# English Ch 3 by chfazan

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```									Q.10: State the algebraic properties of A.M
Ans:
n
(i) Sum of deviation of values from their mean is zero i.e.    (X
i 1
i    X) 0

(ii) Sum of squares of deviation from mean is minimum i.e.
n                     n

 ( X i  X )2 
i 1
(X
i 1
i    P.M ) 2 whereP.M  X .

 n1 X
(iii) Combined mean= X c 
 n1
(iv). A.M is affected by change of origin and scale i.e. if Y  a  bX then Y  a  bX

Q.11: What is difference between weighted and un-weighted mean
Ans: In un-weighted mean all the items are equally important.
In weighted mean all the items are not equally important.

Q.12: Define Geometric mean?
Ans: Nth root of product of “n” positives value is called Geometric mean. OR
The geometric mean (G.M) is defined as the nth root of the product of n positive
values. If X1, X2…..Xn be n positive values, then geometric mean is defined by

GM  n X1  X 2  ........ X n
1
G.M  ( X 1  X 2  ........... X n )   n
Ungrouped data
  f log X 
G.M  anti log                            Grouped data
 f        

Ans:
1. It is well defined                   1. It is not suitable for every kind of
2. It uses all the values                  data
3. It is stable for more action         2. It does not exits if any value is
4. It is stable in repeated                Zero
experiments                         3. It cannot be calculated if any
value is negative
Q.14: Define Harmonic mean (H.M)
Ans: Ratio between number of values and sum of their reciprocals is called
Harmonic mean.
      
 n 
H .M              For ungroup data
 1 
  X 
  
      
 f 
H .M              For group data
 f 
  X 
  
Ans:

i.   It is well defined                     i.   It gives more weight to small
ii.   It uses all the values                      values
iii.   It is stable for more action          ii.   It does not exits if any value is
Zero
iii.   It is highly affected by extremely
small values.

Q.16: Describe the ratio between A.M, G.M, and H, M?
A.M>G.M>H.M           If all the values are not equal
A.M=G.M=H.M           if all the values are equal
Q.17: Define Median?
Ans: The value which divides the array data into two equal parts is called Median. It
is central value if number of values is odd and means of two central values if number
of values is even.

Ans:
i. It is well defined                  i.    It is not based on all values
ii. Its graphic location is possible   ii. It is not able for more action
iii. It is not affected by extreme     iii. For large number of values
values                                    arrangement of data is difficult
iv.  It can be calculated for open end
frequency distribution

Mode
Ans: The most repeated value of data is called Mode. A data may have more than
one values of mode. A data having one mode is called UNI-MODEL. Similarly data
having two modes is called Bi-Modal.
f m  f1
X l                               h Group data
 f m  f1    f m  f 2 

i.     Its graphical location is possible      i.     It is ill defined
ii.     It is not affected by extreme          ii.     It is not based on all values
values                                iii.     It is not able for more action
iii.    It can be calculated for every kind   iv.      For small number of values it may
of data                                        not exist
iv.     It can be calculated for open end
frequency distribution

Q.20: What are the limitations of Mode?
i.    It is ill defined
ii.    It is not based on all values
iii.    It is not able for more action
iv.     For small number of values it may not exist

Q.21: Define Quartiles, Deciles, and Percentiles?
Ans: Quartiles: The values, which divide the array data into four equal parts, are
called Quartiles. There are three Quartiles Q1, Q2 and Q3. Q1 is lower Quartiles Q2 is
Median and Q3 is called Upper Quartiles.
Deciles: The values which divide the array data into ten equal parts are called
Deciles. There are nine Deciles, denoted D1, D2, D3………..D9.
Percentiles: The values, which divide the array data into 100 equal parts, are called
Percentiles. There are 99 Percentiles, denoted as P1, P2, P3…….P99.

Q.22: Under what circumstances (condition) A.M, G.M, H.M, MEDIAN and
MODE can be used properly to describe the measures of central tendency?
Ans:
A.M: Suitable when there are no very small or large values in the data.
G.M: It is suitable if the data is in the form of percentages
H.M: It is suitable if data is in the form rates and ratios.
MEDIAN: It is suitable when middle most value is required or distribution is skewed
MODE: it is suitable, when most common value is required

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