Analysis of Data: Continuous Series Data and Precautions of Using Arithmetic Mean

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Continuous Series Data

In which entire available data is divided into equal intervals. Each group represents different values but with same range. Formulas for calculating Arithmetic mean

Direct Method:

Shortcut method without step deviation:

Shortcut method with step deviation:

In continuous series x is middle value for each class. x =

where is lower limit and is upper limit?

And C is Class interval.

Example: Find out Arithmetic mean for the given data.

Calculation for F
Calculation for F

x (marks)

F (no. of students)

Direct Method

Calculation for Sum(fx)
Calculation for sum(fx)

Class interval

x =

f

fx

= 300

.

Shortcut Method

Without Step deviation:

Calculation for F(dx)
Calculation for f(dx)

Class interval

x =

f

dx = x-A

fdx

= 300

With Step deviation:

Class Interval
Class interval

Class interval

x =

f

dx = x-A

dx’ = dx/C

fdx’

Precautions of Using Arithmetic Mean

  • Arithmetic Mean is a theoretical value which may not represent actual fact.

Ex: Average children per family would be 2.3 but it is unrealistic. There would be either 2 children or 3 children per family. Note: There is a possibility for no children in some families.

  • Arithmetic Mean cannot be calculated for qualitative data such as honesty, beauty etc.

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