MCQ Questions for Class 11 Commerce Applied Mathematics Descriptive Statistics Quiz 10

Find variance of the following data.

Class interval	Frequency
$$4-8$$	$$3$$
$$8-12$$	$$6$$
$$12-16$$	$$4$$
$$16-20$$	$$7$$

0%
$$19$$
0%
$$20$$
0%
$$21$$
0%
$$23$$

If $$\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right) = 9}$$ and $$\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2}} = 45$$, then the standard deviation of the $$9$$ items $${x_1},{x_2},.....,{x_9}$$ is

0%
$$2$$
0%
$$3$$
0%
$$9$$
0%
$$4$$

Suppose a population $$A$$ has $$100$$ observations $$101,102,........,200$$ and another population $$B$$ has $$100$$ observations $$151,152......,250 $$. If $$V_{A}and V_{B}$$ represent the variences of the two populations respectively, then $$V_{A}/ V_{B}$$ is

0%
$$1$$
0%
$$9/4$$
0%
$$4/9$$
0%
$$2/3$$

If the sum of mean and variance of binomial distribution is 4.8 for 5 trials then

0%
mean is 3
0%
variance is 0.6
0%
mean is 3.2
0%
variance is 0.8

Find the standard deviation of 10 observation 111,211,311,....1011.

0%
100$$\sqrt { 3 } $$
0%
250
0%
300
0%
50$$\sqrt { 3 } $$

The mean deviation about the mean of the set of first $$n$$ natural numbers when $$n$$ is an odd number.

0%
$$\dfrac{n^{2}-1}{4n}$$
0%
$$\dfrac{n}{4}$$
0%
$$\dfrac{n^{2}+1}{4n}$$
0%
$$\dfrac{n^{2}-1}{12}$$

Let $$\sigma^{2}$$ is variance of following frequency distribution

$$x_{1}$$	$$1$$	$$2$$	$$3$$	$$4$$	$$5$$	$$6$$	$$7$$	$$8$$	$$9$$
$$f_{1}$$	$$1$$	$$0$$	$$1$$	$$7$$	$$9$$	$$4$$	$$1$$	$$1$$	$$1$$

then $$\sigma^{2}$$ is equal to

0%
$$2.4$$
0%
$$2.5$$
0%
$$2.6$$
0%
$$2.7$$

The mean and variance of a random variable having a binomial distribution are $$4$$ and $$2$$ respectively , then $$P(X=1)$$ is

0%
$$1/32$$
0%
$$1/16$$
0%
$$1/8$$
0%
$$1/4$$

Let $$x_i$$ represents the outcome on a fair die and $$f_i$$ be the corresponding frequency. The variance for random variable $$x_i$$ with following frequency distribution, is

$$x_i$$	1	2	3	4	5	6
$$f_i$$	1	2	3	4	5	6

0%
$$2$$
0%
$$3$$
0%
$$\dfrac{28}{9}$$
0%
$$\dfrac{20}{9}$$

The mean and the standard devition (s.d) of five observations are $$9$$ and $$0$$, respecively. If one of the observations is changed such that the mean of the new set of five obervatons becomes $$10$$, then their s. d. is:

0%
0
0%
1
0%
2
0%
4

Let $$x_{1},\ x_{2},...x_{100}$$ are $$100$$ above observation such that $$\displaystyle \sum { { x }_{ 1 }=0 } ,\ \displaystyle \sum _{ 1\le i<j\le 100 }^{ }{ \left| { x }_{ i }{ x }_{ j } \right| =80000 } $$ & mean deviation from their mean is $$5$$, then their standard deviation, is-

0%
$$10$$
0%
$$30$$
0%
$$40$$
0%
$$50$$

For the observations $${ x }_{ 1, }{ x }_{ 2 },{ x }_{ 3 },........{ x }_{ 18, }$$ it is given that $$\sum _{i =1 }^{ 18 }{ ({ x }_{ i }-8)=9 } $$ and $$\sum _{ j=1}^{ 18 }{ { ({ x }_{ j}-8) }^{ 2 }=45 } $$ then the standard deviation of these eighteen observations is

0%
$$\cfrac { 3 }{ 2 } $$
0%
5
0%
$$\cfrac { 5 }{ \sqrt { 2 } } $$
0%
$$\sqrt { \cfrac { 81 }{ 34 } } $$

If the mean deviation about the median of the numbers $$a,2a,....,50a$$ is $$50$$, then $$|a|$$ equals:-

