Olympiad Mathematics - Data Handling
Exam Duration: 45 Mins Total Questions : 25
A bag has 4 red balls and 2 yellow balls.(The balls are identical in all respect other than color) A ball is drawn from the bag without looking into a bag.The probability of getting a red ball is_____
- (a)
\(\frac { 1 }{ 2 } \)
- (b)
\(\frac { 2 }{ 3 } \)
- (c)
\(\frac { 1 }{ 4 } \)
- (d)
\(\frac { 1 }{ 5 } \)
Total number of balls = 4 + 2 = 6
Number of red balls = 4
∴ Probability of getting a red ball
= \(\frac { Number\quad of\quad red\quad balls }{ Total\quad number\quad of\quad balls } =\frac { 4 }{ 6 } =\frac { 2 }{ 3 } \)
The histogram representing the marks obtained by 60 students in a Mathematics examination
What is the total number of students who obtained more than or equal to 80 marks in the examination?
- (a)
13
- (b)
3
- (c)
8
- (d)
11
Total number of students who obtained more than or equal to 80 marks = 8 + 3 = 11
The histogram representing the marks obtained by 60 students in a Mathematics examination
If the minimum pass marks was 40,how many students failed?
- (a)
1
- (b)
13
- (c)
2
- (d)
7
Number of student failed (i.e. Scored 30 - 40) = 2
The histogram representing the marks obtained by 60 students in a Mathematics examination
How many students were awarded merit,if the minimum marks required for it are 80?
- (a)
10
- (b)
11
- (c)
12
- (d)
8
Number of students awarded for merit = 8 + 3 = 11
A die is thrown.The probability of getting a multiple of 3 is______
- (a)
\(\frac { 1 }{ 2 } \)
- (b)
\(\frac { 1 }{ 3 } \)
- (c)
\(\frac { 1 }{ 4 } \)
- (d)
\(\frac { 1 }{ 5 } \)
Total number of outcomes = 6
Number of multiples of 3 are (3, 6) i.e., 2
∴ Required probability = \(\frac { Number\quad of\quad multiples\quad of\quad 3 }{ Total\quad number\quad of\quad outcomes } \)
= \(\frac { 2 }{ 6 } =\frac { 1 }{ 3 } \)
From the given table,the number of students who got more than or equal to 50 marks,is_____
Marks(class-interval) | No.of Students |
30-40 | 12 |
40-50 | 13 |
50-60 | 4 |
60-70 | 15 |
70-80 | 6 |
- (a)
15
- (b)
21
- (c)
25
- (d)
29
Number of students got 50 or more than 50 marks = 4 + 15 + 6 = 25
The given pie chart gives the marks scored in an examination by a student in English,Hindi,Science & Technology,Social Science and Mathematics.If the total marks obtained by the student were 540,then the subject in which the student scored 105 marks,is____
- (a)
English
- (b)
Mathematics
- (c)
Social Science
- (d)
Hindi
Total marks scored = 540
Marks scored in English =\(\frac { { 55 }^{ o } }{ 360^{ o } } \times 540\) =82.5
Marks scored in Mathematics = \(\frac { { 90 }^{ o } }{ 360^{ o } } \times 540\)=135
Marks scored in Social Science =\(\frac { 65^{ o } }{ 360^{ o } } \times 540\)=97.5
Marks scored in Hindi =\(\frac { 70^{ o } }{ 360^{ o } } \times 540\)=105
Marks scored in Science & Technology =\(\frac { 80^{ o } }{ 360^{ o } } \times 540\)=120
The probability of occurrence of an event is______
- (a)
\(\frac { Number\quad of\quad trials\quad in\quad which\quad an\quad event\quad occured }{ Total\quad number\quad of\quad trials-Number\quad of\quad trials\quad in\quad which\quad an\quad event\quad occured } \)
- (b)
\(\frac { Number\quad of\quad trials\quad in\quad which\quad an\quad event\quad occured }{ Total\quad number\quad of\quad trials } \)
- (c)
\(\frac { Total\quad number\quad of\quad trials }{ Number\quad of\quad trials\quad in\quad which\quad an\quad event\quad occured } \)
- (d)
\(\frac { Total\quad number\quad of\quad trials-Number\quad of\quad trails\quad in\quad which\quad event\quad occured }{ Number\quad of\quad trials\quad in\quad which\quad an\quad event\quad occured } \)
In a survey of 200 ladies, it was found that 82 like coffee while 118 dislike it. From these ladies, one is chosen at random. The probability that the chosen lady dislike coffee is_____
- (a)
\(\frac { 59 }{ 100 } \)
- (b)
\(\frac { 41 }{ 100 } \)
- (c)
\(\frac { 100 }{ 59 } \)
- (d)
\(\frac { 100 }{ 41 } \)
Total number of ladies = 200
Number of ladies who dislike coffee = 118
∴ Probability that chosen lady dislikes coffee = \(\frac { 118 }{ 200 } \)=\(\frac { 59 }{ 100 } \)
The number of times a particular entry occurs in a set of data is known as its
- (a)
Range
- (b)
Class-size
- (c)
Frequency
- (d)
Class-interval
The mid-value of a class-interval is called its
- (a)
Class-limit
- (b)
Class-mark
- (c)
Class-width
- (d)
Range
Class-mark = \(\frac { upper\quad limit+lower\quad limit }{ 2 } \)
Study the graph carefully and answer the question
In which year did the wheat import register highest increase over its preceding year?
