082 1850 1850 3250 3675 3946 4210 868 934 1105 1850 2248 3405 3707 3950 4215 878 934 1124 1850 2592 3458 3746 3970 4215 890 938 1216 1850 2600 3471 3778.5 3990 4225 892 951 1538 1850 2700 3475 3799 3990 4369 893 963 1545 1850 2700 3485 3800 4055 4460 900 985 1589 1850 2782 3494.5 3801 4100 4521 900 991 1621 1850 2832 3515.2 3836.2 4124 4525 Construct a frequency table of the above. Use 8 equal width classes, starting with a lower limit of 795.

4560 4631 4640 4640 4702 4750 4810 4901 4913 5000 5143 5213 5247 5573

Note: to determine minimum class width:

highest value-lowest value 5573  795  597.25 600 number of classes 8 Note: Connect assignments always round up to the next whole number This can then be rounded up (never down): Note: be careful of rounding too much as last category may end up with a frequency of zero, which would actually mean you have one less class than intended. Projected depth (m) 795.0-1394.9 1395.0-1994.9 1995.0-2594.9 2595.0-3194.9 3195.0-3794.9 3795.0-4394.9 4395.0-4994.9 4995.0-5594.9 total

Frequency 38 25 2 10 19 29 12 5 140

There are some variations to frequency: Relative Frequency: rf =

class frequency sum of all frequencies

Cumulative Frequency: the sum of all frequencies for that class and ALL PRECEDING classes.

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Ex 3: Using the values from example 1, determine the relative frequency and the cumulative frequency of each category. Samples

Frequency

6-9 10-13 14-17 18-21 22-25 26-29 Total

2 4 4 2 5 3 20

Relative Frequency 0.1 or 10% 0.2 or 20% 20% 10% 25% 15% 100%

Category for Cumulative Freq....