0%
$$4$$
0%
$$5$$
0%
$$2$$
0%
$$3$$

The variance of first $$50$$ even natural numbers is:-

0%
$$833$$
0%
$$831$$
0%
$$438$$
0%
$$\dfrac {437}{4}$$

If $$\displaystyle\sum _{ i=1 }^{ 18 }{ \left( { x }_{ i }-8 \right) } =153,\displaystyle\sum _{ i=1 }^{ 18 }{ \left( { x }_{ i }-8 \right) ^{ 2 } } =45$$ then standard deviation of $$x_{1},x_{2},........,x_{n}$$ is

0%
$$4/9$$
0%
$$9/4$$
0%
$$3/2$$
0%
$$2/3$$

Standard deviation of four observations $$-1, 0, 1$$ and k is $$\sqrt{5}$$ then k will be?

0%
$$2\sqrt{6}$$
0%
$$1$$
0%
$$2$$
0%
$$\sqrt{6}$$

A student scores the following marks in five test: $$45, 54, 41, 57, 43$$. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six test is

0%
$$\dfrac{10}{\sqrt{3}}$$
0%
$$\dfrac{100}{\sqrt{3}}$$
0%
$$\dfrac{130}{3}$$
0%
$$\dfrac{10}{3}$$

For a random variable $$X$$. If $$E(X)=5$$ and $$V(X)=6$$, then $$E(X^{2})$$ is equal to

0%
$$19$$
0%
$$31$$
0%
$$61$$
0%
$$11$$

If both the mean and the standard deviation of $$50$$ observations $${ x }_{ 1 },{ x }_{ 2 },......,{ x }_{ 50 }$$ are equal to $$16$$, then the mean of $${ \left( { x }_{ 1 }-4 \right) }^{ 2 },{ \left( { x }_{ 2 }-4 \right) }^{ 2 },.....{ \left( { x }_{ 50 }-4 \right) }^{ 2 }$$ is:

0%
$$525$$
0%
$$380$$
0%
$$480$$
0%
$$400$$

If expected value in n Bernoulli trials is $$8$$ and variance is $$4$$. If $$P(x\leq 2)=\dfrac{k}{2^{16}}$$ then value of k is?

0%
$$1$$
0%
$$137$$
0%
$$136$$
0%
$$120$$

If the data $$x_1, x_2, .., x_{10}$$ is such that the mean of first four of these is $$11$$, the mean of the remaining six is $$16$$ and the sum of square of all of these is $$2,000$$; then the standard deviation of this data is?

0%
$$4$$
0%
$$2$$
0%
$$\sqrt{2}$$
0%
$$2\sqrt{2}$$

Let the observations $$x_i(1\leq i \leq 10)$$ satisfy the equations, $$\displaystyle\sum^{10}_{i=1}(x_i-5)=10$$ and $$\displaystyle\sum^{10}_{i=1}(x_i-5)^2=40$$. If $$\mu$$ and $$\lambda$$ are the mean and the variance of the observations, $$x_1-3, x_2-3, ....., x_{10}-3$$, then the ordered pair $$(\mu, \lambda)$$ is equal to?

0%
$$(6, 6)$$
0%
$$(3, 6)$$
0%
$$(3, 3)$$
0%
$$(6, 3)$$

The bar graph as shown in above figure represents the heights (in cm) of $$50$$ students of Class $$XI$$ of a particular school. Study the graph and answer the following questions:
State whether true or false:
The number of a student is the class is in the range of $$160-164$$ cm is $$6$$.

0%
True
0%
False

The bar graph shown in Fig. represents the circulation of newspapers in 10 languages. Study the bar graph and answer the following questions:
State whether true or false:
The number of newspapers published in Telugu is more than those published in Tamil.

0%
True
0%
False

The mean of $$5$$ observation is $$4.4$$ and variance is $$8.24$$. If three of the five observations are $$1,2$$ and $$6$$, then what are the other two observations ?

0%
$$9,16$$
0%
$$9,4$$
0%
$$81,16$$
0%
$$81,4$$

The given bar graph represents the heights (in cm) of $$50$$ students of Class $$XI$$ of a particular school. Study the graph and answer the following question:
State true or false:
Number of students with maximum height (in cm) in the class is $$17$$.

