In view of the coronavirus pandemic, we are making LIVE CLASSES and VIDEO CLASSES completely FREE to prevent interruption in studies
Home > Formulas > Maths Formulas > Mean Deviation Formula
Maths Formulas

Mean Deviation Formula

Mean deviation is a measure of central tendency. We can calculate it from Arithmetic Mean, Median or Mode. It shows us how far are all the observations from the middle, on average? Each deviation is an absolute deviation as it is an absolute value which implies that we ignore the negative signs. Also, the deviations on both the sides of the Mean shall be equal. Let us start learning the mean deviation formula in detail.

Mean Deviation Formula

The mean deviation is the mean of the absolute deviations of the observations or values from a suitable average. This suitable average may be the mean, median or mode. We also know it as the mean absolute deviation. We shall now learn more about some important formulas, for example, the mean deviation formula for an individual series or a continuous series, etc.

Mean Deviation Formula

1] Individual Series

M.D. = \(\frac{\sum \left | X -\overline{X} \right |}{N}\)

Where,

\(\sum\) Summation
X Observations or values
\(\overline{X}\) Mean
N Number of observations

2] Discrete Series

M.D. = \(\frac{\sum f \left | X -\overline{X} \right |}{\sum f}\)

Where,

\(\sum\) Summation
X Observations or values
\(\overline{X}\) Mean
f frequency of observations

3] Continuous Series

M.D.= \(\frac{\sum f \left | X -\overline{X} \right |}{\sum f}\)

Where,

\(\sum\) Summation
X Mid-value of the class
\(\overline{X}\) Mean
f frequency of observations

Mean deviation from Median

1] Individual Series

M.D. = \(\frac{\sum \left | X – M \right |}{N}\)

Where,

\(\sum\) Summation
X Observations or values
M Median
N Number of observations

2] Discrete Series

M.D. = \(\frac{\sum f \left | X – M \right |}{\sum f}\)

Where,

\(\sum\) Summation
X Observations or values
M Median
f frequency of observations

3] Continuous Series

M.D.= \(\frac{\sum f \left | X -\overline{X} \right |}{\sum f}\)

Where,

\(\sum\) Summation
X Mid-value of the class
M Median
f frequency of observations

Mean deviation from Mode

1] Individual Series

M.D. = \(\frac{\sum \left | X – Mode \right |}{N}\)

Where,

\(\sum\) Summation
X Observations or values
M Mode
N Number of observations

2] Discrete Series

M.D. = \(\frac{\sum f \left | X – Mode \right |}{\sum f}\)

Where,

\(\sum\) Summation
X Observations or values
Mode Mode
f frequency of observations

3] Continuous Series

M.D.= \(\frac{\sum f \left | X – Mode \right |}{\sum f}\)

Where,

\(\sum\) Summation
X Mid-value of the class
Mode Mode
f frequency of observations

Steps to Calculate the Mean Deviation:

  1. Calculate the mean, median or mode of the series.
  2. Calculate the deviations from the Mean, median or mode and ignore the minus signs.
  3. Multiply the deviations with the frequency. This step is necessary only in the discrete and continuous series.
  4. Sum up all the deviations.
  5. Apply the formula.

The formula for the Co-efficient of Mean Deviation

  • Co-efficient of Mean Deviation from Mean = \(\frac{M.D.}{ \overline{X}}\)
  • Co-efficient of Mean Deviation from Median = \(\frac{M.D.}{M}\)
  • The Co-efficient of Mean Deviation from Mode = \(\frac{M.D.}{Mode}\)

Solved Examples

Q.1. Calculate the mean deviation from the median and the co-efficient of mean deviation from the following data:

Marks of the students: 86, 25, 87, 65, 58, 45, 12, 71, 35.

Solution: Arrange the data in ascending order: 12, 25, 35, 45, 58, 65, 71, 86, 87.

Median = Value of the \(\frac{N+1}{2}^{th} term\)

= Value of the \(\frac{9+1}{2}^{th} term = 58\)

Calculation of mean deviation:

X \(\left | X – M \right |\)
12 46
25 33
35 23
45 13
58 0
65 7
71 13
86 28
87 29
N = 9 \(\sum \left | X – M \right | = 460\)

M.D. = \(\frac{\sum \left | X – M \right |}{N}\)

= \(\frac{460}{9}\)

= 51.11

Co-efficient of Mean Deviation from Median = \(\frac{M.D.}{M}\)

= \(\frac{51.11}{58}\)

= 0.881

Share with friends

Customize your course in 30 seconds

Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
tutor
tutor
Ashhar Firdausi
IIT Roorkee
Biology
tutor
tutor
Dr. Nazma Shaik
VTU
Chemistry
tutor
tutor
Gaurav Tiwari
APJAKTU
Physics
Get Started

Leave a Reply

avatar
  Subscribe  
Notify of

Stuck with a

Question Mark?

Have a doubt at 3 am? Our experts are available 24x7. Connect with a tutor instantly and get your concepts cleared in less than 3 steps.
toppr Code

chance to win a

study tour
to ISRO

Download the App

Watch lectures, practise questions and take tests on the go.

Get Question Papers of Last 10 Years

Which class are you in?
No thanks.