Class 10 | Statistics Direct mean method| Assumed Mean method| Step deviation method

Описание: 📘 STATISTICS – MEAN (Average) FINDING METHODS FOR YOUTUBE

1️⃣ Direct Mean Method (Simple Mean Method)

Definition:
In this method, we calculate the mean directly by multiplying each value (class mark) with its frequency and then dividing the total by the sum of frequencies.

Use when:
Numbers are small and easy to multiply.

Formula:

\bar{x} = \frac{\sum fx}{\sum f}

Steps:

1. Find class mark (midpoint) .


2. Multiply frequency with class mark → .


3. Add all .


4. Divide by total frequency.



Simple Example:
If numbers are small like 10, 20, 30, 40… use this method.


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2️⃣ Assumed Mean Method (A.M. Method)

Definition:
When the numbers are big, we choose one value as “assumed mean” to make calculations easier.
Instead of multiplying big numbers, we work with differences.

Use when:
Class marks are large (like 125, 135, 145…).

Formula:

\bar{x} = A + \frac{\sum fd}{\sum f}

Steps:

1. Choose any one class mark as assumed mean .


2. Find deviation: .


3. Multiply frequency and deviation → .


4. Mean = .



Why useful:
Reduces big multiplications, makes calculation faster.


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3️⃣ Step Deviation Method (SD Method)

Definition:
When class intervals are equal and big numbers repeat (like 100–120, 120–140…), we divide deviations by class width to make numbers even smaller.

Use when:
Class intervals are large and equal (h = constant).

Formula:

\bar{x} = A + \left( \frac{\sum f d'}{\sum f} \right) \times h

Steps:

1. Choose assumed mean .


2. Find deviation .


3. Divide by class width (h): .


4. Multiply frequency & new deviation → .


5. Mean = .