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CBSE Questions for Class 11 Commerce Applied Mathematics Descriptive Statistics Quiz 8 - MCQExams.com
CBSE
Class 11 Commerce Applied Mathematics
Descriptive Statistics
Quiz 8
The given pictograph shows the number of students of class V participated in different games at Annual Diwali Mela. How many students tried the dart board?
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0%
$$45$$
0%
$$182$$
0%
$$140$$
0%
$$136$$
Explanation
If we study the given pictograph carefully, we can see that one ball represents $$17$$ students.
Against dart board, we can see $$8$$ balls.
So, the number of students who participated in dart board $$=17\times 8=136$$
Hence, $$136$$ students tried the dart board.
The given bar graph shows the number of residents at 6 places. Study the graph and answer the questions. How many more residents were residing at China town than at Lajpat nagar?
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0%
$$1600$$
0%
$$1800$$
0%
$$1400$$
0%
$$1200$$
Explanation
Number of residents at China town = $$6000$$
Number of residents at Lajpat nagar = $$4400$$
Required difference = $$6000-4400=1600$$
The bar graph shows the number of traffic accidents in a country from year $$2000$$ to $$2014$$ . What is the difference between accidents in the year $$2001$$ and $$2004$$.
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0%
$$60,000$$
0%
$$40,000$$
0%
$$20,000$$
0%
$$45,000$$
Explanation
The letter $$k$$ is used to denote $$1000$$
Therefore, Number of traffic accidents in the year $$2001$$ $$=260k$$
$$=260\times1000$$
$$=260,000$$
Number of traffic accidents
in year $$2004$$ $$=220k$$
$$=220\times1000$$
$$=220,000$$.
Then, the difference $$=260,000-220,000$$
$$=40,000$$
Therefore, option $$B$$ is correct.
The given pictograph shows the number of wall clocks sold by a company during a week.
Each clock in the pictograph represents $$5$$ wall clocks.
On what day was the sale maximum?
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0%
Monday
0%
Tuesday
0%
Saturday
0%
Thursday
Explanation
As shown in the figure, the sale was maximum on Thursday.
Hence the correct answer is option D
Study the graph and answer the following questions.
How many less burgers were sold on Thursday than on Monday?
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0%
$$50$$
0%
$$20$$
0%
$$35$$
0%
$$10$$
Explanation
Number of burgers sold on Thursday $$= 30$$
Number of burgers sold on Monday $$= 50$$
Required difference $$= 50 - 30$$
$$ = 20$$
What temperature does the given thermometer shows?
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0%
$$35^{\circ}C$$
0%
$$77^{\circ}F$$
0%
$$95^{\circ}C$$
0%
$$122^{\circ}F$$
Explanation
Thermometer shows $$35^o C$$ or $$95^o F$$
Hence the correct answer is option A.
How many scooters were sold on Mondays?
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0%
$$30$$
0%
$$35$$
0%
$$40$$
0%
$$45$$
Explanation
$$1$$ scooter's photo$$= 6$$ scooters
On Monday, there are $$5$$ scooters' photo.
So the total no. of scooters sold are $$5\times 6=30$$
How many school teachers does each smiley represent?
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0%
$$500$$
0%
$$600$$
0%
$$700$$
0%
$$800$$
Explanation
We have given that $$7$$ smiley is equal to $$4200$$.
So one smiley $$=\dfrac { 4200 }{ 7 } =600 $$
So option $$ B $$ is correct.
Four balls A, B, C and D are placed inside a container, one after another. The bar graph shows the weight of the container when empty and when different balls are placed in it. Which ball is the heaviest?
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0%
A
0%
B
0%
C
0%
D
Explanation
From the above graph we can conclude that
Weight of the bucket is $$80$$
Weight of the ball A= $$180-80=100$$
Weight of the ball B= $$360-180=180$$
Weight of the ball C= $$500-360=140$$
Weight of the ball D= $$580-500=80$$
Hence the correct answer is option B.
Study the graph carefully and answer the question given below it.
In which year did the import register highest increase over its preceding year ?
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0%
$$1973$$
0%
$$1974$$
0%
$$1975$$
0%
$$1978$$
Explanation
Year
Wheat Import (in thousand Tonnes)
1971
3465
1972
1811
1973
2413
1974
4203
1975
7016
1976
5832
1977
2000
1978
2500
Clearly as show in the graph,
Highest Wheat import is in Year $$1975$$ $$=$$ $$7016$$ Thousand Tonnes
The hours in which maximum number of students watched TV , is ______ .
