Step Deviation Method for Calculating Standard Deviation

Step deviation method is a statistical method used to calculate standard deviation. It involves calculating the deviation of each observation from the mean of the data, and then grouping the deviations into intervals or steps. The interval size is usually chosen to be a convenient number, such as 5 or 10. The deviations are then expressed as a multiple of the interval size, and the standard deviation is calculated using the formula:

Standard deviation = (sum of the squares of the step deviations / N)^(1/2)

Calculating Standard Deviation using Step Deviation Method with Given Data

Given data:

C.I. 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 10 15 25 25 10 10 5

Step deviation method involves calculating mid-values of each class interval. Hence, mid-value of first class interval is 5, second is 15, and so on.

Step 1: Calculate the Mean

Mean can be calculated as:

Mean = (sum of (mid-value * frequency) / sum of frequency)

Mean = (5*10 + 15*15 + 25*25 + 35*25 + 45*10 + 55*10 + 65*5) / (10+15+25+25+10+10+5)

Mean = 32.5

Step 2: Calculate the Deviations

Deviations can be calculated as:

Deviations = (mid-value - mean)

Deviations = (-27.5, -17.5, -7.5, 7.5, 17.5, 27.5, 37.5)

Step 3: Determine the Interval Size and Calculate the Step Deviations

Interval size can be chosen as 10, and step deviations can be calculated as:

Step deviations = (deviations / interval size)

Step deviations = (-2.75, -1.75, -0.75, 0.75, 1.75, 2.75, 3.75)

Step 4: Calculate the Squared Step Deviations

Squared step deviations can be calculated as:

Squared step deviations = (step deviations)^2

Squared step deviations = (7.56, 3.06, 0.56, 0.56, 3.06, 7.56, 14.06)

Step 5: Calculate the Sum of Squared Step Deviations

Sum of squared step deviations can be calculated as:

Sum of squared step deviations = sum of (squared step deviations * frequency)

Sum of squared step deviations = (7.56*10 + 3.06*15 + 0.56*25 + 0.56*25 + 3.06*10 + 7.56*10 + 14.06*5)

Sum of squared step deviations = 704.3

Step 6: Calculate the Standard Deviation

Standard deviation can be calculated as:

Standard deviation = (sum of squared step deviations / N)^(1/2)

Standard deviation = (704.3 / 100)^(1

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