0%
True
0%
False

The mean and variance of $$20$$ observations are found to be $$10$$ and $$4$$, respectively. On rechecking, it was found that an observation $$9$$ was incorrect and the correct observation was $$11$$. Then the correct variabce is:

0%
$$3.98$$
0%
$$4.02$$
0%
$$4.01$$
0%
$$3.99$$

The standard deviation of the data $$6,5,9, 13, 12, 8, 10$$ is

0%
$$\dfrac{\sqrt{52}}{7}$$
0%
$$\dfrac{52}{7}$$
0%
$$\dfrac{\sqrt{53}}{7}$$
0%
$$\dfrac{53}{7}$$
0%
$$6$$

The mean and the standard deviation (s.d) of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by $$p$$ and then reduced by $$q$$, where $$p \neq 0$$ and $$q \neq 0$$. If the new mean and new s.d. become half of their original values, then $$q$$ is equal to:

0%
$$-10$$
0%
$$-5$$
0%
$$-20$$
0%
$$10$$

Explanation

$${\textbf{Step -1: Let initial mean}}$$ $${\mathbf{\left( {\overline x } \right)}}$$ $${\textbf{and standard deviation}}$$ $${\mathbf{\left( {{\sigma _1}} \right)}}$$$${\textbf{of 10 observation are 20 and 2 respectively.}}$$

$${\text{Now, each of these observations is multiplied by p and reduced by q.}}$$

$${\text{Thus, The new mean}}$$ $$ = \overline {{x_1}} = p\overline x - q \ldots \left( 1 \right)$$

$${\text{Also, it is given that the new mean is half of the original mean}}{\text{.}}$$

$$ \Rightarrow \overline {{x_1}} = \dfrac{1}{2}\overline x = \dfrac{1}{2} \times 20$$

$$ \Rightarrow \overline {{x_1}} = 10$$

$${\text{Substitute this value of new mean in equation 1.}}$$

$$ \Rightarrow 10 = p\left( {20} \right) - q$$

$$ \Rightarrow 20p - q = 10 \ldots \left( 2 \right)$$

$${\textbf{Step -2: Find the value of p and q using the standard deviation.}}$$

$${\text{New standard deviation is given by,}}$$

$${\sigma _2} = \left| p \right|{\sigma _1} \ldots \left( 3 \right)$$

$${\text{As it will not be affected by subtraction of q from each observation.}}$$

$${\text{It is given that new standard deviation is half of the original.}}$$

$$ \Rightarrow {\sigma _2} = \dfrac{1}{2}{\sigma _1} = \dfrac{1}{2} \times 2 = 1$$

$${\text{Substitute this value in equation 3.}}$$

$$ \Rightarrow \left| p \right| \times 2 = 1$$

$$ \Rightarrow p = \pm \dfrac{1}{2}$$

$${\textbf{Step -3: Find the value of q using p.}}$$

$${\text{If }}$$ $$p = \dfrac{1}{2}$$

$${\text{Then from equation 2 we have,}}$$

$$ \Rightarrow 20 \times \dfrac{1}{2} - q = 10$$

$$ \Rightarrow 10 - 10 = q$$

$$\Rightarrow q = 0$$ $$[\textbf{Rejected, as q}\neq 0]$$

$${\text{If }}$$ $$p = - \dfrac{1}{2}$$

$${\text{Using equation 2, we have,}}$$

$$ \Rightarrow 20 \times \left( { - \dfrac{1}{2}} \right) - q = 10$$

$$ \Rightarrow q = - 10 - 10$$

$$ \Rightarrow q = - 20$$

$${\textbf{Hence, option C. i.e.}}{\mathbf{\left ( -20 \right )}} {\textbf{ is the correct answer.}}$$

In a bar graph, each bar (rectangle) represents only one value of the numerical data.

0%
True
0%
False

In a bar graph, bars of uniform width are drawn
vertically only.

0%
True
0%
False

In a bar graph, the gap between two consecutive bars may not be the same.

0%
True
0%
False

The following bar graph represents the data for different sizes of shoes worn by the students in a school. Read the graph and state whether true or false:
The total number of students wearing shoe sizes $$5$$ and $$8$$ is
the same as the number of students wearing shoe size $$6$$.

0%
True
0%
False

Data was collected on a student's typing rate and graph was drawn as shown below. Approximately how many words had this student typed in $$30$$ seconds?

0%
$$20$$
0%
$$24$$
0%
$$28$$
0%
$$34$$

Observe the adjoining bar graph, showing the number of one-day international matches played by cricket teams of different countries. Choose the correct answer from the given four options:
How many matches did South Africa play?

0%
$$16$$
0%
$$18$$
0%
$$20$$
0%
$$24$$

0%
$$6$$
0%
$$12$$
0%
$$24$$
0%
$$30$$

Observe the following pictograph which shows the number of ice cream cones sold by school canteen during a week. Chose the correct answer from the given options:
Ratio of the number of ice cream cones sold on Saturday to the number of ice cream cones sold on Wednesday is.

