Grouped Frequency Distribution Table Example

Frequency is the measure of how how often an event appears. The frequency distribution table is a tool which can help in comparing the frequencies of different events occurrence. There are two type of frequency distributions which are used in statistics: grouped frequency distribution and ungrouped frequency distribution. The first one is utilized for a high quantity of data, when it is impossible to list all of them in the table (“Grouped Frequency Distributions”, 2016).

In order to develop a group frequency distribution, the data is grouped to several classes. The next five rules should be followed in order to create classes (“Grouped Frequency Distributions”, 2016):

  • The boundaries of the class should not overlap each other;
  • Each data should be included in any of the classes;
  • The boundaries between any neighbor classes should not have any gaps;
  • The length of each class mush be the same;
  • The length of the class should be odd.

The next steps are to be accomplished in order to create a grouped frequency distribution (“Statistics: Grouped Frequency Distributions”, 2016):

  1. The larges and the smallest values should be determined;
  2. The range, equaled to the difference between the maximum and the minimum values, should be calculated;
  3. The amount of desired classes should be selected;
  4. The length of the class should be found as a ratio of the range (from the second step) and the number of classes (from the third step);
  5. The staring point, less or equaled to the minimum value (from the first step) should be selected for the first class. In order to determine the starting points for the further classes the length of the class should be added to the starting point of the previous class;
  6. The upper limit of the class should be calculated by subtracting 1 from the lower limit of the further class;
  7. The data should be tallied;
  8. The frequencies are to be calculated;
  9. The cumulative frequencies are to be estimated;
  10. The relative frequencies and relative cumulative frequencies should be found.

Problem #1. The heart rate measurements were performed in one of the health care center in order to find the resting heart rate for Men. The data is presented in the table below.

Man’s number Resting heart rate Man’s number Resting heart rate Man’s number Resting heart rate Man’s number Resting heart rate Man’s number Resting heart rate
#1 62 #10 53 #19 74 #28 59 #37 55
#2 61 #11 64 #20 54 #29 68 #38 58
#3 51 #12 75 #21 65 #30 77 #39 78
#4 74 #13 81 #22 76 #31 78 #40 67
#5 82 #14 52 #23 51 #32 57 #41 68
#6 49 #15 63 #24 72 #33 56 #42 69
#7 57 #16 74 #25 66 #34 76 #43 58
#8 66 #17 53 #26 57 #35 81 #44 64
#9 78 #18 64 #27 68 #36 64 #45 65

Solution:

Step #1. The minimum value of Resting heart rate is: 49 beats per minute. The maximum value of Resting heart rate is: 82 beats per minute.
Step #2. The Range is: R=82-49+1=34
Step #3. The width of classes is 4
Step #4. The lowest apparent limit is 48.
Step #5. The number of groups is: 34/5=7.

The results of calculations are shown in the Grouped frequency distribution table below.

Interval Real or exact limits Mid-point f p % Cf Cp C%
78-82 77.5-82.5 80 6 6/45=0.133 13,3 45=N 1 100
73-77 72.5-77.5 75 7 0.156 15,6 39 0.867 86,7
68-72 67.5-72.5 70 5 0.111 11,1 32 0.711 71,1
63-67 62.5-67.5 65 10 0.222 22,2 27 0.6 60
58-62 57.5-62.5 60 5 0.111 11,1 17 0.378 37,8
53-57 52.5-57.5 55 8 0,178 17,8 12 0.267 26,7
48-52 47.5-52.5 50 4 0,089 8,9 4 0.089 8,9
Σf=45 Σp=1 Σ%=100

 

Problem #2. The grades which students gained after passing the exam are shown in the table below. Create the Grouped frequency distribution table.

68 78 94 54 67 77 96 100 97 86
87 76 77 98 99 78 65 64 79 90
80 79 72 71 64 62 53 100 65 84

Solution: The same steps as in the previous problem were accomplished.

  1. min=53; max=100
  2. Range: 100-53=47
  3. The width of the classes: 5
  4. The lowest apparent limit is 50
  5. The number of groups is: 47/5=10

The results of calculations are shown in the Grouped frequency distribution table below.

Interval Real or exact limits Mid-point f p % Cf Cp C%
95-100 94.5-100.5 97.5 7 0.233 23,3 30=N 1 100
89-94 88.5-94.5 91.5 2 0.067 6,7 23 0,767 76.7
83-88 82.5-88.5 85.5 3 0.100 10 21 0,700 70
77-82 76.5-82.5 79.5 7 0.233 23,3 18 0,600 60
71-76 70.5-76.5 73.5 3 0.100 10 11 0,367 36.7
65-70 65.5-70.5 67.5 4 0.133 13,3 8 0,267 26.7
59-64 58.5-64.5 61.5 2 0.067 6,7 4 0,133 13.3
53-58 52.5-58.5 55.5 2 0.067 6,7 2 0,067 6.7
Σf=30 Σp=1 Σ%=100

References
Grouped Frequency Distributions. (2016). Mathsolutions.50webs.com. Retrieved 18 May 2016, from http://mathsolutions.50webs.com/freqdist.html

Statistics: Grouped Frequency Distributions. (2016). People.richland.edu. Retrieved 18 May 2016, from https://people.richland.edu/james/lecture/m170/ch02-grp.html

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