Mean Deviation for individual series

 MEAN DEVIATION

We have learnt RANGE and  QUARTILE DEVIATION in earlier blog. If you want to revise click on them. Now we are moving to a new topic called mean Deviation.
There are three types of mean Deviations
  • Mean Deviation about mean.
  • Mean Deviation about median.
  • Mean Deviation about mode.

Individual series

If  data is given in individual series.
Ex 1:- Find the value of mean Deviation about mean for the following numbers.
5,8,6,3,4.
Sol :- Firstly, find their meanthe
                (sum of observations)
Mean =—————————————
               Number of observations

Mean = (5+8+6+3+4)/5 = 26/5 = 5.2

Mean Deviation                             
about mean =( Σ|x- mean|) / n.
Here x means values given in data.
   |5-5.2|+|8-5.2|+|6–5.2|+|3–5.2|+|4–5.2|
=  ———————————————————.
                                5
     |-0.2|+|2.8|+|0.8|+|–2.2|+|–1.2|
= ————————————————.
                            5
         0. 2 + 2.8+ 0.8+ 2.2+ 1.2  
= —————————————
                            5
         7.2
    = —— =  1.44
          5                                              
So 1.44 is the mean Deviation about mean

Ex 2:- If the data is given in individual series.
Ex 1:- Find the value of mean Deviation about median for the following numbers.
5,8,6,3,4.
Sol :- Firstly, find their median.
Median of the data is 5

Mean Deviation                                              
          about median =( Σ|x- median|) / n
 
         |5-5|+|8-5|+|6-5|+|3-5|+|4-5|
   =  ————————————————
                              5
            0+|-3|+|-1|+|-2|+|-1|
    = ———————————————
                                5
            0+ 3+ 1+ 2+1
    =  ————————
                       5
    =  7/5  =  1.4

Ex 3:-  If  data is given in individual series.
Find the value of mean Deviation about mode for the following numbers.
5,8,3,4,4,5,5.

Sol :- First find mode
Mode of the data is 5 ( repeated 3 times)

Mean Deviation                                               
                about mode =( Σ|x- mode|) / n

 |5-5|+|8-5|+|3-5|+|4-5|+|4-5|+|5-5| +|5-5|
= ————————————————
                                7
           0+|-3|+|-2|+|-1|+|-1|+0+0
    = ———————————————
                                7
            0+ 3+ 2+1+ 1+ 0+ 0
    =    ——————————
                       7
           = 7/7   =   1

Comments

Post a Comment

Popular posts from this blog

RATIO & PROPORTION :- Points to remember

RATIO AND PROPORTION. Introduction and Main points. Ratio :- ratio is a comparison of two or more quantities of the same kind by division.     Ex:-  the ratio between two weights 35kgs and 65 kgs. The term a:b first term a is called antecedent in the second term b is called consequent . Ratio exists only between quantities of the same kind. Quantities to be compared must be in the same units. The order of terms in the ratio is important. A  ratio as no units. Usually a ratio is expressed in lowest terms. Duplicate ratio of a:b is a² : b². Sub-duplicate ratio of a:b is √a: √b. Triplicate ratio of a:b is a³:b³  . Sub-triplicate ratio of a:b is ³√a : ³√ b  . one ratio is inverse of another is their product is 1. compound ratio of a:b , c:d and e:f   is a×c×e : b×d×f . i.e, the product of the antecedent : product of the consequent. Compounded ratio is the ratio between three are more quantities of same kind is called their continued ratio....
Read more

Quartile deviation all formulas with examples.

 QUARTILE DEVIATION In measures of dispersion the first concept is Range which we have completed earlier in previous blog. If you want visit again CLICK HERE => RANGE Now, we have to start the 2nd topic, Quartile Deviation. CONCEPT suppose think there is a number line staring from 0 and ending with 8. Now I asked you divide this number line into 4 equal parts. You may show like this                      Q1.            Q2           Q3.                                   |              |               |           0—–1——2–—3–—4–—5——6–—7–—8 So, you divided like this. There are 4 parts divided by using 3 lines. These lines are named as quartiles. For every 25% area on number ...
Read more

Theory of SUPPLY & Elasticity of supply: - topic

Image
 Theory of Supply. Supply refers to quantity of goods and services that producers are willing and able to offer at market at various prices during a given period of time. For perishable goods whatever is produced must be sold i.e; supply=stock. For non-perishable goods supply and stock are different. Supply refers to what a firm offered for sale in the market not necessarily mean for what they succeed in selling. Supply is flow concept. Determinants of Supply Price of the product Price of related good. State of Technology. Government policies (Taxes). Time. Nature of computation and size of industry. Floods, market structure, war, labour strikes, communal riots. Law of supply It explains Direct relation between price and supply. Quantity of goods produced and offered for sale increase as the price increases and decrease as the price decreases. Supply curve Exceptions to Law of supply . 1) Rare commodity 2) Land 3) Supply of labour. Expansion and contraction of supply. When the supp...
Read more