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Shortcut method for calculating mean deviation about mean - class-X

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The median of the following observations is
$10, 8, -9, -12, 15, 0, 23, -3, -2, 13, -24, 28, 35, 42$

  1. $4$

  2. $-2$

  3. $7$

  4. $-9.75$


Correct Option: A

When all the observations are same, the relation between A.M., G.M and H.M is _________.

  1. A.M. = G.M. = H.M.

  2. A.M. = G.M. > H.M.

  3. A.M. > G.M. > H.M.

  4. A.M. < G.M. < H.M.


Correct Option: A

Geometric mean of two observations can be calculated only if ________.

  1. both the observations are positive

  2. one of the two observations is zero

  3. one of them is negative

  4. both of them are zero


Correct Option: A

For further algebraic treatment geometric mean is _______.

  1. suitable

  2. not suitable

  3. sometime suitable

  4. none of the above


Correct Option: B

If modal value is not clear in a distribution, it can be ascertained by the method of ________.

  1. grouping

  2. guessing

  3. summarizing

  4. trial and error


Correct Option: A

For further algebraic treatment harmonic mean is ______.

  1. suitable

  2. not suitable

  3. sometime suitable

  4. none of the above


Correct Option: B

Mean deviation of $7,10,10,15,10,8,8,7,3,2,10$ through mean is

  1. $3.14$

  2. $8$

  3. $\dfrac {4}{5}$

  4. None of these


Correct Option: A
Explanation:

mean $=\dfrac{\sum {x _1}}{n}=\dfrac{90}{11}\approx 8.18$

derivation through mean = $|x _i-\bar x|$
& mean of it is $=\dfrac{\sum|{x _i-\bar x}|}{n}$
$=\dfrac{(1.18+1.82+1.82+6.82+8.18+0.18+0.18+1.18+5.18+6.18+1.82)}{11}$
$=\dfrac{34.54}{11}=3.14$

If a constant value $40$ is subtracted from each observation of a set, the mean of the set is __________.

  1. increased by $40$

  2. decreased by $40$

  3. is not affected

  4. zero


Correct Option: B

The second quartile of the following observations is
$10, 19, 22, 16, 15, 18, 20, 18, 14, 18, 23$.

  1. $17.55$

  2. $18$

  3. $15$

  4. $20$


Correct Option: B

If Md, Q, D and P Stands for median, quartile, decile and percentile respectively, then which of the following relation between them is true?

  1. $M _d = Q _2 = D _6 = P _50$

  2. $M _d = Q _3 = D _6 = P _75$

  3. $M _d = Q _5 = D _5 = P _50$

  4. $M _d = Q _2 = D _5 = P _50$


Correct Option: D

Which of the following relation is true between $3^{rd}$ decile and $30^{th}$ percentile?

  1. $D _7 = P _{70}$

  2. $D _7 = P _{30}$

  3. $D _3 = P _{30}$

  4. $D _3 = P _{70}$


Correct Option: C

Mode is that value in a frequency distribution which possesses __________.

  1. minimum frequency

  2. maximum frequency

  3. frequency one

  4. none of the above


Correct Option: B

In a discrete series having $(2n+1)$ observations, median is ______.

  1. nth observation

  2. $(n+1)$th observation

  3. $[(n+2)/2]th$ observation

  4. $[(2n+1)/2]th$ observation


Correct Option: B

The average runs of a cricketer in four innings is $32$. How many runs he should score in the fifth inning so that his averages score becomes $50$ runs?

  1. $132$

  2. $122$

  3. $128$

  4. $126$


Correct Option: B

In a moderately skewed distribution the arithmetic mean is $10$ units and the mode is $7$ units, the median is ______.

  1. $9$

  2. $5$

  3. $8$

  4. $6$


Correct Option: A

The mean annual salary of all employees in a company is Rs$25,000$. The mean salaries of male and female employees are Rs$27,000$ and $Rs17,000$ respectively, the percentage of males and females employees by the company is _______.

  1. $80,20$

  2. $20,80$

  3. $30,70$

  4. $70,30$


Correct Option: A
Explanation:

Given, the mean annual salary of all employees in a company is $Rs\ 25,000$ & mean salaries of male and female employees are $Rs\ 27,000$ and $Rs\ 17,000$ respectively.


Let us consider mean salaries of male as $Rs. 27000$ and female as $17,000$

$\dfrac{27,000x+17,000y}{x+y}=25,000$
$27,000x+17,000y=25,000x+25,000y$
$2000x=8000y$

$x=4y$

Percentage of males $(4y/5y)\times 100=80\%$

Percentage of females $=20\%$

In distribution $25\%$ of the observations are less than $46$ and $25\%$ of the observations are more than $54$. The quartile deviation of the distribution is _______.

  1. $3$

  2. $7$

  3. $4$

  4. $6$


Correct Option: C
Explanation:

Quartile deviation divides the series into four equal parts and measures the distance average between the third and the first quartile. The first quartile is denoted as Q1 and the third quartile is denoted as Q3 . 

Q1= 46 and Q3=54

Quartile deviation = (Q3-Q1) /2

                             = (54-46)/2

                             = 8/2

                             = 4

Probability is expressed as _______.

  1. percentage

  2. ratio

  3. proportion

  4. all (a), (b), (c)


Correct Option: D
Explanation:
Probability shows the relationship between two variables in the form of ratio, percentage or proportion where there the chances of occurrence of one variable is expressed in terms of other variable. Since the value of one variable belongs to the range of value of another variable, the range o probability varies from 0 to 1.
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