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Statistics Test - 31

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Statistics Test - 31
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  • Question 1
    1 / -0
    If the upper and the lower limits of a class interval are $$16$$ and $$10$$, the class-interval is?
    Solution
    The upper limit of a class interval is the maximum value of that interval and the lower limit of a class interval is the minimum value of that interval.
    Given that upper limit is $$16$$ and lower limit is $$10$$.
    Therefore the class interval is $$10-16$$.
  • Question 2
    1 / -0
    Which class-interval has the minimum frequency ?

    Solution

    We will form a table from the above histogram:
    Class IntervalFrequency
     $$0-10$$$$15$$ 
     $$10-20$$$$10$$ 
     $$20-30$$$$20$$ 
     $$30-40$$$$25$$ 
     $$40-50$$$$10$$ 
     $$50-60$$$$5$$ 
    $$\Rightarrow$$  From above table table we can see, $$50-60$$ has frequency $$5$$ which is minimum.
    $$\therefore$$  The class-interval that has the minimum frequency is $$50-60$$

  • Question 3
    1 / -0
    What is the mean of first 8 whole numbers?
    Solution
    First $$8$$ whole numbers are $$ 0,1,2,3,4,5,6,7$$

    We know that, $$\text{Mean}=\dfrac{\text{Sum of all observations}}{\text{Total number of observations}}$$

    $$\therefore \ \text{Mean}=\dfrac {0+1+2+3+4+5+6+7}{8}$$
    $$\Rightarrow \dfrac {28}{8}=3.5$$
    Hence, the mean of first $$8$$ whole numbers is $$3.5$$.
  • Question 4
    1 / -0
    If $$25$$ is the arithmetic mean of $$ X$$ and $$46,$$ then find $$X.$$
    Solution
    Since $$25$$ is the arithmetic mean of $$X$$ and $$46$$, 

    $$\therefore 25=\displaystyle \frac{(X+46)}{2}$$
    $$\therefore  X+46=50$$
    $$\therefore  X=4$$
  • Question 5
    1 / -0
    If the range of $$14, 12, 17, 18, 16, x$$ is $$20$$ and $$x>0$$, the value of $$x$$ is:
    Solution
    The range is the difference between the smallest value and the largest value of the data set.
    Given data set is $$14, 12, 17,18,16,x$$ and the range is given as $$20$$.
    In the given set the smallest value is $$12$$ and the largest value is $$18$$.
    Therefore the range is $$18-12=6\neq20$$
    Hence, $$18$$ is not the largest value. Variable $$x$$ is the largest value.
    Therefore, range is $$x-12=20$$
                          $$\implies x=20+12=32$$
  • Question 6
    1 / -0
    Following are the marks obtained by 30 students in an examination :
    15
    16
    44
    27
      7
    37
    20
    17
    47
    25
    11
    47
    8
    20
    38
    28
    21
    23
    9
    24
    36
    30
    31
    20
    10
    30
    40
    19
    41
    17
    Taking class intervals 0-10, 10-20, ..................., 40-50, construct a frequency table.
    Solution
    Create class intervals $$0 - 10$$, $$11 - 20$$, $$21- 30$$ an so on.and count the frequency in each interval:
    C.I.              
    Tally Marks.                                     Frequency
      0-10
    10-20
    20-30
    30-40
    40-50
    |||
    $${||||}\! \! \! \! \! \! {\diagdown}\:\: ||$$
    $${||||}\! \! \! \! \! \! {\diagdown}\:  ||||$$
    $${||||}\! \! \! \! \! \! {\diagdown}\:  |$$
    $${||||}\! \! \! \! \! \! {\diagdown}$$
    3
    7
    9
    6
    5
  • Question 7
    1 / -0
    In the following distribution :
    Monthly income range (in Rs.)
    Number of families
    Income more than Rs. $$10000$$        
    $$100$$
    Income more than Rs. $$13000$$$$85$$
    Income more than Rs. $$16000$$
    $$69$$
    Income more than Rs. $$19000$$
    $$50$$
    Income more than Rs. $$22000$$
    $$33$$
    Income more than Rs. $$25000$$
    $$15$$
    The numbers of families having income range (in Rs) $$16000 - 19000$$ is:
    Solution
    Number of families having income range from Rs. $$16000 - 19000$$
    $$= $$ Number of families having income more than Rs. $$16000 -$$ Number of families having income more than Rs. $$19000$$
    $$ = 69-50$$ 
    $$ = 19$$
    Hence, the answer is $$19$$.
  • Question 8
    1 / -0
    The upper-class limit of 24 - 30 is?
    Solution
    Upper class limit is the maximum value of the class interval.
    Therefore the upper class limit for $$24-30$$ is $$30$$.
  • Question 9
    1 / -0
    The mean of first five prime numbers is
    Solution
    First five prime numbers are: $$2,3,5,7,11$$
    Mean $$= \cfrac{\text{Sum}}{\text{Count of Numbers}}$$
    Mean $$= \cfrac{2 + 3 + 5 + 7 + 11}{5}$$
    Mean $$= \cfrac{28}{5}$$
    Mean $$= 5.6$$
  • Question 10
    1 / -0

    Directions For Questions

    Answer the question based on the below frequency table:
    Ages
    No. of students
    Below $$4$$
    $$0$$
    Below $$7$$
    $$85$$
    Below $$10$$
    $$140$$
    Below $$13$$
    $$243$$
    Below $$16$$
    $$300$$

    ...view full instructions

    State the number of students in the age group $$10 - 13.$$
    Solution
    From the table, number of students below age $$10$$ is $$140$$ and
    the number of students below age $$13$$ is $$243$$.
    Therefore number of students in the age group of $$10-13$$ is $$243-140=103$$.
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