Measures of Dispersion

  • Question 1
    CBSEENST11024272

    Which measure of dispersion is the best and how?

    Solution

    Standard deviation is the best measures of dispersion, because it posseses most of the characterstics of an ideal measure of dispersion.

    Question 2
    CBSEENST11024273

    Some measures of dispersion depend upon the spread of values whereas some calculate the variation of values from a central value. Do you agree?

    Solution

    Yes we agree with the statement Range and quartile deviation measure the dispersion by calculating the spread within which the values lie i.e. they depend on the spread of values. On the other hand, mean deviation and standard deviation calculate the variation of value from a central value.

    Question 3
    CBSEENST11024274

    In a town 25% of the persons earned more than Rs. 45000, whereas 75% earned more than Rs. 18000. Calculate the absolute and relative values of dispersion.

    Solution

    Absolute value of dispersion i.e.

    Question 4
    CBSEENST11024275

    A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their five previous scores which are:

    X

    Y

    25

    50

    85

    70

    40

    65

    80

    45

    120

    80

    Which batsman should be selected if we want

    (i) a higher run getter, or

    (ii) a more reliable batsman in the team?

    Solution

    Batsman -A

    Scores (X)

    (X)

    (X2)

    25

    –45

    2025

    85

    +15

    225

    40

    –30

    900

    80

    +10

    100

    120

    +50

    2500

    ΣX= 350

     

    Σx2= 50

    Batsman B

    X

    (X)

    n2

    50

    -12

    144

    70

    +8

    64

    65

    +3

    9

    45

    -17

    289

    80

    +18

    324

    ΣX=310

     

    ΣX2= 830

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