Arithmetic Mean [ Individual Series] Direct Method and Short-cut Method

Measures of Central Tendency or Averages

Measures of central tendency refers to all those methods of statistical analysis which are used to calculate the average of a set of data.

According to Clark and Sekkade, “Average is an attempt to find one single figure to describes whole of figures”.

Types of averages-

1-    Mathematical averages: The mathematical averages are Arithmetic mean, Geometric mean and Harmonic mean.

2-    Positional averages: The positional averages are Median and Mode.

Arithmetic mean

Arithmetic mean or arithmetic average is defined as the sum of all values divided by the number of values. 

There are two types of Arithmetic mean:

1-Simple Arithmetic mean

2-Weighted Arithmetic mean

Simple Arithmetic mean- Individual series

Direct Method- The simple arithmetic mean of a series is equal to the sum of variables divided by their number.

Question 1[a]- Calculate the arithmetic mean from the following data by using direct method:

Roll No- 1,   2,   3,   4,   5,   6,    7,   8,    9,  10

Marks: 40, 50, 55, 78, 58, 60, 73, 35, 43, 48

Short cut method- The arithmetic mean can also be calculated by short cut method. This method reduces the amount of calculation. It involves the following steps:

1- Assume any one value as an assumed mean which is also known as working mean or arbitrary average [A].

2- Find out the difference of each value [deviation] from the assumed mean [d = X-A].

3- Add all the deviation [Σd].

4- Apply the formula

Question 1[b]- Calculate the arithmetic mean from the following data by using short cut method:

Roll No- 1,   2,   3,   4,   5,   6,    7,   8,    9,  10

Marks: 40, 50, 55, 78, 58, 60, 73, 35, 43, 48

Question 2[a]- Calculate the arithmetic mean of the following data of marks of a group of students by using direct method:

Students- 1,   2,   3,   4,   5,   6,    7,   8,    9,  10

Marks: 10, 15, 18, 20, 22, 25, 30, 35, 25, 17

Question 2[b]- Calculate the arithmetic mean from the following data by using short cut method.

Students: 1,   2,   3,   4,   5,   6,    7,   8,    9,  10

Marks: 10, 15, 18, 20, 22, 25, 30, 35, 25, 17

Question 3[a]- Calculate the arithmetic mean of the following data of marks of a group of students by using direct method:

Students- 1,   2,   3,   4,   5,   6,    7,   8,    9,  10

Marks [X]-  25, 30, 21, 55, 47, 10, 15, 17, 45, 35

Question 3[b]- Calculate the arithmetic mean from the following data by using short cut method.

Students- 1,   2,   3,   4,   5,   6,    7,   8,    9,  10

Marks [X]-  25, 30, 21, 55, 47, 10, 15, 17, 45, 35

Question 4[a]- Calculate the arithmetic mean from the following data by using direct method.

Month: Jan, Feb, Mar, Apr, May, Jun

                              

Income (Rs): 25000, 30000, 45000, 20000, 25000, 20000

Question 4[b]- Calculate the arithmetic mean from the following data by using short cut method.

Month: Jan, Feb, Mar, Apr, May, Jun                  

Income (Rs): 25000, 30000, 45000, 20000, 25000, 20000

Question 5[a]-Calculate the arithmetic mean from the following data by using direct method.

Families- 1,   2,   3,   4,   5,   6,    7,   8,    9,  10

Daily Income in Rs. [X]- 18, 20, 35, 55, 38, 54, 100, 85, 37, 53

 

Question 5[b]-Calculate mean from the following data by using short cut method.

                           Families- 1,   2,   3,   4,   5,   6,    7,   8,    9,  10

Daily Income in Rs. [X]- 18, 20, 35, 55, 38, 54, 100, 85, 37, 53

Dr. Swati Gupta

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