11th class statistics chapter 4,Measure of Dispersion,important definitions and short questions,1st year class

 Here you will see important short   questions and important definitions of chapter 4.

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11th class statistics chapter 4,Measure of Dispersion,important definitions and short questions,1st year class 


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Chapter 4: Measure of  Dispersion

These are very important   question  according to paper pattern.

 

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 Chpter#4 ,Measure of Dispersion


(IMPORTANT   SHORT QUESTIONS) CHAPTER # 4

Questions

Answers

1.      Define variance.

The Sum of square deviations of values (x’s) from mean is called variance. It is denoted by “S2”. Symbolically,

        For ungroup data

        For group data

 

2.      Define absolute dispersion.

An absolute dispersion is one that measures the dispersion in terms of the same units or in the square of units, as the units of the data. For example, if the units of the data are rupees, meters, kilograms, etc., the units of the measures of dispersion will also be rupees, meters, kilograms, etc.

3.      Define relative dispersion.

Relative dispersion is one that is expressed in the form of a ratio, co-efficient of percentage and is independent of the units of measurement.

A relative dispersion is useful for comparison of data of different nature.

4.      Define coefficient of variation.

The percentage ratio between standard deviation and mean of data is called coefficient of variation. symbolically

5.      Define standard deviation.

The positive square root of variance is called standard deviation. It is denoted by “S”. Symbolically,                              

         For ungroup data

For group data

6.      Define skewness.

Lack of symmetry in a frequency distribution is called skewness.

7.      Given  

Find the coefficient of variation.


8.      In a symmetrical distribution Q1=40, Q3=60,find median

Since In a symmetrical distribution

Med-Q1=Q3-Med

Or     2Med= Q3+ Q1

         2Med=60+40

          Med=100/2       

          Med=50

 

9.      Given                              

X  =   4, 6, 8, 10, 12             Find mean deviation from mean


4 6
8

10

12



4

2

0

2

4


 

 

 

 

 

Mean Deviation from mean:

10.  Differentiate between absolute dispersion and relative dispersion.

An absolute dispersion is one that measures the dispersion in terms of the same units or in the square of units, as the units of the data.

On the other hand, relative dispersion is one that is expressed in the form of a ratio, co-efficient of percentage and is independent of the units of measurement. So relative dispersion is Pure number but absolute is not a pure number.

 

11.  The mean of 200 items is 48 and S.D=3  find

.

Given  n=200,

12.  For what purpose are computed?

 is used to check the skewness of data,

 

While  is used to check the kurtosis of data.

 

 

 

 

 

13.  Given comments the skewness.

 

Since mean<mod   so the distribution is negatively skewed.

14.  Given that what is the value of median and why?

Median=12 because the sum of absolute deviation of values from median is minimum.

15.  What do you understand by dispersion?

The degree to which numerical data tend to spread on average value is called the Dispersion or Variation.

16.  If var(x)=5 and var(y)=2, then find

 var(2x-3y)=?

Var(2x-3y)= 22 var(x)+32var(y)=

17.  If the range of values is 46 and smallest value of the series is 10,then find maximum number.

Given   R=46  ,Xo=10

R=Xm-Xo

18.  What will be the shape and name of the distribution for which mean>med>mod.

 

If   mean>med>mod    then shape of the distribution is skewed to the right and the distribution is positively skewed.

 

 

19.  Give any two properties of variance.

 

20.  Find the range of data; C,C,C,C,C,C

R=Xm-Xo=C-C=0

21.  Define quartile deviation.

It is the half of the difference between third and first quartiles. It is denoted by Q.D. Symbolically,

Where     ,   

22.  Define moments about zero.

If x1,x2,x3,...,xn are n observations on a variable X,then their r-th moment about zero/origin can be defined  as:

Where      r=1,2,3,...                                                                                           

23.  In normal distribution what are the values of .

For normal distribution 

24.  Define kurtosis

The height and sharpness of the peak relative to the rest of the data are measured by a number called kurtosis.

25.  Given mean=100, mode=95 and s.d=10 find coefficient of skewness.

We know that

So coefficient of skewness is 0.5

26.  What are the names of most common measure of Absolute dispersion?

The most commonly used  measures of dispersion are:

(i)Range(ii) Quartile Deviation(iii)Mean Deviation (iv)Standard Deviation

27.  Define range.

The difference between the smallest value and the largest value is called

 

 

28.  What are the names of the measure of dispersion?

There are two types of dispersion

i-                    Absolute Dispersion

ii-                  Relative Dispersion

29.  Find the range of -1,-3,0,2,3

Here    Xm=3, Xo=-3

R= Xm- Xo

R=3-(-3)

R=6

30.  If range a series is 46 and smallest vale is 10,then find the maximum number in the series

Given

R=46  ,  Xo=10

We have

R= Xm- Xo

46= Xm-10

Xm=46+10

Xm=56

31.  What will be the shaped name of the distribution for which Mean>Med>Mode

If

Mean>Med>Mode

The distribution is called Positively Skewed.

32.  Given mean = 100, mode=95 and S.D=10 then find the coefficient of skewness.

We have

So coefficient is  0.5

33.  Differentiate between inter quartile range and quartile deviation.


34.  What are the values of for a symmetrical distribution?

In case of symmetrical distribution =0   and  

35.  Find the coefficient of quartile deviation.

Coefficient of  

36. Differentiate between symmetry and skewness?

A distribution is said to be symmetrical if mean=med=mod      otherwise it’s called skewed or asymmetry. 

37. Give any two properties of variance.

(i) The variance of a constant is equal to zero. For constant “a”

Var(a)=0

(ii) The variance is not affected by change of origin i.e

Var(X+a)=Var(X)        OR

Var(X-a)= Var(X)

38. For moderately skewed distribution med=65, mode=85. Find the value of mean.

We know that

Mode =3med-2mean

       85=3(65)-2mean

       85=195-2mean

2Mean=195-85

Mean=110/2

Mean=55

 

 

 

 

 

39. Find c.v.

We have

40. For what purpose

is used to check the skewness of the given data.

is used to check the kurtosis of the given data.

41.Given

comments the skewness

We know that

Here we have

Mode> Mean

2.9>2.47

So the distribution is negatively skewed as mean is less than mode.

42 . For moderately skewed distribution med=65, mode=85. Find the value of mean.

We know that

Mode =3med-2mean

       85=3(65)-2mean

       85=195-2mean

2Mean=195-85

Mean=110/2

Mean=55

 

 

 

 

 

 

 

 

 

 

 

 

43. Find c.v.

We have

44. For what purpose

is used to check the skewness of the given data.

is used to check the kurtosis of the given data.

45.Given

comments the skewness

We know that

Here we have

Mode> Mean

2.9>2.47

So the distribution is negatively skewed as mean is less than mode.

 

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