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0%
$$3-4$$ hours
0%
$$5-6$$ hours
0%
$$4-5$$ hours
0%
$$2-3$$ hours
Explanation
Hours of TV Watched
Number of Students
1-2
4
2-3
8
3-4
22
4-5
32
5-6
8
6-7
6
As clearly seen from the Graph and Corresponding Table,
Maximum number of Students watched TV between $$4$$-$$5$$ Hours.
What is the ratio of the highest marks to the lowest marks obtained by the student?
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0%
$$2 : 11$$
0%
$$9 : 2$$
0%
$$2 : 9$$
0%
$$11 : 2$$
Explanation
According to bargraph, his scores are as follows :
English $$= 55$$
Mathematics $$= 90$$
Hindi $$= 40$$
Science $$= 80$$
History $$= 20$$
Highest marks obtained in Mathematics $$= 90$$
Lowest marks are obtained in History $$= 20$$
Ratio $$= 90:20 = 9:2$$
The line graph shows the amount of water used by Jamie from March to July. Express the amount of water used in June as a fraction of the total amount of water used.
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0%
$$\displaystyle \frac{3}{14}$$
0%
$$\displaystyle \frac{1}{7}$$
0%
$$\displaystyle \frac{2}{7}$$
0%
$$\displaystyle \frac{3}{140}$$
Explanation
Total amount of water used = $$20+15+30+40+35=140$$L
Amount of water used in june=$$40$$L
Amount of water used in June to the total amount of water=$$\dfrac{40}{140}=\dfrac{2}{7}$$
The given bar graph shows the number of matches played by different teams. Read the bar graph and answer the questions:
How many matches did both India and Bangladesh play?
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0%
$$34$$
0%
$$22$$
0%
$$38$$
0%
$$40$$
Explanation
From the bar graph,
The number of matches played by India $$=26$$.
The num
ber of matches played by Bangladesh $$=8$$.
Therefore, the total number of matches played by both India and Bangladesh $$=26 + 8 = 34$$.
Thus,
total number of matches played by both India and Bangladesh $$34$$.
Hence, option $$A$$ is correct.
What is the average marks obtained by the student?
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0%
$$57$$
0%
$$63$$
0%
$$80$$
0%
$$48$$
Explanation
According to bargraph, his scores are as follows :
English $$= 55$$
Mathematics $$= 90$$
Hindi $$= 40$$
Science $$= 80$$
History $$= 20$$
Total marks obtained $$= 55+90+40+80+20 = 285$$
Average marks obtained $$=$$ Total Marks $$\div$$ Number of subjects
$$\Rightarrow$$ Average marks obtained $$= \dfrac{285}{5} = 57$$
Which of the following methods of measuring correlation is the most popular method?
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0%
Product Moment Correlation
0%
Spearman's Rank Correlation
0%
Concurrent Deviation Method
0%
Karl Pearson's Co-efficient of Correlation
Explanation
Karl pearson's coefficient of correlation determines how strongly the two variables are related to each other i.e. measure the linear correlation between the variables.
The formula of Karl Pearson's co-efficient of correlation is ________.
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0%
$$r = 1 - \dfrac{6\Sigma{{D}_2}}{{{N}_{3}} - N}$$
0%
$$r = \dfrac{{\Sigma}{x}{y}}{{N}{\sigma}{x}{\sigma}{y}}$$
0%
$$ r = \dfrac {{\sigma}{x}}{{\sigma}{y}}$$
0%
$$ r = \dfrac {{\sigma}{y}}{{\sigma}{x}}$$
Explanation
The correct formula foe the karl pearson's coefficient if correlation is given in the option B. The value of coefficient always lies between -1 to +1 that measures the strength of linear relationship between two variables.
The pictograph shows different subject books which are kept in a library. Observe the graph and answer the following question:
How many more Science books than the History books are there in the library?
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0%
$$400$$
0%
$$200$$
0%
$$300$$
0%
$$500$$
Explanation
$$\Rightarrow$$ In pictograph, one book symbol equal to $$100$$ books.
$$\therefore$$ From given pictograph, we have made following frequency distribution table :
$$Subject$$
$$No.of\,books$$
$$Hindi$$
$$6\times 100=600$$
$$English$$
$$8\times 100=800$$
$$History$$
$$2\times 100=200$$
$$Science$$
$$4\times 100=400$$
$$Maths$$
$$3\times 100=300$$
$$Total$$
$$2300$$
$$\Rightarrow$$ Number of science books in library $$=400$$
$$\Rightarrow$$ Number of History books in library $$=200$$
$$\Rightarrow$$ Difference between science and history books $$=400-200=200$$
$$\therefore$$ In library, there are $$200$$ science books more than history books.