0%
$$3 : 2$$
0%
$$2 : 3$$
0%
$$4 : 5$$
0%
$$4 : 7$$

0%
India
0%
England
0%
Pakistan
0%
Australia

Observe the following pictograph which shows the number of ice cream cones sold by school canteen during a week. Chose the correct answer from the given options:
Total number of ice cream cones sold during the whole week was:

0%
$$33$$
0%
$$67$$
0%
$$65$$
0%
$$57$$

Observe the following pictograph which shows the number of ice cream cones sold by school canteen during a week. Chose the correct answer from the given options:
If the cost of one ice cream cone is $$Rs. 20,$$ then the sale value on friday was:

0%
Rs.$$70$$
0%
Rs.$$140$$
0%
Rs.$$280$$
0%
Rs.$$1340$$

0%
$$4 : 5$$
0%
$$5 : 4$$
0%
$$4 : 3$$
0%
$$7 : 6$$

In a series $$\sum x^{2} = 100, n = 5 $$ and $$\sum x = 20 $$ , then standard deviation is

0%
16
0%
2
0%
4
0%
8

Standard deviation of data $$6, 10, 4, 7, 4, 5$$ is -

0%
$$\sqrt{\dfrac{13}{3}} $$
0%
$$\dfrac{13}{3} $$
0%
$$\sqrt{26} $$
0%
$$\dfrac{\sqrt{26}}{6}$$

If the student wants to raise his total score upto $$225$$, then how many more marks should he score?

0%
$$125$$
0%
$$100$$
0%
$$200$$
0%
$$25$$

The exam scores of all $$500$$ students were recorded and it was determined that these scores were normally distributed. If Jane's score is $$0.8$$ standard deviation above the mean, then how many, to the nearest unit, students scored above Jane?(Area under the curve below $$z=0.8 \ is \ 0.7881$$)

0%
$$394$$
0%
$$250$$
0%
$$400$$
0%
$$106$$

Find the variance of the series 5, 8, 11, 14 and 17.....

0%
17
0%
18
0%
16
0%
12

The probability distribution of a random variable $$X$$ is given below:

$$X=x$$	0	1	2	3
$$P(X=x)$$	$$\frac{1}{10}$$	$$\frac{2}{10}$$	$$\frac{3}{10}$$	$$\frac{4}{10}$$

Then the variance of $$X$$ is

0%
1
0%
2
0%
3
0%
4

Which two years did the least number of boys attend the convention?

0%
1995 and 1996
0%
1995 and 1998
0%
1996 and 1997
0%
1996 and 1992
0%
1997 and 1998

The federal government in the United States has the authority to protect species whose populations have reached dangerously low levels. The figure above represents the expected populations of a certain endangered species before and after a proposed law aimed at protecting the animal is passes. Based on the graph, which of the following statements is true?

0%
The proposed law is expected to accelerate the decline in population.
0%
The proposed law is expected to stop and reverse the decline in population.
0%
The proposed law is expected to have no effect on the decline in population.
0%
The proposed law is expected to slow, but not stop or reverse, the decline in population.

For two data sets, each of size $$ 5$$, the variances are given to be $$4$$ and $$5$$ and the corresponding means are given to be $$2$$ and $$4,$$ respectively. The variance of the combined data set is

0%
$$\displaystyle \frac{11}{2}$$
0%
$$6$$
0%
$$\displaystyle \frac{13}{2}$$
0%
$$\displaystyle \frac{5}{2}$$

CBSE Questions for Class 11 Commerce Applied Mathematics Descriptive Statistics Quiz 10 - MCQExams.com

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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers

$$C.I$$	$$x_i$$	$$f_i$$	$$f_ix_i$$	$$(x_i-\overline{x})^2$$	$$f_i(x_i-\overline{x})^2$$
$$4-8$$	$$6$$	$$3$$	$$18$$	$$49$$	$$147$$
$$8-12$$	$$10$$	$$6$$	$$60$$	$$9$$	$$54$$
$$12-16$$	$$14$$	$$4$$	$$56$$	$$1$$	$$4$$
$$16-20$$	$$18$$	$$7$$	$$126$$	$$25$$	$$175$$
		$$\sum f_i=20$$	$$\sum f_ix_i=260$$	$$\sum(x_i-\overline{x})^2=84$$	$$\sum f_i(x_i-\overline{x})^2=380$$

CBSE Questions for Class 11 Commerce Applied Mathematics Descriptive Statistics Quiz 10 - MCQExams.com

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Practice Class 11 Commerce Applied Mathematics Quiz Questions and Answers

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