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Questions Related to statistics

Multiple choice statistics measures of central tendency geometric and harmonic mean geometric mean mean

The harmonic mean of the roots of equation $(5+\sqrt {2})x^{2}-(4+\sqrt {5})x+8+2\sqrt {5}=0$ is

  1. $2$
  2. $4$
  3. $6$
  4. $none\ of\ these$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\begin{array}{l} \left( { 5+\sqrt { 2 }  } \right) { x^{ 2 } }-\left( { 4+\sqrt { 5 }  } \right) x+8+2\sqrt { 5 } =0 \ a=5+\sqrt { 2 }  \ b=-\left( { 4+\sqrt { 5 }  } \right)  \ c=8+2\sqrt { 5 }  \ Harmonic\, \, mean\, \, of\, \, \lambda ,\beta  \ =\frac { { 2\lambda \beta  } }{ { \lambda +\beta  } }  \ \lambda \beta =\frac { c }{ a } =\frac { { 8+2\sqrt { 5 }  } }{ { 5+\sqrt { 2 }  } }  \ \lambda +\beta =\frac { { -b } }{ a } =\frac { { 4+\sqrt { 5 }  } }{ { 5+\sqrt { 2 }  } }  \ Harmonic\, \, mean=\,  \ \frac { { 2\frac { { \left( { 8+2\sqrt { 5 }  } \right)  } }{ { 5\sqrt { 2 }  } }  } }{ { \frac { { 4+\sqrt { 5 }  } }{ { 5+\sqrt { 2 }  } }  } }  \ =\frac { { 2\left( { 8+2\sqrt { 5 }  } \right)  } }{ { 4+\sqrt { 5 }  } }  \ =4\, \, \,  \end{array}$

Multiple choice statistics measures of central tendency geometric and harmonic mean geometric mean mean

The mean of the following frequency distribution is 62.8 and the sum of all the frequencies is 50. Compute the missing frequency $\displaystyle f _{1}$ and $\displaystyle f _{2}$.

Class 0-20 20-40 40-60 60-80 80-100 100-120
Frequency 5 $\displaystyle f _{1}$ 10 $\displaystyle f _{2}$ 7 8
  1. $5, 8$
  2. $6, 12$
  3. $8, 11$
  4. $8, 12$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Class       Frequency(f)  ClassMark (x)         fx
0-20         5      10         50
20-40     ${f} _{1} $      30       $ 30{f} _{1} $
40-60         10       50          500
60-80      ${f} _{2} $        70        $ 70{f} _{2} $
80-100          7         90          630
100-120           8         110           880
Total $30 + {f} _{1} +{f} _{2} $   $ 2060  + 30{f} _{1}+70{f} _{2} $

Given $ 30 + {f} _{1} +{f} _{2} = 50 $
$ => {f} _{1} +{f} _{2} = 20 $   -- (1)

Given, Mean $ = \cfrac { \sum { fx }  }{ \sum { f }} =62.8 $
$ => \cfrac { 2060  + 30{f} _{1}+70{f} _{2}}{30 + {f} _{1} +{f} _{2}} = 62.8 $

$ =>  2060  + 30{f} _{1}+70{f} _{2} = 1884 + 62.8{f} _{1} + 62.8{f} _{2} $ 

$ 32.8{f} _{1} - 7.2{f} _{2} =176 $

=> $ 8.2{f} _{1} - 1.8{f} _{2} = 44 $

=> $ 4.1{f} _{1} - 0.9{f} _{2} = 22 $ -- (2)

Solving both equations 1, 2, we get
$ {f} _{1} = 8, {f} _{2} = 12 $

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

Let m be the mid-point be the upper class limit of a continuous frequency distribution The lower class limit of the class is

  1. $2m+L$
  2. $2m-L$
  3. $m-L$
  4. $m+2L$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Mid point=$\dfrac{upper  limit+ lower  limit}{2}$

