Tag: maths

Questions Related to maths

The coefficient of mean deviation from median of observations 40, 62, 54, 90, 68, 76 is

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

  1. 2.16

  2. 1.2

  3. 5

  4. none of these

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Correct Option: B
Explanation:

Arranging the given data in ascending order
40,54,62,68,76,90
Here, $n=6 (even)$
$M= \dfrac{\text{value of }3^{rd}\text{observation}+\text{value of }4^{th}\text{observation}}{2}$
Median $M=\dfrac{62+68}{2}=65$

Mean deviation about median $M.D=\dfrac{|40-65|+|54-65|+|62-65|+|68-65|+|76-65|+|90-65|}{65}$

$=\dfrac{25+11+3+3+11+25}{65}=1.2$

The difference between the maximum and the minimum observations in the data is

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

  1. class interval

  2. frequency

  3. cumulative frequency

  4. range

Show answer
Correct Option: D
Explanation:

The difference between maximum and the minimum observation in the data is range.

For example, suppose an experiment involves finding out the weight of lab rats and the values in grams are 320, 367, 423, 471 and 480. In this case, the range is simply computed as 480-320 = 160 grams.

The coefficient of range of a set of data is given to be $\dfrac18$. Then the ratio of the maximum value in the data to the minimum value is:

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

  1. $\dfrac81$

  2. $\dfrac98$

  3. $\dfrac97$

  4. $\dfrac87$

Show answer
Correct Option: C
Explanation:

Coefficient of range of a set of data is given by $\dfrac{max-min}{max+min}$
$\dfrac{max-min}{max+min}=\dfrac{1}{8}$
$8max-8min=max+min$
$7max=9min$
$\dfrac{max}{min}=\dfrac{9}{7}$

The following are the wages of 8 workers in a factory. Find the range and coefficient of range. Wages are in dollars: 1400, 1450, 1520, 1380, 1485, 1495, 1575, 1440.

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

  1. $0.0231$

  2. $0.03112$

  3. $0.66$

  4. $0.02314$

Show answer
Correct Option: C
Explanation:

The largest value of data is $x _m=1575$

The smallest value of data is $x _0=1380$
Range$=x _m-x _0=1575-1380=195$

Coefficient of data$=\dfrac{1575-1380}{1575+1380}=\dfrac{195}{2955}=0.0659\approx 0.66$

If the coefficient of range is $0.18$ and the largest value is $7.44$,then the smallest value is?

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

  1. $3.23$

  2. $4.15$

  3. $5.17$

  4. $5.14$

Show answer
Correct Option: C
Explanation:

Coefficient of range$=\dfrac{x _m-x _0}{x _m+x _0}=\dfrac{7.44-x _0}{7.44+x _0}$

$0.18(7.44+x _0)=7.44-x _0$
$1.18x _0=7.44-7.44\times 0.18$
$1.18x _0=6.1008$
$x _0=5.17016\approx 5.17$

Find the coefficient of range for the data $43,24,38,56,22,39,45$

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

  1. $0124$

  2. $0.212$

  3. $0.236$

  4. $0.436$

Show answer
Correct Option: D
Explanation:
Given data is $43, 24, 38, 56, 2, 39,45$.
The largest value of data is $x _m=56$
The smallest value of data is $x _0=22$
Coefficient of data $=\dfrac{56-22}{56+22}=\dfrac{34}{78}=0.4359\approx 0.436$
Hence, option D is correct.

The weight in Kg of 13 students in a class are $42.5,47.5,48.6,50.5,49,46.2,49.8,45.8,43.2,48,44.7,46.9,42.4$.Find the coefficient of range.

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

  1. $0.077$

  2. $0.213$

  3. $0.0803$

  4. $0.093$

Show answer
Correct Option: C
Explanation:

The largest value of data is $x _m=49.8$

The smallest value of data is $x _0=42.4$
Coefficient of data$=\dfrac{49.8-42.4}{49.8+42.4}=\dfrac{7.4}{92.2}=0.08026\approx 0.0803$

Find the coefficient of range for the given data
$59,46,30,23,27,40,52,35,29$

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

  1. $0.46$

  2. $0.44$

  3. $0.56$

  4. $0.124$

Show answer
Correct Option: B
Explanation:
Given data is $59, 46, 30, 23, 27, 40, 52, 35, 29$.
The largest value of data is $x _m=59$
The smallest value of data is $x _0=23$
Coefficient of data $=\dfrac{59-23}{59+23}=\dfrac{36}{82}=0.49\approx 0.44$

A sector of a circle with sectorial angle of $\displaystyle 36^{\circ} $ has an area of 15.4 sq cm The length of the arc of the sector is

maths circle measures length of an arc area of a sector of a circle sector and arc of a circle

  1. $8.8 m$

  2. $4.4 m$

  3. $0.22 m$

  4. $0.44 m$

Show answer
Correct Option: D
Explanation:

$\displaystyle \frac{36}{360}\times \frac{22}{7}r^{2}=15.4\Rightarrow r^{2} =\frac{15.4\times 5\times 7}{11}=49$
$\displaystyle \Rightarrow r=7$
$\displaystyle C=2\pi r=2\times \frac{22}{7}\times 7=44cm$
$\displaystyle =0.44 m$

In a circle of radius 21 cm an arc subtends an angle of $\displaystyle 56^{\circ} $ at the centre of the circle. The length of the arc is

maths circle measures length of an arc area of a sector of a circle sector and arc of a circle

  1. $20.53$ cm

  2. $17.53$ cm

  3. $15.53$ cm

  4. $16.53$ cm

Show answer
Correct Option: A
Explanation:

$\displaystyle \theta =56^{\circ},r=21cm$
Length. of $\displaystyle AB=\dfrac{56^{\circ}}{360^{\circ}}\times 2\times \dfrac{22}{7}\times 21$
$\displaystyle =\dfrac{616}{30}=20.53cm$