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NDA - Frequency Distribution Test 1111
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NDA - Frequency Distribution Test 1111

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  • Question 1/5
    1 / -0.33
    Which one of the following can be considered as an appropriate pair of values of regression coefficient of y on x and regression coefficient of x on y?
    Solutions

    The product of regression coefficients of y on x and regression coefficient of x on y is always less than or equal to 1

    Also, the sign of both coefficients should be the same

    So, there is only one pair which has to satisfy the given condition

  • Question 2/5
    1 / -0.33
    Consider the following statements :

    1) Variance is unaffected by change of origin and change of scale.

    2) Coefficient of variance is independent of the unit of observations.

    Which of the statements given above is/are correct?

    Solutions

    Case -1: Variance is independent of the change of origin as the change in origin is uniformly added to all the values and hence the mean also and hence, when  is calculated, it remains unaffected.

    Case -2: But, change of scale alters all values unevenly and hence, variation changes.

    Case – 3: The coefficient of variance is standard deviation by mean which doesn't depend on the unit of observation.

    So, Statement 1 is incorrect Statement 2 is correct

  • Question 3/5
    1 / -0.33
    The value of  for the following distribution is

    Marks group: 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45

    No of Student: 5       6       15      10       5       4        2       1

    Solutions

    The cumulative frequency distribution is as given below:

    Here,  because we calculate . So first we find

    We have,

    The cumulative frequency just greater than  is 41. The corresponding class is 25-30. It is the upper quartile class.

     Lower limit =25, frequency = 5, width  = 5

    And cumulative frequency of the class preceding the quartile class = 36

    We have,

     
    The second quartile, Q2, is also the median. The upper or third quartile, denoted as Q3, is the central point that lies between the median and the highest number of the distribution.

  • Question 4/5
    1 / -0.33
    Find standard deviation of the above data.
    Solutions
     Standard deviation =  =
  • Question 5/5
    1 / -0.33
    In a partially destroyed record the following data are available :

    Regression equation of x on y and regression equation of y on x are 3x+y=12 and x+2y=14 respectively then find the sum of mean values of x and y.

    Solutions
     The mean values of x and y lie on the regression lines and are obtained by solving the given regression equations.

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