Direction (9-10) : Following pictograph shows the number of tractors in five villages. Observer the pictograph and answer the following questions.
How many villages have 6 number of tractors?
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0%
4
0%
3
0%
2
0%
5
Explanation
$$\Rightarrow$$ From pictograph we have made following frequency distribution table :
$$Villages$$
$$No.\,of\,Tractors$$
$$A$$
$$6$$
$$B$$
$$5$$
$$C$$
$$8$$
$$D$$
$$3$$
$$E$$
$$6$$
$$Total$$
$$28$$
$$\Rightarrow$$ From above table we can see, village $$A,C$$ and village $$E$$ have same number of tractors i.e. $$6$$
$$\therefore$$ Number of villages have 6 number of tractor is $$3$$.
The formula of product moment correlation is ______________.
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0%
$$r=\dfrac{S_{xy}}{\sqrt{S_xS_y}}$$ ; S= Standard error
0%
$$ r = \dfrac {{\sigma}_{xy}}{{N}{\sigma}_{x}{\sigma}_{y}}$$ ; N=number of variables
0%
$$ r = \dfrac {{-r}^2}{\sqrt{N}}$$
0%
$$ r = \dfrac {{6}{\sigma}^2_{{d}}}{n({n}^2 - {1})}$$
Explanation
The formula for product moment correlation given in the option A is correct and measures the linear relationship between two variables. The formula basically tries to show how strongly are the two variables (x and y in this case) are related to each other. A correlation could be weakly or strongly correlated depending on the value of 'r'.
Direction (16-17) : The pictograph shows different subject books which are kept in a library. Observe the graph and answer the following questions.
How many English books are there in the library?
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0%
800
0%
700
0%
500
0%
600
Which of the following method is generally adopted by governments?
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0%
Indirect oral interview
0%
Direct personal observation
0%
Valid questionnaries
0%
Information through agencies
Explanation
Indirect oral interview is helpful in the case where information cannot be collected directly. Governments generally use this method to collect information related to the nation or economy.
The sale of electric fans on different days of the week is shown above. Observe the pictograph and answer the following questions.
If one fan was sold of $$900.$$ What were the total earnings on Friday?
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0%
$$6300$$
0%
$$6500$$
0%
$$18900$$
0%
$$21000$$
Explanation
There are $$7$$ images of fan in the row of Friday and $$1$$ fan corresponds to $$3$$ units so,
Number of fans sold $$=$$ $$3\times 7$$
$$=21$$
Cost of $$1$$ fan $$= 900$$
$$\therefore$$ Cost of $$21$$ fans $$= 21\times 900$$
$$ = 18900$$
Direction (9-10) : Following pictograph shows the number of tractors in five villages. Observer the pictograph and answer the following questions.
Total number of tractors in all the five villages is _____.
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0%
28
0%
30
0%
32
0%
25
Explanation
$$\Rightarrow$$ From pictograph we have made following frequency distribution table :
$$Villages$$
$$No.\,of\,Tractors$$
$$A$$
$$6$$
$$B$$
$$5$$
$$C$$
$$8$$
$$D$$
$$3$$
$$E$$
$$6$$
$$Total$$
$$28$$
$$\Rightarrow$$ Total number of tractors in all five villages is $$28$$
Defects of Karl Pearson's method is/are________.
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0%
it consumes more time
0%
the value of correlation is affected by extreme values
0%
if the data are not homogeneous, the co-efficient of correlation will give a wrong picture
0%
all of the above
Explanation
Disadvantages of using karl pearson's method is that it is avery time consuming and lengthy process and it gets affected by extreme values and it may give a wrong image if the variables are not of same nature or homogeneous.
The average marks of $$10$$ students in a class was $$60$$ with standard deviation $$4$$. While the average marks of other $$10$$ students was $$40$$ with a standard deviation $$6$$. If all the $$20$$ students are taken together, their standard deviation will be.