$\Rightarrow m=\dfrac{L+lower  limit}{2}$
$\Rightarrow Lower   limit=2m-L$

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

The class marks in a frequency table are given to be $5,10,15,20,25,30,35,40,45,50$. The class limits of the first classes are 

  1. $3-7,7-17,13-17,17-23,23-27$
  2. $2.5-7.5,7.5-12.5,12.5-17.5,17.5-22.5,22.5-27.5$
  3. $1.5-8.5,8.5-11.5,11.5-18.5,18.5-21.5,21.5-28.5$
  4. $2-8,8-12,12-18,18-22,22-28$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$2.5 - 7.5, 7.5 - 12.5, 12.5 - 17.5, 17.5 - 22.5, 22.5 - 27.5$


Given,

$5,10,15,20,25,30,35,40,45,50$

the class limit is given by,

$\dfrac{5}{2}=2.5$

$\dfrac{5+10}{2}=7.5$

$\dfrac{10+15}{2}=12.5$

$\dfrac{15+20}{2}=17.5$

$\dfrac{20+25}{2}=22.5$

$\dfrac{25+30}{2}=27.5$

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

Class mark of a particular class is 6.5 and class size is 3 then class interval is:

  1. $5-8$
  2. $6.5-9.5$
  3. $3.5-6.5$
  4. $4-7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the a be the lower limit of the class interval

Class size of the class interval =3
$\therefore$ Upper limit of the class interval$=a+3$
Class mark=6.5
$\therefore \dfrac{a+a+3}{2}=6.5$
$\Rightarrow 2a+3=6,5\times 2$
$\Rightarrow 2a=13-3$
$\Rightarrow 2a=10\Rightarrow a=\dfrac{10}{2}=5$
$\therefore a+3=5+3=8$
Hence class interval= $5-8$

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

The class marks of a frequency distribution are given as follow 15,20,25,...
The class corresponding to the class mark 20 is 

  1. $12.5-17.5$
  2. $17.5-22.5$
  3. $18.5-21.5$
  4. $19.5-20.5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Width=5

Class marks=20
$\therefore  Lower\  limit=20-\dfrac{5}{2}$
$\Rightarrow \dfrac{40-5}{2}=\dfrac{35}{2}=17.5$
$Upper\  limit=20+\dfrac{5}{2}$
$\Rightarrow \dfrac{40+5}{2}=\dfrac{45}{2}=22.5$
Hence the class corresponding to the class mark 20 is $17.5-22.5.$

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

Person $A$ $B$ $C$ $D$ $E$
Profeesion Hort. Indust. Phys. Journa. Advocate
Choice Tea Coffee Tea Coffee Tea

Which of the following groups includes a person who likes tea but is not an advocate?

  1. $ACE$
  2. $DE$
  3. $BCE$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From table,A and C prefer Tea who are not advocate.

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

The data for test scores out of $5$ for $10$ students is given below:
$3,4,1,3,5,2,4,1,3,2$
Tabulate the given data and answer the questions.
How many students scored $4$ or more than $4$?

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Two students scored $4$ and one student scored $5$

So the number of students scored $4$ or more than $4$ $=3$
Option $C$ is correct.

Multiple choice statistics vital statistics and official statistics guiding rules for tabulation vital statistics textual and tabular presentation of data

The total agricultural land in a village is $1200$ hectares. This is distributed among $320$ families who form four groups in the following pattern. It is assumed that the land is distributed equally within each group. Identify the group of small farmers

Group Number of families Total amount of land owned and operatedby each group (in hectares)
A 100 300
B 180 300
C 30 300
D 10 300

  1. A

  2. B

  3. C

  4. D
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In group of small farmers, it would be minimum land available to each farmer.

So we will find the ration of total amount of land owned and operated by each group to the number of families.
From A,  $\dfrac {300}{100} = 3$
From B,  $\dfrac {300}{180} = 1.67$
From C,  $\dfrac{300}{30} = 10$
From D,  $\dfrac {300}{10} = 30$
B is the group of small farmers.
Option B is correct.