- (a)
1973
- (b)
1974
- (c)
1975
- (d)
1978
In 1973 increase over preceding year
= (2413 - 1811) = 602 thousand tonnes
In 1974 it is (4203 - 2413) = 1790 thousand tonnes
In 1975 it is (7016 - 4203) = 2813 thousand tonnes and in
1978 it is (2500 - 2000) = 500 thousand tonnes
So, maximum increase is in year 1975
Study the graph carefully and answer the question
The wheat import in 1976 was approximately how many times to that of the year 1972 ?
- (a)
0.31
- (b)
1.68
- (c)
2.41
- (d)
3.22
Import in 1976 = 5832 thousand tonnes
And import in 1972 = 1811 thousand tonnes
Required number =\(\frac { 5832 }{ 1811 } \)=3.22 (approx)
Study the graph carefully and answer the question
The increase in wheat import in 1978 was what percent of the wheat import in 1977 ?
- (a)
25 %
- (b)
5 %
- (c)
125 %
- (d)
80 %
Import in 1978 = 2500 thousand tonnes
And import in 1977 = 2000 thousand tonnes
∴ Increase = 2500 - 2000 = 500 thousand tonnes
∴ Required Percentage =\(\frac { 500 }{ 2000 } \times 100\) =25 %
Study the graph carefully and answer the question
The wheat import in 1974 is approximately what percent of the average wheat import for the given years?
- (a)
125 %
- (b)
115 %
- (c)
190 %
- (d)
85 %
Total imports in all years
= 3465 + 1811 + 2413 + 4203 + 7016 + 5832 + 2000 + 2500
= 29240 thousand tonnes.
So, average import for the given years
= = 3655 thousand tonnes
Import in 1974 = 4203 thousand tonnes
∴ Required percentage =\(\frac { 4203 }{ 3655 } \times 100\)=115 % (approx)
In a school only 3 out of 5 students can participate in a competition. What is the probability of the students who do not make it to the competition?
- (a)
0.65
- (b)
0.4
- (c)
0.45
- (d)
0.6
Total number of students = 5
Number of students who do not make it to the competition = 5-3=2
∴ Required probability =\(\frac { 2 }{ 5 } \)=0.4
Rohan and Shalu are playing with 5 cards as shown in the figure. What is the probability of Rohan picking a card without seeing that has the number 2 on it?
- (a)
\(\frac { 2 }{ 5 } \)
- (b)
\(\frac { 1 }{ 5 } \)
- (c)
\(\frac { 3 }{ 5 } \)
- (d)
\(\frac { 4 }{ 5 } \)
Total number of cards = 5
Number of cards having number 2 = 2
∴ Probability of picking a card having number 2 = \(\frac { 2 }{ 5 } \)
Monthly salary of a person is Rs.15000. The central angle of the sector representing his expenses on food and house rent on a pie chart is 60o. The amount he spends on food and house rent is
- (a)
Rs. 5000
- (b)
Rs. 2500
- (c)
Rs. 6000
- (d)
Rs. 9000
Monthly salary of a person = Rs.15000
Central angle of expenses on food and house rent = 60o
∴ Amount spent on food and house rent
=\(\frac { Central\quad angle }{ 360^{ o } } \times Monthly\quad salary=Rs.\left( \frac { { 60 }^{ o } }{ 3{ 60 }^{ o } } \times 15000 \right) \)=Rs.2500
A glass jar contains 6 red, 5 green, 4 blue and 5 yellow marbles of same size. Hari takes out a marble from the jar at random. What is the probability that the chosen marble is of red colour?