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0%
$$5.0$$
0%
$$7.5$$
0%
$$9.8$$
0%
$$11.5$$
Explanation
Here,
$$n_1=10,\overline{x}_1=60$$ and $$\sigma_1=4$$
$$\therefore$$ $$\sum x_i=60\times 10=600$$
Now, $$n_2=10,\overline{x}_2=40$$ and $$\sigma_2=6$$
$$\therefore$$ $$\sum x_i=10\times 40=400$$
$$\Rightarrow$$ Total marks of $$20$$ students $$(\sum_{i=1}^{20} x)=400+600=1000$$
$$\Rightarrow$$ $$\overline{x}=\dfrac{1000}{20}=50$$
Now, $$\sigma_1^2=(4)^2$$
$$\Rightarrow$$ $$\dfrac{1}{n_1}\sum_{i=1}^{10}x_i^2-(\overline{x_1})^2=16$$
$$\Rightarrow$$ $$\sum_{i=1}^{10}x_i^2=n_1(16+(\overline{x_1})^2)$$
$$=10(16+3600)$$
$$\Rightarrow$$ $$\sum_{i=1}^{10}x_i^2=36160$$
Now, $$\sigma_2^2=(6)^2$$
$$\Rightarrow$$ $$\dfrac{1}{n_2}\sum_{i=11}^{20}x_i^2-(\overline{x_2})^2=36$$
$$\Rightarrow$$ $$\sum_{i=11}^{20}x_i^2=(36+(\overline{x_2})^2)n_2$$
$$=(36+1600)10$$
$$\Rightarrow$$ $$\sum_{i=11}^{20}x_i^2=16360$$
Now, required standard deviation $$(\sigma)=\sqrt{\dfrac{1}{n}\sum x_i^2-\overline{x}^2}$$
$$=\sqrt{\dfrac{1}{20}(36160+16360)-(50)^2}$$
$$=\sqrt{2626-2500}$$
$$=\sqrt{126}$$
$$=11.2$$
Direction (10-13) : The given bar graph shows the marks obtained by a student in different subjects. The maximum marks of each subject is $$100$$.
What is the ratio of the highest marks to the lowest marks obtained by the student?
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0%
$$2 : 11$$
0%
$$9 : 2$$
0%
$$2 : 9$$
0%
$$11 : 2$$
Explanation
Highest marks obtained by student $$= 90$$
Lowest marks obtained by student $$= 20$$
Thus ratio $$= 90 : 20 = 9 : 2$$
The given bar graph shows the production of Rice and Wheat in five states.
Which of the following states is the largest producer of wheat?
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0%
M.P.
0%
Haryana
0%
Maharashtra
0%
U.P.
Explanation
Given graph shows the production of rice and wheat in five states. The black bar represents the rice production and the white bar represents the wheat production.
From the graph, we can observe that the U.P. is the largest producer of wheat.
The line graph shows the number of storybooks Armaan read in the last $$4$$ months of a year.
The number of storybooks that he read in October as a fraction of the total number of storybooks read is
Report Question
0%
$$\dfrac {1}{12}$$
0%
$$\dfrac {3}{4}$$
0%
$$\dfrac {1}{2}$$
0%
$$\dfrac {5}{12}$$
Explanation
Total number of storybooks read $$= 4 + 2 + 10 + 8 = 24$$
Number of storybooks read in October $$= 2$$
Therefore, required fraction is $$\dfrac {2}{24}$$ $$=$$ $$\dfrac {1}{12}$$
Karl Pearson's method helps to__________.
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0%
give direction and degree of relationship between the two variables.
0%
calculate the unknown value from a known value.
0%
both (A) and (B).
0%
calculate the known value from an unknown value.
Explanation
Karl pearson's coefficient of correlation helps in measuring the degree of relationship between two variable i.e. how strongly they are connected and it also calculate the unknown value from the known values.
The given bar graph shows the marks obtained by a student in different subjects. The maximum marks of each subject is 100.
In which subject did the student score highest marks?
Report Question
0%
English
0%
Mathematics
0%
Science
0%
S.St
Explanation
Given graph shows the marks obtained in different subjects.
From the graph, the highest marks are $$90$$ which is obtained in Mathematics
Kinds of classification used in tabulation are _______.
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0%
qualitative
0%
quantitative
0%
temporal
0%
all of the above
Explanation
The classification of data using tabulation method can be done in different ways based on the features of the data. The kinds of classification possible under tabulation are:
1. Qualitative classification is possible when the data is collected of the qualitative characteristics of the population, e.g., gender, occupation, etc.
2. Quantitative classification is done when the data collected is numerical in nature, e.g., age, income, etc.
3. Temporal classification refers to classification done based on the time-period, e.g., GDP growth in 10 years.
In a tabular presentation, data is presented in ______ and ______.
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0%
rows and columns
0%
lines and graphs
0%
texts and paragraphs
0%
A and B
Explanation
The process of classifying data into tabular form is called "Tabulation".
