1120 LearnersLast updated on June 18th, 2025
Step Deviation Method
The step deviation method is a shortcut technique for finding the mean of grouped data more efficiently and easily. It simplifies the calculations of larger datasets and is especially useful when the class intervals are uniform. Let us see more about step deviation method and how it is used in the topic below.
What is step deviation method
The step deviation method is a statistical technique that is used to calculate the mean of a grouped data efficiently and easily. It simplifies the calculation by selecting an assumed mean, determining the class midpoints and class width to standardize deviations. This method reduces the larger numbers into manageable values. This makes it useful for datasets with uniform class intervals.
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What is the formula for Step Deviation Method
The formula for Step deviation is given below:
Mean = A + c (Σfiui / Σfi)
Where,
c is the class width
A is the assumed mean
Σfiui is the sum of the product of frequency and deviation values
Σfi is the number of frequencies.
Steps for Using Step Deviation Method
To use step deviation, we must follow the following steps:
Step 1: Create a table containing 5 columns: class interval, class marks (xi), deviations di = xi - A, the values of ui = di/h, and frequencies.
Step 2: Find the mean:
∑xiui / ∑ui
Step 3: Calculate the mean by adding the assumed mean A to the product of the class width h with mean of ui.
Real life applications of Step Deviation Method
The step deviation method have numerous applications across various fields. Let us explore how the step deviation method is used in different areas:
- Education: The step deviation method is used by teachers and researchers to calculate the average marks of students from large data sets. It also helps in analyzing the performance distribution of students in different subjects.
- Economics: The step deviation method helps economists to determine the average income of individuals in different income brackets. It is also used to study income inequality by analyzing grouped data of households income.
- Business: Step deviation method is used by companies to calculate the average sales revenue for different product categories. It also helps in understanding customer purchase behavior.
Common mistakes and How to Avoid Them in Step Deviation Method
Students tend to make some mistakes while solving problems related to step deviation method. Let us now see the different types of mistakes students make while solving problems related to step deviation method and their solutions:
Mistake 1
Choosing Wrong Assumed Mean (A)
Students tend to select the assumed mean that is far from the actual mean. They must choose the class midpoint that is closest to the actual mean to minimize the deviations and helps in simplifying calculations.
Mistake 2
Incorrectly Calculating the Class Width (h)
Students sometimes use inconsistent class widths and miscalculate the class midpoint. They must practice and double-check the formula, and also check if h is uniform across all the classes.
Mistake 3
Misplacing Negative Signs in Deviations
Students sometimes incorrectly handle the negative values while summing fu, this affects the final mean value. Students must clearly distinguish negative and positive values and use brackets where it is necessary
Mistake 4
Rounding Off Too Early
Students should not round off immediately while solving the problem, which causes significant errors in the final result. Students should keep at least 4 decimal places in intermediate steps before rounding off in the final answer.
Mistake 5
Copying Errors from the Table
Students tend to misplace the values from the frequency distribution table, this causes incorrect calculations. The students must double-check each value from the table before proceeding with their calculations.
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Solved examples on Step Deviation Method
Problem 1
Given the following frequency distribution, find the mean.
The mean is approximately 31.56.
Explanation
Determine midpoint:
10–20: 15
20–30: 25
30–40: 35
40–50: 45
Selecting assumed mean:
Choose a = 35
Class width:
h = 10
Calculate step deviations:
For 15: u = (15-35)/10 = -2
For 25: u = (25-35)/10 = -1
For 35: u = (35-35)/10 = 0
For 45: u = (45-35)/10 = 1
Compute: f and fu:
f = 5 + 8 + 12 + 7 = 32
fu = 5(-2) + 8(-1) + 12(0) + 7(1) = -10 - 8 + 0 + 7 = -11
Calculate the mean:
x = 35 + 10 (-11/32) = 35 – (110/32) 35 – 3.44 = 31.56.
Problem 2
Compute the mean from the grouped data below.
The mean is approximately 21.36.
Explanation
Midpoints:
5, 15, 25, 35
Assumed mean a = 15
Class width h = 10
Step deviations:
For 5: u = (5-15)/10 = -1
For 15: u = 0
For 25: u = 1
For 35: u = 2
Sums:
f = 3 + 6 + 9 + 4 = 22
fu = 3(-1) + 6(0) + 9(1) + 4(2) = -3 + 0 + 9 + 8 = 14
Mean:
x = 15 + 10 (14/22) 15 + 6.36 = 21.36.
Problem 3
Calculate the mean for the distribution below.
The mean is approximately 61.89.
Explanation
Midpoints:
45, 55, 65, 75
Assumed mean a = 65
Class width h = 10
Step deviations:
For 5: u = (45-65)/10 = -2
For 15: u = -1
For 25: u = 0
For 35: u = 1
Sums:
f = 8 + 10 + 15 + 12 = 45
fu = 8(-2) + 10(-1) + 15(0) + 12(1) = -16 - 10 + 0 + 12 = -14
Mean:
x = 65 + 10 (-14/45) 65 - 3.11 = 61.89.
Problem 4
Find the mean using the following grouped data.
The mean is approximately 40.71.
Explanation
Midpoints:
25, 35, 45, 55
Assumed mean a = 35
Class width h = 10
Step deviations:
For 5: u = (25-35)/10 = -1
For 15: u = 0
For 25: u = 1
For 35: u = 2
Sums:
f = 4 + 10 + 8 + 6 = 28.
fu = 4(-1) + 10(0) + 8(1) + 6(2) = -4 + 0 + 8 + 12 = 16
Mean:
x = 35 + 10 (16/28) 35 + 5.71 = 40.71.
Problem 5
Determine the mean for the following distribution.
The mean is approximately 117.60.
Explanation
Midpoints:
105, 115, 125, 135
Assumed mean a = 125
Class width h = 10
Step deviations:
For 105: u = (105-125)/10 = -2
For 115: u = -1
For 125: u = 0
For 135: u = 1
Sums:
f = 12 + 18 + 15 + 5 = 50.
fu = 12(-2) + 18(-1) + 15(0) + 5(1) = -24 - 18 + 0 + 5 = -37
Mean:
x = 125 + 10 (-37/28) 125 - 7.40 = 117.6.
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FAQs on Step Deviation Method
1.What is the step deviation method?
2.Why do we use step deviation method?
3.How does step deviation method work?
4.What is the assumed mean in this method?
5.What is the formula for calculating the mean using the step deviation method?
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
