(a) Inclusive and Exclusive limits.

(b) Continuous and discrete data.

(C) Qualitative and Quantitative data

(d) Class limits and class intervals.

**a)**

Inclusive and exclusive limits are relevant from data tabulation and class intervals point of view.

Inclusive series is the one which doesn't consider the upper limit, for example,

Inclusive series is the one which doesn't consider the upper limit, for example,

00-10

10-20

20-30

30-40

40-50

10-20

20-30

30-40

40-50

In the first one (00-10), we will consider numbers from 00 to 9.99 only. And 10 will be considered in 10-20. So this is known as inclusive series.

Exclusive series is the one which has both the limits included, for example,

00-09

10-19

20-29

30-39

40-49

10-19

20-29

30-39

40-49

Here, both 00 and 09 will come under the first one (00-09). And 10 will come under the next

one.

**(b)**

Several differences between discrete and continuous data would be that "continuous" data is:

· Measured and represented by an infinite number of values and can possess any value, and

· Has no natural category, meaning we cannot precisely measure its category.

For example, categories such as:

· The number of weight

· The number of width, or

· The number in length

Cannot be measured because their values could be or are infinite.

Whereas

**discrete data**can only possess:
· A specific value and can only represent a few values. (It is what it is and it's measures are limited).

Discrete data however, unlike continuous, does possess:

· Natural categories.

In Statistics for example, when determining the age of 100 people, discrete data sets are used in categories to classify the different ages of the 100 people. My example below is considered a "natural category."

**For Example,**

- Category 1 could represent 1 year -10 years old
- Category 2 is 11 - 20 years old...and so on...up to any category, e.g. 20 is 190 years old - 200 years old.

Each category represents a population or group of people. Although category 20 is highly unlikely, it will keep rising higher and higher until determined by the statistician that higher categories will not be required or will eventually stop when all of the 100 people are placed in their specific categories, thus placing a discrete limit on the number of categories.

**( c )**

**Qualitative**data is a categorical measurement expressed not in terms of numbers, but rather by means of a natural language description. In statistics, it is often used interchangeably with "categorical" data. Although we may have categories, the categories may have a structure to them. When there is not a natural ordering of the categories, we call these

**nominal**categories. Examples might be gender, race, religion, or sport.

**Quantitative**data is a numerical measurement expressed not by means of a natural language description, but rather in terms of numbers. However, not all numbers are continuous and measurable. For example, the social security number is a number, but not something that one can add or subtract.

**(d)**The arrangement of data according to magnitude or size is called a frequency distribution. It is the method of putting data into different groups which are called class intervals or simply classes. From the frequency distribution comes the concept of grouped data (data presented in frequency distribution) and ungrouped data (data in original form). The concept of frequency distribution and other related terms can be explained with the help of following table.

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Class Intervals (C.I.)

There are five groups in the above table namely 201 – 210, 211 – 220, 221 – 230, less than 200.5 and 230.5 or more. These groups are called class intervals.

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Size or Width of Class Interval

Size or width of class interval is the total number of observations on which a class interval is formed. There are two types of class intervals i.e. equal size class intervals (size of each class interval is same) and unequal size class interval (size of each class interval is different). In the above table size of each class interval is same i.e. 10 (211- 201 = 10 Or 220 – 210 = 10).

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Class Limits

Class limits are the opening and closing limits of a class interval. There are two class limits of each interval i.e. Lower Class Limit and Upper Class Limit.

**a. Lower class limit**

Lower class limit is that limit at which class interval starts for example 201, 211 and 221.

**b. Upper class limit**

Upper class limit is that limit at which class interval ends e.g. 210, 220 and 230.

**c. Open class limit**

Open class limit has either no lower class limit or no upper class limit e.g. less than 200.5 and 230.5 or more.

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