TERMS USED IN FREQUENCY DISTRIBUTIONS
Class Boundaries: Imagine we’re dealing with a set of data, and we want to organize it into groups to better understand it. Class boundaries, also known as true class limits, are numbers that help us define these groups. For instance, in a series of points like 59.5, 62.5, and so on, these points are called class boundaries. The smaller value, 59.5, represents the lower class boundary, while the larger value, 62.5, is the upper class boundary.
Class Intervals and Class Limits: Now, let’s move on to class intervals. A class interval, represented by a symbol like “60-62,” defines a group of data points within a certain range. The numbers at the ends of this interval, in this case, 60 and 62, are known as class limits. The bigger value, 62, is referred to as the upper class limit, and the smaller one, 60, is the lower class limit.
Open Class Intervals: Sometimes, we encounter open class intervals. These intervals lack either an upper or lower limit. Consider the example of “75 years and over.” It doesn’t have an upper class limit because it’s open-ended.
Size of a Class Interval: The size or width of a class interval, also called the class width, class size, or class strength, is the difference between the upper and lower class limits. If we look at data like 62.5-59.5-65.5-62.5, or simplify it to 63-60-66-63, the class interval size is 3, as these classes are of equal size.
Calculation of Class Boundaries: To calculate class boundaries, add the upper limit of one class to the lower limit of the next higher class and divide by 2. For instance, if we have the class 60-62, the upper class boundary is calculated by adding 62 and 63, then dividing by 2 to get 62.5.
Class Marks: Another term to know is class mark, also called the class midpoint or class center. To find this, add the lower and upper class limits and divide by 2. For instance, for the class 60-62, the class mark is calculated as (60+62)/2, resulting in 61.
Arrays: Finally, let’s talk about arrays. An array is an arrangement of numerical data in either ascending or descending order of magnitude. The difference between the largest and smallest numbers in an array gives us the range of the data.
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Evaluation
1. The smaller number in class boundaries is the __________ class boundary.
a) Upper
b) Lower
c) Central
2. A symbol defining a group, such as “60-62,” is called a __________ interval.
a) Class
b) Data
c) Boundary
3. The difference between the upper and lower class limits is known as the __________ of a class interval.
a) Width
b) Range
c) Limit
4. An open class interval lacks either an upper or lower __________ limit.
a) Central
b) Class
c) Boundary
5. The calculation of class boundaries involves adding the upper class limit of one class to the lower class limit of the next higher class and dividing by __________.
a) 2
b) 3
c) 4
6. The class boundary of the second class (63-65) is calculated by adding 65 to 66 and dividing by __________.
a) 2
b) 3
c) 4
7. The class mark or class midpoint is obtained by adding the lower and upper class limits and dividing by __________.
a) 1
b) 2
c) 3
8. An array is an arrangement of numerical data in __________ order of magnitude.
a) Random
b) Descending
c) Ascending
9. The range of data is the difference between the __________ and smallest numbers in an array.
a) Largest
b) Middle
c) Median
10. The size or width of a class interval is the difference between the __________ class limits.
a) Middle
b) Upper
c) Lower
11. The upper class boundary of the first class (60-62) is calculated by adding 62 and 63 and dividing by __________.
a) 1
b) 2
c) 3
12. The class boundary of the third class (66-68) is calculated by adding 68 and 69 and dividing by __________.
a) 2
b) 3
c) 4
13. The class mark of the class 60-62 is calculated by adding 60 and 62 and dividing by __________.
a) 1
b) 2
c) 3
14. An array is an arrangement of numerical data in __________ order of magnitude.
a) Random
b) Descending
c) Ascending
15. The size or width of a class interval is the difference between the __________ class limits.
a) Middle
b) Upper
c) Lower
Some Basic Statistical Concepts and Notations
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