Statistical Method

(C) Calculation of arithmetic mean in Frequency distribution:

There are two methods of calculation: (i) Direct method and (ii) Indirect method

(i) Direct method:

Step:

  • Take mid value of each group as the value of Equation

  • Multiply x with to obtain Equation

  • Take sum of Equation to obtain Equation

  • Divide Equation by Equation to get Equation

  • Use the formula Equation

Direct method of arithmetic mean in Frequency distribution

Direct Method of Arithmetic Mean in Frequency Distribution

Direct method of arithmetic mean in Frequency distribution

(ii) Indirect method:

There are two versions of indirect method.

(a) Based on assumed mean

Steps:

  • Take mid value (x) of each group.

  • Take some value of x as assumed mean (A)

  • Deduct A from x to get Equation

  • Multiply Equation by f to get Equation

  • Take sum of all value of Equation to obtain Equation

  • Divide Equation by Equation to get Equation

  • Use the formula Equation

Indirect method based on assumed mean in Frequency distribution

Indirect Method Based on Assumed Mean in Frequency Distribution

Indirect method based on assumed mean in Frequency distribution

(a) Step Deviation Method

Steps:

  • Take mid value of group X.

  • Take some assumed mean (A)

  • Deduct A from x to get Equation

  • Take common factor (i) from amongst value of dx.

  • Divide each value of dx by this factor to get Equation

  • Multiply Equation by f to get Equation

  • Take sum of all value of Equation to obtain Equation

  • Use the formula Equation

Indirect method step deviation Method in frequency distribution

Indirect Method Step Deviation Method in Frequency Distribution

Indirect method step deviation Method in frequency distribution

Weighted Arithmetic Mean

Number Equation certain weighting factors or weights Equation depending on the significance attached to the numbers. At that time we calculate mean is called weighted mean.

Formula Equation

Advantages and Disadvantages of arithmetic mean

Advantages:

  • Easy and simple computation.

  • Based on all observations of the series.

  • Easily understood average.

  • Treated as algebraically.

Disadvantages:

  • Not representative in case:

    • Unequal classes Equation

    • Open-end classes Equation

  • Affected by extreme values in the series of extremely large and small.

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