- (a)
\(\frac { 7 }{ 10 } \)
- (b)
\(\frac { 3 }{ 10 } \)
- (c)
\(\frac { 4 }{ 5 } \)
- (d)
\(\frac { 2 }{ 5 } \)
Total number of marbles = 6 + 5 + 4 + 5 = 20
Number of red colour marbles = 6
∴ Probability of choosing red colour marble = \(\frac { 6 }{ 20 } =\frac { 3 }{ 10 } \)
Ram put some buttons on the table. There were 4 blue, 7 red, 3 black and 6 white buttons in all. All of a sudden, a cat jumped on the table and knocked out one button on the floor. What is the probability that the button on the floor is blue?
- (a)
\(\frac { 7 }{ 10 } \)
- (b)
\(\frac { 3 }{ 5 } \)
- (c)
\(\frac { 1 }{ 5 } \)
- (d)
\(\frac { 1 }{ 4 } \)
Total number of buttons = 4 + 7 + 3 + 6 = 20
Number of blue buttons = 4
Probability that the button on the floor is blue \(\frac { 4 }{ 20 } =\frac { 1 }{ 5 } \)
The given pie chart shows the spendings of a family on various heads during a month. Study the graph and answer the question
If the total income of the family is Rs.25000, then the amount spent on rent and food together is_______
- (a)
Rs.17250
- (b)
Rs.14750
- (c)
Rs.11250
- (d)
Rs.8500
Total income of the family = Rs.25000
Amount spent on rent =\(\frac { 14 }{ 100 } \times 25000\)=Rs.3500
Amount spent of food =\(\frac { 45}{ 100 } \times 25000\)=Rs.11250
∴ Amount spent on rent and food together
= Rs.(3500 + 11250) = Rs.14750
The given pie chart shows the spendings of a family on various heads during a month. Study the graph and answer the question
What is the ratio of the expenses on education to the expenses on food?
- (a)
1:3
- (b)
3:1
- (c)
3:5
- (d)
5:3
Expense on education = \(\frac { 15 }{ 100 } \times 25000\)
= Rs.3750
Expenses on food=\(\frac { 45 }{ 100 } \times 25000\)=Rs.11250
∴ Required Ratio =\(\frac { 3750 }{ 11250 } =\frac { 1 }{ 3 } \) i.e 1:3
The given bar graph shows the number of students in a hostel speaking different languages. Study the bar graph and answer the following question
(i) How many students are there in the hostel?
(ii) What is the ratio of the number of students speaking Punjabi to those speaking English?
(iii) What is the percentage of the students speaking Marathi over those speaking Hindi ?
- (a)
(i) (ii) (iii) 152 3:4 27.9% - (b)
(i) (ii) (iii) 152 4:5 25% - (c)
(i) (ii) (iii) 145 7:5 27.2% - (d)
(i) (ii) (iii) 145 7:9 30%
(i) Total number of students in hostel = 5 +10 + 15 + 25 + 35 + 55 = 145
(ii) Number of students speaking Punjabi = 35
Number of students speaking English = 25
∴ Required ratio =\(\frac { 35 }{ 25 } \)=7:5
(iii) Number of students speaking Marathi = 15
Number of students speaking Hindi = 55
∴ Required percentage =\(\frac { 15 }{ 55 } \times 100\)=27.2 %
Look at the given below data
39,25,5,33,19,21,12,48,13,21,9,1,10,8, 12, 17,41,40,12,46,37,17,27,30,6,2,23, 19
The frequency distribuition of the data is given here
Group | Tally Marks | Frequency |
0-10 | 6 | |
10-20 | 11 | |
20-30 | IIII | 4 |
30-40 | 5 | |
40-50 | III | 3 |
Group | Tally Marks | Frequency |
0-10 | 6 | |
10-20 | 10 | |
20-30 | 5 | |
30-40 | IIII | 4 |
40-50 | III | 4 |
Which of the above tables is the frequency table of the given data?
- (a)
Only P
- (b)
Only Q
- (c)
Neither P nor Q
- (d)
Can't be determined
The correct frequency distribution table for the given data is as follows
Group | Tally Marks | Frequency |
0-10 | 6 | |
10-20 | 9 | |
20-30 | | 5 |
30-40 | IIII | 4 |
40-50 | III | 4 |
The given pie chart represents the distribuition of proteins in parts of a human body.What is the ratio of distribuition of proteins in the muscles to that of proteins in the bones?
- (a)
3:1
- (b)
1:2
- (c)
1:3
- (d)
2:1
Fraction of distribution of proteins in muscles = 1/3
Fraction of distribution of proteins in bones = 1/6
∴ Required ratio =\(\frac { 1 }{ 3 } \div \frac { 1 }{ 6 } =\frac { 1 }{ 3 } \times \frac { 6 }{ 1 } =\frac { 2 }{ 1 } \) i.e 2:1