Tag: maths

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Questions Related to maths

Multiple choice maths lines equations of lines parallel to the x-axis and y-axis graphs of linear equations graph of linear equations in two variables

Read the following statements carefully and select the correct option.
Statement-I : The graph of the linear equation x + 2y = 6 passes through (8, -1).
Statement II : Every point which satisfies the linear equation is a solution of the equation.

  1. Both Statement-I and Statement-II are true.

  2. Only Statement-I is true.

  3. Only Statement-II is true.

  4. Neither Statement-I nor Statement-II are true.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement I: Substituting (8, -1) into x + 2y = 6 gives 8 + 2(-1) = 6, which is true. Statement II is a standard definition of a solution to an equation.

Multiple choice range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

Coefficient of deviation is calculated by the formula:

  1. $\cfrac { \bar { X } }{ \sigma } \times 100$
  2. $\cfrac { \bar { X } }{ \sigma }$
  3. $\cfrac { \sigma } {\bar { X }} \times 100$
  4. $\cfrac{ \sigma } { \bar { X }}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

It is a fundamental concept.
coefficient of deviation $=\cfrac{\sigma}{\bar{x}}\times 100$
where $\sigma$ and $\bar{x}$ are standard deviation and mean respectively.

Multiple choice range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

For a symmetrical distribution lower quartitl is 20 and upper quartile is 40.The value of 50th percentile is

  1. 20

  2. 40

  3. 30

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First quartile also called the lower quartile or the 25th percentile(splits off the lowest 25% of data from the highest 75%)
Second quartile also called the median or the 50th percentile (cuts data set in half)
Third quartile  also called the upper quartile or the 75th percentile (splits off the highest 25% of data from the lowest 75%)
Since its a symmetrical distribution therefore the median will be 30

Multiple choice range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

The formula for the coefficient of range is $\dfrac{\text{Range}}{a+b}$. Here, $a$ and $b$ denote:

  1. the mean and median of the data set

  2. the maximum and the minimum value of the data set

  3. the mean and mode value of the data set

  4. the minimum and mean value of the data set
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Range is the difference between the maximum value and the minimum value of the data set.


Let $a$ be the maximum value of the data set and
$b$ be the minimum value of the data set

Therefore, $range = a-b$

Coefficient of range is the relative measure of the dispersion.

It is given by $\text{coefficient of range}=\dfrac{a-b}{a+b}=\dfrac{range}{a+b}$

Multiple choice range and mean deviation statistics and probability maths coefficient of variance variance and standard deviation

The largest of $50$ measurements is $3.84$kg. If the range is $0.46$kg, find the smallest measurement.

  1. $3.38$kg.
  2. $2.38$kg.
  3. $6.38$kg.

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

$\Rightarrow$  Here, $L=3.84$ and $R=0.46$

$\Rightarrow$  $R=L-S$
  $0.46=3.84-S$
  $S=3.84-0.46$
$\therefore$  $S=3.38\,kg$
$\therefore$   Smallest measurement is $3.38\,kg$