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Statistics Test - 39

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Statistics Test - 39
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  • Question 1
    1 / -0
    The average rainfall for a week, excluding Sunday, was $$10\ \text{cms}$$. Due to heavy rainfall on Sunday, the average for the week rose to $$15\ \text{cms}$$. How much rainfall was on Sunday?
    Solution

  • Question 2
    1 / -0

    Directions For Questions

    Study the number series given and answer the questions 
    Series: $$6, 4, 1, 2, 2, 8, 7, 4, 2, 1, 5, 3, 8, 6, 2, 1, 7, 1, 4, 3, 1, 2, 8, 6$$.

    ...view full instructions

    Which numbers have equal frequencies?
    Solution
    Given series is $$6,4,1,2,2,8,7,4,2,1,5,3,8,6,2,1,7,1,4,3,1,2,8,6$$
    Numbers having equal frequencies $$=4, 6, 8$$.
    Number        Frequency
    $$1$$$$5$$
    $$2$$$$5$$
    $$3$$$$2$$
    $$4$$$$3$$
    $$5$$$$1$$
    $$6$$$$3$$
    $$7$$$$2$$
    $$8$$$$3$$
  • Question 3
    1 / -0
    If there are $$N$$ individual observations $$X1, X2, ....Xn$$, Arithmetic mean $$=$$?
    Solution
    $$\overline {X} = \dfrac {X_{1} + X_{2} + X_{3} +......X_{n}}{N}=\dfrac{\sum{X}}{N}$$ 
    This is the direct method of calculating arithmetic mean.
  • Question 4
    1 / -0
    The average marks of three batches of students having 70, 50 and 30 students respectively are 50, 55 and 45. Find the average marks of all the 150 students, taken together.
    Solution
    Given that, the average marks of 70, 50 and 30 students respectively are 50, 55 and 45 marks. 
    $$\therefore\ $$ the total marks of 70, 50 and 30 students will be,
    $$70 \times 50, 50 \times 55$$ and $$30 \times 45$$ respectively. 
    The average marks of all the 150 students will be: 
    $$= \dfrac{ (3500 + 2750 + 1350 )}{( 70+50+30)}$$          $$\left[\text{Average}=\dfrac{\text{Sum of all quantities}}{\text{Number of quantities}}\right]$$
    $$\Rightarrow \dfrac{7,600 }{150}$$
    $$\Rightarrow 50.67$$

    Hence, the average marks of all the 150 students, taken together are $$50.67$$
  • Question 5
    1 / -0
    Secondary data in statistics is the data collected from :
    Solution
    Data is classified as both primary and the secondary data.
    Primary data is the data which is collected for the first time.
    Secondary data is the data which are collected by someone else (secondary sources) and passed through the statistical process.
  • Question 6
    1 / -0
    The bar graph shows the number of traffic accidents in a country from year $$2000$$ to $$2014$$ . What is the difference between accidents in the year $$2001$$ and $$2004$$.

    Solution
    The letter $$k$$ is used to denote $$1000$$

    Therefore, Number of traffic accidents in the year $$2001$$ $$=260k$$

                                                                                                  $$=260\times1000$$

                                                                                                  $$=260,000$$

    Number of traffic accidents in year $$2004$$ $$=220k$$

                                                                         $$=220\times1000$$

                                                                         $$=220,000$$.

    Then, the difference $$=260,000-220,000$$

                                       $$=40,000$$

    Therefore, option $$B$$ is correct.
  • Question 7
    1 / -0

    Directions For Questions

    The number of hours for which students of a particular class watched television during holidays is shown through the given graph.
    Answer the following questions:

    ...view full instructions

    The number of students watched TV for less than $$4$$ hours , is ______ .

    Solution
             Hours of TV Watched          Number of Students
                        $$1-2$$                     $$4$$
                        $$2-3$$                     $$8$$
                        $$3-4$$                    $$22$$
                        $$4-5$$                    $$32$$
                        $$5-6$$                     $$8$$
                        $$6-7$$                     $$6$$
    As clearly seen from the Graph and Corresponding Table,

    Number of Students who watched TV for less than $$4$$ Hours
    $$=$$ Number of Students who are lying in Class $$1$$-$$2$$ , $$2$$-$$3$$ , $$3$$-$$4$$ hours
    $$= 4 + 8 + 22 = 34$$.

    Hence, option $$C$$ is correct.
  • Question 8
    1 / -0
    Consider the following observation relating to marks obtained by $$10$$ students in CS Foundation Exam: $$201, 202, 207, 222, 276, 201, 246, 212, 285, 312$$.
    Arithmetic mean $$=$$?
    Solution
    Mean refers to the average amount in a given group of data. In this measure of central tendency, all the data are added up and then divided by the number of figures in the data in order to ascertain the mean.

    Mean $$\dfrac{(201+ 202+207+222+276+201+246+212+285+312}{10}$$
    $$= 236.4 $$
  • Question 9
    1 / -0
    The mean is_____________________.
    Solution

    Mean refers to the average amount in a given group of data. There are many ways to calculate arithmetic mean like direct method where all the data are added up and then divided by the number of figures in the data in order to ascertain the mean class or assumed mean method and step deviation method, the data of the given class is reduced into smaller units which makes it easy to do calculation and ascertain the mean of the class. 

    i.e.

    $$Arithmetic\ mean= \dfrac{Sum\ of\ given\ numbers}{Total\ numbers}$$
  • Question 10
    1 / -0
    The arithmetic mean between $$\cfrac { x+a }{ x } $$ and $$\cfrac { x-a }{ x } $$ when $$x\ne 0$$, is (the symbol $$\ne$$ means "not equal to"):
    Solution
    The arithmetic mean between two quantities is given by,
    A.M.=$$\dfrac{\dfrac{x+a}{x}+\dfrac{x-a}{x}}{2}$$
      =$$\dfrac{x+a+x-a}{2x}$$
       =$$\dfrac{2x}{2x}$$
    =1
    Hence A.M.=1
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