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Descriptive Statistics Test 39

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Descriptive Statistics Test 39
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  • Question 1
    1 / -0
    Variance of first $$20 $$ natural number is 
    Solution
    Variance of first $$n$$ natural numbers is $$\displaystyle =\dfrac{\sum(x_i)^2}{n}-(Mean)^2$$
    $$=\dfrac{1^2+2^2+3^2.....n^2}{n}-(\dfrac{n+1}{2})^2$$
    $$\sigma^2=\dfrac{n(n+1)(2n+1)}{6n}-\dfrac{(n+1)^2}{4}$$
    $$\boxed{\sigma^2=\dfrac{n^2-1}{12}}$$
    So variance of first $$20$$ natural number
    $$=\sigma^2=\dfrac{20^2-1}{12}=\dfrac{399}{12}=\dfrac{133}{4}$$ 
  • Question 2
    1 / -0

    Directions For Questions

    The bar graph below shows the number of cars passing through a toll tax.

    ...view full instructions

    Find the total number of cars passed through the toll tax.

    Solution
     In bar graph each bar graph shows total number of cars passing through toll tax.
    hence total number of cars passing through the toll tax is = sum of cars of all bar graph
    = $$50+175+250+125=600$$ cars 
    hence option $$B$$ is correct 
  • Question 3
    1 / -0
    The maximum value a correlation coefficient can have is
  • Question 4
    1 / -0
    Value of each sample observation is decreased by $$25$$, the range of the sample observation will ____________.
  • Question 5
    1 / -0

    Directions For Questions

    Study the bar graph given and answer the questions.

    ...view full instructions

    From 2011 to 2016, find the difference between the total number of people who preferred to play Basketball and Badminton (in millions)?

    Solution
    Total no of people who preferred to play Basketball from $$2011$$ to $$2016$$ $$ = 400+375+375+250+350+300=2050$$ (in millions)
    Total no of people who preferred to play Badminton from $$2011$$ to $$2016$$ $$=375+400+300+200+250+275=1800$$ (in millions)
    $$\therefore$$ Required difference $$= 2050-1800=250$$ millions
    Answer : D
  • Question 6
    1 / -0
    Lottery method is an example of _______ sampling.
  • Question 7
    1 / -0
    Range of a set of values is $$60$$ and maximum value in the series is $$80$$. The minimum value of the series is _______.
    Solution

    Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion. 

    Range = 60 

    In the given series, H= 80 and L= x 

    Range => 80-x = 60

                => x = 80-60 = 20 

  • Question 8
    1 / -0
    Which measure of dispersion is most affected by extreme values?
    Solution

    Range is the most simple and commonly understandable measures of dispersion.Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. Therefore, it is the most affected measures of dispersion by the extreme values of the series. 

  • Question 9
    1 / -0
    The first quartile is also known as ______.
  • Question 10
    1 / -0
    The Additive Model of a time series is expressed as :
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