Classification & Frequency Distribution Lecture - 02

Classification 

& 

Frequency Distribution

Lecture - 02

Classification

The sorting data into homogenous (or classes) according to their resemblances is called classification 

Examples:

i. The population of a country is classified into urban & rural.

ii. The human population is classified into males & females.

iii. The population of a city is classified into poor, middle-, and high-income groups.

Frequency Distribution

The organization of data in a table showing the distribution of data into groups (or classes) together with the number of observations in each group (or class) is called frequency distribution. The number of observations falling in a particular group is called class frequency (or frequency) and denoted by f.

 

Steps involved in the construction of frequency distribution.

Step 1: State the data in an array.

Step 2: Find the range.

Step 3: Number of classes; k

Step 4: Class interval; h

Step 5: The first-class limit is obtained from the smallest value of data or a bit less than the smallest value, and the remaining class limits are obtained according to a predesigned pattern.

Step 6: Tally Column

Example 01: The scores of 15 students in a class test are given below:

5, 7, 5, 5, 6, 7, 9, 10, 11, 13, 12, 8, 7, 10, 11

Construct the frequency distribution.

Solution:

Marks	Number of students (f)
5	3
6	1
7	3
8	1
9	1
10	2
11	2
12	1
13	1
Total	15

Example 02: The prices of spicy pizza in the various shops in the USA are given below:

33 34 34 35 35 35 36 36 37 37 14 22 23 25 26 27 30 31 31 32

38 38 38 39 39 39 39 40 41 42 43 44 44 44 44 45 45 48 48 49

50 50 50 50 51 51 53 53 56 63

Construct a frequency distribution table. 

Solution:

Step 1: Write the data in ARRAY.

14 22 23 25 26 27 30 31 31 32 33 34 34 35 35 35 36 36 37 37

38 38 38 39 39 39 39 40 41 42 43 44 44 44 44 45 45 48 48 49

50 50 50 50 51 51 53 53 56 63.

Step 2:  Find the range

Step 3: Number of classes = 6 

Step 4: Class interval; h

Step 5: Class limits.

Class Boundaries

The class boundaries are the precise points that separate one class from the other. The class boundaries are also called continuous grouping. It is derived from class limits by subtracting the lower limit from the preceding upper limit and dividing by 2. The resultant figure is subtracted from the lower limits and added with the upper limits.

Class marks

The class mark is a midpoint of a class and used at various places in statistical analysis.

It is obtained as:

Class Interval

(Width of class)

The difference between upper- and lower-class boundaries, denoted by h.

Where:

L1 & L2 are the lower- and upper-class boundaries of a class, respectively.

Example 03: Determine the class boundaries and class marks of the following frequency distribution.

Class	14 – 22	23 – 31	32- 40	41 – 49	50-58	59-67
Frequency	2	7	19	12	9	1

Solution:

Multiple Choice Questions

Choose and circle the best answer

i.                    The origin of statistics can be traced to

a.     Commerce

b.    Industry

c.     State

d.    Economics

ii.                  In descriptive statistics, we study

a.       The method to make decisions about population based on sample results

b.      The method for organizing, displaying and describing data

c.       How to describe probability distribution

d.      None of the above.

iii.                In inferential statistics, we study...

a.       The method for organizing, displaying and describing data

b.      How to describe probability distribution

c.       The method to make decisions about population based on sample results

d.      None of the above.

iv. When data are collected in a statistical study for only a subset of all elements of interest, we are using:

a.       A sample

b.      A parameter

c.       A population

d.      Both b and c

v.                  In statistics, a sample means

a.       A portion of the sample

b.      A portion of the population

c.       All items under investigation

d.      None of the above

vi.                  .......     Statistic is a numerical quantity, computed from...

a.       Population

b.      Sample

c.       Data

d.      Both (a) and (b)

vii. In statistics, a population consists of...

a.       All people living in a country

b.      All people living in the under study

c.       All subjects or objects whose characteristic are being studied

d.      None of them

viii.            A parameter is a measure which is computed from

a.        Sample

b.      Population

c. Group information

d.      Discrete data

1

Fill in the blanks

i.  A numerical summary of a sample is ---------- (statistic)

ii. A variable... assume numerical values. (quantitative)

iii. The number of students in a class is an example of a --------- variable. (Discrete)

iv.  A quantitative variable that has an infinite number of possible values in the given interval is ---------- (Continuous)

v. The variable that cannot be measured is called a --------- variable. (Qualitative)

vi. The placement of data into mutually exclusive qualitative groups is --------- scale. (Nominal scale).

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