Step deviation method

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

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

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

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

The step deviation method is a fast way to find the mean of grouped data when class widths are equal. Mean = A + [Σf_i u_i / Σf_i] x h, where u_i = (x_i - A)/h and h is class width. If class width is 10 and a deviation is 20, then the coded deviation is 2.

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. Mean = A + [Σf_i u_i / Σf_i] x h, where u_i = (x_i - A)/h and h is class width. For class marks 15, 25, 35 with frequencies 2, 3, 5, choose A = 25 and h = 10. Then u_i values are -1, 0, 1. So Σf_i u_i = 2(-1) + 3(0) + 5(1) = 3. Mean = 25 + (3/10)x10 = 28. Students may be asked to compute the mean of a long grouped table using coded deviations and a common class width. A common wrong answer is to forget multiplying the coded deviation sum by class width at the end.