There are two types of variable Categorical and Numerical variable. And then we have two types of Numerical variable that is Discrete Continuous

**Organizing numerical data**

- Recall, a discrete variable usually involves a count of something, whereas a continuous variable usually involves a measurement of something.
- First group the observations into classes (also known as categories or bins) and then treat the classes as the distinct values of qualitative data.
- Once we group the quantitative data into classes, we can construct frequency and relative-frequency distributions of the data in exactly the same way as we did for categorical data.

**Organizing discrete data (single value)**

- If the data set contains only a relatively small number of distinct, or different, values, it is convenient to represent it in a frequency table.
- Each class represents a distinct value (single value) along with its frequency of occurrence.

**Example**

- Suppose the dataset reports the number of people in a household. The following data is the response from 15

individuals. - 2,1,3,4,5,2,3,3,3,4,4,1,2,3,4
- The distinct values the variable, number of people in each household, takes is 1,2,3,4,5.
- The frequency distribution table is

Value | Tally mark | Frequency | Relative frequency |
---|---|---|---|

1 | |||

2 | |||

3 | |||

4 | |||

5 | |||

Total |

**Organizing continuous data**

Organize the data into a number of classes to make the data understandable. However, there are few guidelines that need to be followed. They are

- Number of classes: The appropriate number is a subjective choice, the rule of thumb is to have between 5 and 20 classes.
- Each observation should belong to some class and no observation should belong to more than one class.
- It is common, although not essential, to choose class intervals of equal length.

**Some new terms**

- Lower class limit: The smallest value that could go in a class.
- Upper class limit: The largest value that could go in a class.
- Class width: The difference between the lower limit of a class and the lower limit of the next-higher class.
- Class mark: The average of the two class limits of a class.
- A class interval contains its left-end but not its right-end boundary point.

**Example**

- The marks obtained by 50 students in a particular course.
- 68, 79, 38, 68, 35, 70, 61, 47, 58, 66, 60, 45, 61, 60, 59, 45, 39, 80, 59, 62, 49, 76, 54, 60, 53, 55, 62, 58, 67, 55, 86, 56, 63, 64, 67, 50, 51, 78, 56, 62, 57, 69, 58, 52, 42, 66, 42, 56, 58.

class Interval | Tally mark | Frequency | Relative frequency |
---|---|---|---|

30-40 | |||

40-50 | |||

50-60 | |||

60-70 | |||

70-80 | |||

80-90 | |||

Total |

**Section summary**

- Frequency table for discrete single value data.
- Frequency table for continuous data using class intervals.

**Steps to construct a histogram**

**Step 1**Obtain a frequency (relative-frequency) distribution of the data.**Step 2**Draw a horizontal axis on which to place the classes and a vertical axis on which to display the frequencies (relative frequencies).**Step 3**For each class, construct a vertical bar whose height equals the frequency (relative frequency) of that class.**Step 4**Label the bars with the classes, the horizontal axis with the name of the variable, and the vertical axis with “Frequency” (“Relative frequency” ).

**Stem-and-leaf diagram**

- In a stem-and-leaf diagram (or stemplot) , each observation is separated into two parts, namely, a stem-consisting of all but the rightmost digit-and a leaf, the rightmost digit.
- For example, if the data are all two-digit numbers, then we could let the stem of a data value be the tens digit and the leaf be the ones digit.

**Steps to construct a stemplot**

**Step 1**Think of each observation as a stem—consisting of all but the rightmost digit—and a leaf, the rightmost digit.**Step 2**Write the stems from smallest to largest in a vertical column to the left of a vertical rule.**Step 3**Write each leaf to the right of the vertical rule in the row that contains the appropriate stem.**Step 4**Arrange the leaves in each row in ascending order.

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