medium difficulty8 min

Step deviation method

The step deviation method is a fast way to find the mean of grouped data when class widths are equal.

In one line: Same width, smaller numbers, faster mean.

Understand it

This method is used when the class intervals have the same width. We choose an assumed mean, divide deviations by class width to get small coded values, and then use a simpler formula. It is especially helpful in long tables because the numbers become easier to manage.

Example

If class width is 10 and a deviation is 20, then the coded deviation is 2.

Formula and rule

Mean = A + [Σf_i u_i / Σf_i] x h, where u_i = (x_i - A)/h and h is class width.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

For class marks 15, 25, 35 with frequencies 2, 3, 5, choose A = 25 and h = 10.

1Then u_i values are -1, 0, 1.
2So Σf_i u_i = 2(-1) + 3(0) + 5(1) = 3.
3Mean = 25 + (3/10)x10 = 28.

Method you can reuse

1Check whether class width is common.
2Choose an assumed mean.
3Compute deviations from it.
4Divide by class width to get u_i.
5Multiply by frequencies and apply the formula.

Sketch it in your answer

Draw a table with columns for class mark, deviation, u_i, frequency, and f_i u_i.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

When is the step deviation method most suitable?

Think first, then show answer

It is most suitable when all class intervals have the same width. Then we can divide deviations by the common width and reduce the calculation to smaller, easier numbers.

Common wrong answer

A common wrong answer is to forget multiplying the coded deviation sum by class width at the end.

Don't mix this up

Students forget that this method works best when all class widths are equal, so they apply it blindly to unequal intervals.

Exam tip

Check the class width first. If all intervals are equal, step deviation can save time in the board exam.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Students may be asked to compute the mean of a long grouped table using coded deviations and a common class width.

1
Enough for 1 mark
The step deviation method is a fast way to find the mean of grouped data when class widths are equal.
2
Add for 2 marks
Example: If class width is 10 and a deviation is 20, then the coded deviation is 2.
3
Add for 3 marks
This method is used when the class intervals have the same width.

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