Frequency Tables For Numerical Data | StudyTution

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.