Understanding Class Limits, Boundaries, Intervals, Width and Midpoint in Statistics, Summaries of Calculus

The concepts of class limits, boundaries, intervals, width and midpoint in statistics. It provides examples and formulas to calculate lower and upper class limits, class boundaries, class width and class midpoint using a frequency table.

Typology: Summaries

2021/2022

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Class limit, boundary, interval, width and midpoint
Class Limits
Class limits are the smallest and largest observations (data, events etc) in each class. Hence, each
class has two limits: a lower and upper limit.
Example:
Class
Frequency
300 โ€“ 399
13
400 โ€“ 499
20
500 โ€“ 599
7
600 โ€“ 699
3
700 โ€“ 799
12
800 โ€“ 899
8
900 โ€“ 999
7
Total Frequency
70
By means of the frequency table above, what are the lower and upper class limits for the first three
classes? One can definitely see that;
For the first class, 300 โ€“ 399
The lower class limit is 300
The upper class limit is 399
For the second class, 400 โ€“ 499
The lower class limit is 400
The upper class limit is 499
For the third class, 500 โ€“ 599
The lower class limit is 500
The upper class limit is 599
Class Boundaries
Class Boundaries are the midpoints between the upper class limit of a class and the lower class limit
of the next class in the sequence. It is 0.5 more or less of a class limit. Therefore, each class has an
upper and lower class boundary.
Example:
Class
Frequency
300 โ€“ 399
13
400 โ€“ 499
20
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Class limit, boundary, interval, width and midpoint Class Limits Class limits are the smallest and largest observations (data, events etc) in each class. Hence, each class has two limits: a lower and upper limit. Example: Class Frequency 300 โ€“ 399 13 400 โ€“ 499 20 500 โ€“ 599 7 600 โ€“ 699 3 700 โ€“ 799 12 800 โ€“ 899 8 900 โ€“ 999 7 Total Frequency 70 By means of the frequency table above, what are the lower and upper class limits for the first three classes? One can definitely see that; For the first class, 300 โ€“ 399 The lower class limit is 300 The upper class limit is 399 For the second class, 400 โ€“ 499 The lower class limit is 400 The upper class limit is 499 For the third class, 500 โ€“ 599 The lower class limit is 500 The upper class limit is 599 Class Boundaries Class Boundaries are the midpoints between the upper class limit of a class and the lower class limit of the next class in the sequence. It is 0.5 more or less of a class limit. Therefore, each class has an upper and lower class boundary. Example: Class Frequency 300 โ€“ 399 13 400 โ€“ 499 20

By means of the frequency table above, find the class boundaries of the first three classes.

Class Intervals, width and size Class interval for example is 300-399 and the class width or size is the difference between the upper and lower class boundaries of any class. Example:

  • 500 โ€“
  • 600 โ€“
  • 700 โ€“
  • 800 โ€“
  • 900 โ€“
  • Total Frequency
  • For the first class, 300 โ€“
  • The lower class boundary is the midpoint between 299 and 300, that is 2 99.
  • The upper class boundary is the midpoint between 399 and 400, that is 3 99.
  • For the second class, 400 โ€“
  • The lower class boundary is the midpoint between 399 and 400, that is 39 9.
  • The upper class boundary is the midpoint between 499 and 500, that is 4 99.
  • For the third class, 500 โ€“
  • The lower class boundary is the midpoint between 499 and 500, that is 4 99.
  • The upper class boundary is the midpoint between 599 and 600, that is 5 99.
    • 300 โ€“ Class Frequency
    • 400 โ€“
    • 500 โ€“
    • 600 โ€“
    • 700 โ€“
    • 800 โ€“
    • 900 โ€“
    • Total Frequency
  • For the first class, 300 โ€“ Using the table above, find the class width for the first class.
  • Upper class boundary = 399. The class width = Upper class boundary โ€“ lower class boundary
  • Lower class boundary = 299.
  • Therefore, the class width = 399.5 โ€“ 2 99.5=