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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.
Chpter#4 ,Measure of Dispersion
(IMPORTANT SHORT QUESTIONS) CHAPTER # 4
Questions |
Answers |
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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
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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. |
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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. |
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4. Define coefficient of variation. |
The percentage ratio between standard deviation and mean of data is called coefficient of variation. symbolically
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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 |
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6. Define skewness. |
Lack of symmetry in a frequency distribution is called skewness. |
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7. Given Find the coefficient of variation. |
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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
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9. Given X = 4, 6, 8, 10, 12 Find mean deviation from mean |
Mean Deviation from mean:
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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.
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11. The mean of 200 items is 48 and S.D=3 find . |
Given n=200,
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12. For what purpose are computed? |
is used to check the skewness of data,
While is used to check the kurtosis of data.
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13. Given comments the skewness. |
Since mean<mod so the distribution is negatively skewed. |
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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. |
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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. |
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16. If var(x)=5 and var(y)=2, then find var(2x-3y)=? |
Var(2x-3y)= 22 var(x)+32var(y)= |
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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
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18. What will be the shape and name of the distribution for which mean>med>mod.
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If mean>med>mod then shape of the distribution is skewed to the right and the distribution is positively skewed.
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19. Give any two properties of variance. |
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20. Find the range of data; C,C,C,C,C,C |
R=Xm-Xo=C-C=0 |
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21. Define quartile deviation. |
It is the half of the difference between third and first quartiles. It is denoted by Q.D. Symbolically,
Where , |
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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,... |
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23. In normal distribution what are the values of . |
For normal distribution |
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24. Define kurtosis |
The height and sharpness of the peak relative to the rest of the data are measured by a number called kurtosis. |
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25. Given mean=100, mode=95 and s.d=10 find coefficient of skewness. |
We know that
So coefficient of skewness is 0.5 |
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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 |
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27. Define range. |
The difference between the smallest value and the largest value is called
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28. What are the names of the measure of dispersion? |
There are two types of dispersion i- Absolute Dispersion ii- Relative Dispersion |
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29. Find the range of -1,-3,0,2,3 |
Here Xm=3, Xo=-3 R= Xm- Xo R=3-(-3) R=6 |
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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 |
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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. |
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32. Given mean = 100, mode=95 and S.D=10 then find the coefficient of skewness. |
We have
So coefficient is 0.5 |
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33. Differentiate between inter quartile range and quartile deviation. |
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34. What are the values of for a symmetrical distribution? |
In case of symmetrical distribution =0 and |
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35. Find the coefficient of quartile deviation. |
Coefficient of |
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36. Differentiate between symmetry and skewness? |
A distribution is said to be symmetrical if mean=med=mod otherwise it’s called skewed or asymmetry. |
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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) |
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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
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39. Find c.v. |
We have
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40. For what purpose |
is used to check the skewness of the given data. is used to check the kurtosis of the given data. |
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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. |
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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
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43. Find c.v. |
We have
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44. For what purpose |
is used to check the skewness of the given data. is used to check the kurtosis of the given data. |
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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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