A table is a symmetric arrangement of data in
rows and columns
The variance of the elements of the row which contains $$2019$$ is $$K$$ then the value of
$$3 K$$ is
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0%
$$2024$$
0%
$$2000$$
0%
$$1800$$
0%
$$1024$$
Direction (10-13) : The given bar graph shows the marks obtained by a student in different subjects. The maximum marks of each subject is 100.
What is the average marks obtained by the student?
Report Question
0%
57
0%
63
0%
80
0%
48
Explanation
Formula for average marks= $$\dfrac{Sum\ of \ marks \ of \ all\ subjects}{Total\ number\ of\ subjects}$$
Average marks
= $$(\dfrac {55+90+40+80+20}{5})$$
= $$\dfrac {285}{5}$$$$ = 57$$
Range =
Report Question
0%
Largest value - Smallest value
0%
Largest value divided by 2
0%
Both A and B
0%
None of the above
Explanation
Range refers to the value of variation between the largest and the smallest values in a particular data set. It can be calculated as the difference between the upper limit and lower limit of a particular set of data.
When data are tabulated on the basis of hours, days, weeks, months,
years, etc it is called _________ classification.
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0%
spatial
0%
temporal
0%
quantitative
0%
none of the above
Explanation
When data are tabulated on the basis of hours, days, weeks, months,
years, etc it is called
temporal
classification.
If more than one
table is presented, it is the _____ that distinguishes one table
from another.
Report Question
0%
title
0%
caption
0%
table number
0%
stub
Explanation
If the observations are in large in number they can be divided into two or three tables and accordingly the tables can be distinguished from one another with table numbers.
When classification is done in such a
way that place becomes the classifying
variable, it is called ______ classification.
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0%
temporal
0%
qualitative
0%
spatial
0%
none of the above
Explanation
When classification is done in such a
way that place becomes the classifying
variable, it is called
spatial
classification.
Classification on the basis of age, height, production, income, etc are examples of _______ classification.
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0%
temporal
0%
qualitative
0%
quantitative
0%
spatial
Explanation
Quantitative is something which is related to measurement. It related to measurement of a particular quantity. It does not include feelings, quality, attributes.etc. Age, height, production, income.etc can be measured respectively. Hence, classification on the basis of age, height, production, income,etc. are examples of quantitative classification.
In _______ classification, the data
are classified on the basis of characteristics which can be measured
quantitatively..
Report Question
0%
quantitative
0%
temporal
0%
spatial
0%
none of the above
Explanation
In
quantitative
classification, the data
are classified on the basis of characteristics which can be measured
quantitatively
When classification is done according to qualitative characteristics like social status, physical status, nationality, etc., it is called ______ classification.
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0%
temporal
0%
qualitative
0%
spatial
0%
none of these
Explanation
When classification is done according to qualitative characteristics like social status, physical status, nationality, etc., it is called
qualitative
classification.
Fill in the blanks from the alternatives given in the brackets.
Random sampling is sampling by _________.
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0%
chance
0%
choice
0%
purpose
0%
quota
The extreme values of the classes are called _________.
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0%
class-mark
0%
tally mark
0%
class-limit
0%
class-frequency
________ is the difference between the upper and the lower limit of the class.
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0%
Class Interval
0%
Class Tally
0%
Class Frequency
0%
Class Mark
Explanation
The difference between the upper and lower limit of class is the class interval.
Example class interval 10-20, here 10 is the lower limit and 20 is the upper limit.
Statistics is a __________.
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0%
science
0%
art
0%
language
0%
mathematics
Lottery method is an example of _______ sampling.
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0%
deliberate
0%
random
0%
census
0%
None of these
The Additive Model of a time series is expressed as :
Report Question
0%
$$Y_{t} = T_{t} \times C_{t} \times S_{t} \times R$$
0%
$$Y_{t} = T_{t} - C_{t} - S_{t} - R_{t}$$
0%
$$Y_{t} = T_{t} + C_{t} + S_{t} + R_{t}$$
0%
$$Y_{t} = T_{t}\cap C_{t} \cup S_{t} \cup R_{t}$$
how many people (in millions) have preferred to play Tennis in all the years altogether?
Report Question
0%
$$3200$$
0%
$$2100$$
0%
$$1200$$
0%
$$1700$$
Explanation
Total Number of people preferred to play Tennis in all years
$$=300+350+325+275+150=1700$$ millions
Thus the correct answer is option $$D$$
Which measure is based on only the central fifty percent of the observations?
Report Question
0%
Standard deviation
0%
Quartile deviation
0%
Mean deviation
0%
All of above
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